le cha n hung pham oinh thiet -...
TRANSCRIPT
LE TRONG TUONG (Chu bien) Ll/ONG TAT OAT - LE C H A N HUNG
PHAM OiNH THIET - BUI TRONG TUAN
i^elp f m^^ m m fkm m •
r
• m •
ng cao
NHA XUAT BAN GIAO DUC VIET NAM
Lfi TRONG TUONG (Chu bien) LUONG TAT DAT - Lfi C H A N HUNG
PHAM DINH THI^T - BUI TRONG TUAN
Bai tap
VAT U10 Ndng cao
(Tdi bdn ldn thit tu)
NHA XUAT BAN GIAO DUG VIET NAM
Ban quyen thuoc Nha xuat ban Giao due Viet Nam.
01-2010/CXB/639-1485/GD Ma s6': NB006T0
Ldi MOI BAIJ=
Cac em hoc sinh than men I
Cuon Bai tap Vat ll 10 nang cao la mgt bo phan hihi cO cOa sach giao khoa Vat li 10 nang cao, no se giup cac em hoc tot han mon Vat ll. Sach duac chia lam hai phan, mdi phan g6m cac chuang tuang umg vdi cac cht/ang cCia sach giao khoa Vat li 10 nang cao.
Phan mot gom cac bai tapvi du va de bai. Cac bai tap vi du la nhumg bai tap.di^n hinh trong cac chuang nen duac trinh bay chi tiet. Cac em co the tim thay phuang phap giai chung cho cac bai tap trong chuang do.
Phan hai la cac hudng dan va ldi giai. Cac em hay co gang tim each giai cac bai tap, dUng voi doc phan nay. Hay xem lai bai hoc mdi khi chua tim ducfc each giai mot bai tap nao dd. Ch! khi nao thuc su khdng tim dUdc each giai cac em mdi xem hudng din hoac ldi giai.
Cudi mol chuang cd cac bai tap ve thi nghiem rat li thu, gan gui vdl ddi song hang ngay cQa chung ta. Hay thuc hien cac thi nghiem trinh bay d day. Cac so lieu do dac cOa chinh cac em cung se la nhumg bai tap hay.
Chuc cac em hoc gioi va ngay cang yeu thich bo mdn Vatli.
Cac tac gia
Phan mot DEBAI
DONG HOC CHAT DI€M
I - BAI TAP VI DU
Ba! 1
M6t cha t dilm chuyin d6ng'tr6n m6t dvrofag thang. D6 thi chuyin d6ng cua no duac ve tr6n Hinh LL
1. Hay m6 ta chuyin ddng cua chSft dilm.
2. Tinh van tdc trung binh va tdc d6 trung binh cua chft dilm trong cac
khoang thoi gian sau : 0 s - ^ l s ; 0 s - ^ 4 s ; l s - ^ 5 s ; 0 s - ^ 5 s . x(cm)M
Hinh 1.1
Bdi gidi
1. Trong khoang thod gian tur t = 0 s din t = 1 s, d6 thi chuyin ddng la m6t
dudng thang di I6n va lam mdt goc aj v6i true Ot. Nhu vay ch^t dilm chuyin
ddng thing diu theo chilu duong cua true toa dd, tut vi tri cd toa dd bang 0 din vi
tri ed toa dd bang 4 cm. Van tdc cua ch& dilm bang :
4 V = tan ttj = — = 4 cm/s
TiJf luc t = 1 s din t = 2,5 s, dd thi la mdt duorng thang di xudng va lam mdt goc a2 vdi true Ot. Nhu vay chat dilm chuyin ddng diu theo ehilu nguoe lai, tctc la theo chieu am cua true toa dd, tur vi tri x = 4 cm den vi tri x = -2 em. Van tdc cua chat dilm la : .
- 2 - 4 , , V = tana- = — = - 4 cm/s
• - 2 1 , 5 . ' • ' . • .
Txt luc t = 2,5 s den liic t = 4 s, d6 thi la mdt dudng nam ngang song song vdi true thdi gian, chat diem diing yen d vi tri cd toa do x = - 2 cm.
Tu: liic t = 4 s din t = 5 s, dd thi la mdt dudng thang di ldn va lam mdt gdc a3 vdi true Ot. Nhu vay chat dilm chuyin ddng thang deu theo chieu duofng eua true toa do tit vi tri X = - 2 em den vi tri x = 0 em. Van tde eua eh^t dilm la :
0 - (-2) ^ , V = tan a , = = 2 cm/s
1 • • ' . . • . , ' .
2. Van tde trung binh duoc tinh theo edng thiic : ,
dd ddi X9 - X, . V t b = '• ^ - ^
khoang thdi gian t2 - tj .
Tdc dd trung binh dugc tinh theo cdng thtic :
T -' -»->. u- u quang dudng di duoc Toe do tmng binh = — S;—— -—
khoang thdi gian a) Luc tj = 0 s thi Xj = 0 om ; luc t2 = 1 s thi X2 = 4 cm, hay la
At = t2 - tl = 1 s - 0 = 1 s Dd ddi trong khoang thdi gian dd la :
Ax = X2 - X] = 4 - 0 = 4 cm
Vay : tb = ^ = Y ^ " ' " Z -
Quang dudng di dugfc trong khoang thdi gian dd la :
As = |x2 - XJI = 4 - 0. = 4 cm
As vay : Tdc dd trung binh = — = 4 cm/s.
b) Liic tj = 0 s thi Xj = 0 em ; luc t2 = 4 s thi X2 = -2 cm.
At = t2 - t i = 4 - 0 = 4s
Ax =
Vtb
= X2 - Xj
_ ^^ _ ~ At ~
= - 2 -
-2 _ 4
-0 =
-0 ,5
-2 cm
cm/s. v a y :
Do chuyin ddng khdng theo mdt ehilu eho nen ta tmh quang dudng di dugc nhu sau :
Tilf tl = 0 s din tj = 1 s, quang dudng di dugc la Asi = |x2 - x 11 = |4 - 0| = 4 cm.
Tuf t'l = 1 s den tj = 2 s, quang dudng di dugc la As2 = |0 - 4| = 4 em. Tii t'{ = 2 s
din t'l" = 2,5 s, quang dudng di duge la AS3 = 1-2 - 0| = 2 cm. Ttr tj" - 2,5 s din
t2 = 4 s, chat dilm diing lai d dilm x = - 2 cm, quang dudng di dugc la AS4 - 0.
vay quang dudng di dugc trong khoang thdi gian tuf ti = 0 s den t2 = 4 s la :
As = Asi + As2 + AS3 = 4 + 4 + 2 = 10 cm
Tdc dd trung binh trong khoang thdi gian dd la :
Tdc dd trung binh =-— = —- = 2,5 cm/s • At 4
Ta nhan thay gia tri eua van tdc trung binh va tdc dd trung binh trong cdng khoang thdi gian dd la khae nhau.
c) Tuong tu, trong khoang thdi gian At = t2 - ti = 5 - 1 = 4 s, ta ed .•
Ax = X2 - Xi = 0 - 4 = - 4 cm
Ax ' 4 , . ^ ^ = AT = - 4 = "^'^"^/^
As = As2 + AS3 + AS4 + AS5 = 4 + 2 + 0 + 2 = 8 cm
As 8 Tdc dd trung binh = -:— = -r = 2 cm/s
At 4
d) Trong khoang thdi gian At = t2 - ti = 5 - 0 = 5 s, ta cd :
Ax = X2 - Xl = 0 - 0 = 0 cm
Vtb = T = 0 c"^/s
As = Asi + As2 + AS3 + AS4 + Asg = 4 + 4 + 2 + 0 + 2 = 12 cm A 10
Tdc dd trung binh =-— = -— =2,4 em/s At 5
Bai 2 Mdt xe nho trugt trdn mang nghidng ddm khf. Oign true toa dd Ox triing vdi
mang va cd ehilu duong hudng xudng phia dudi. Biet rang, gia tdc cua xe khdng ddi la 8 cm/s , va We xe di ngang qua gdc toa dd, van tdc cua nd la VQ = - 6 cm/Si
1. Vilt phuong tnnh chuyin ddng cua xe, l^y gdc thdi gian la liic xe di ngang qua gdc toa dd.
2. Hdi xe chuyin ddng theo hudng nao, sau bao lau thi xe dutng lai ? Luc dd xe nam d vi tri nao ?
3. Sau dd xe chuyin ddng nhu the nao ? Hay tinh van tdc cua xe sau 3 s kl tur luc diing lai. Liic dd xe nam d vi tri nao ?
Bdi gidi
1. Phuong trinh chuyin ddng evia xe la phuong tnnh chuyin ddng thang biln ddi diu vdi van tdc ban ddu VQ = - 6 em/s, gia tdc bang 8 em/s va vi tri ban ddu XQ = 0 em. Phuang trinh dd la :
X = - 6.t + - .8.t^ (1) 2
2. a) Xe chuyin ddng di ldn phia trdn theo ehilu am cua true Ox va diing lai khi van tde bang khdng. Ta cd :
v = Vo + at = - 6 + 8.t = 0 (2) Tut dd suyra:
8.t = 6 , hay t = - = 0,75 s o
b) Vi tri cua xe luc do la :
X = - 6 . 0,75 + - .8.(0,75)^ = - 2,25 em > 2
3. a) Sau khi dat van tde bang 0 thi xe chuyin ddng nhanh ddn diu theo chilu ngugc lai xudng phia dudi (chilu duong eiia true Ox).
b) van tde eua xe dugc tmh theo edng thiie (2). Sau 3 s kl tur Wc xe diing lai, tlie la d thdi dilm t = 0,75 + 3 = 3,75 s, van tdc cua xe liic dd bang :
v = VQ + at = - 6 + 8.3,75 = 24 cm/s
c) Liic dd vi tri ciia xe la :
X = - 6 .3,75 + ^ .8.(3,75)2 = 33,75 cm
n - D^ BAI
Ll . Trong mdt ldn thtt xe d td, ngudi ta xac dinh duge vi tri cua xe tai cac thdi dilm each nhau ciing mdt khoang thdi gian 1 s (xem bang dudi day). Hay xac dinh van tdc trung binh cua d td : a) Trong giay ddu tidn. b) Trong 3 gidy cudi ciing. e) Trong sudt thdi gian quan sat.
x(m)
t(s)
0
0
2,3
1,0
9,2
2,0
20,7
3,0
36,8
4,0
57,5
5,0
1.2. Mdt ngudi tap thi due chay trdn mdt dudng thang. Luc ddu ngudi dd chay vdi vdn tdc trung binh 5 m/s trong thdi gian 4 min. Sau dd ngudi a'y giam van tdc cdn 4 m/s trong thdi gian 3 min. a) Hdi ngudi dd chay dugc quang dudng bang bao nhidu ? b) van tdc trung binh trong toari bd thdi gian chay bang bao nhieu ?
1.3. Mdt ngudi bed dgc theo chilu dai 50 m ciia bl boi hit 40 s, rdi quay lai vl chd xudt phat trong 42 s. Hay xdc dinh van tdc trung binh va tdc dd trung binh : a) Trong ldn boi ddu ti6n theo chilu dai cua bl bod. b) Trong ldn boi vl. c) Trong sudt quang dudng di va vl.
1.4. Hai d td ciing xud't phat tur Ha Ndi di Vinh, chile thii nhat chay vdi van tde trung binh 60 km/h, chile thii hai chay vdi van tdc trung binh 70 km/h. Sau 1 h 30 min chile thii hai dufng lai nghi 30 min rdi tilp tuc chay vdi van tdc nhu trude. Coi cac d td chuyin ddng tr6n mdt dudng thang.
a) Bilu diln dd thi chuyin ddng cua hai xe tren cung mdt h6 true toa dd. b) Hdi sau bao lau thi xe thii hai dudi kip xe ddu ? c) Khi dd hai xe each Ha Ndi bao xa ?
1.5. Dd thi chuyin ddng cua mdt ngitdi di bd va mdt ngudi di xe dap duge bilu diln nhu Hinh 1.2! a) Hay lap phuang trinh chuyin ddng cua tumg ngudi. b) Dua tr6n dd thi, xac dinh vi tri va thdi dilm hai ngudi gap nhau.
c) Tur cdc phuang trinh chuyin ddng da thanh ldp d cdu a, tim vi tri va thdi' dilm hai ngudi gap nhau. So sanh cac kit qua tim dugc d cdu a va b.
Hinh 1.2
1.6. Lue 6 h, mdt doan tau tur Thanh phd Hd Chi Minh di Nha Trang vdi vdn tde 45 km/h. Sau khi chay dugc 40 min thi tau dumg lai d mdt ga trong 10 min. Sau dd lai tilp tuc chay vdi van td'e bdng lue ddu. Liic 6 h 50 min, mdt d td khdi hanh txt Thanh phd Hd Chi Minh di Nha Trang vdi vdn td'e 60 km/h. Coi chuyin ddng cua tau va d td la thang diu.
a) Ve d6 thi chuyin ddng cua tau va ciia d td trfin ciing mdt hd true toa dd, b) Can cii vao dd thi, xac dinh vi tri va thdi gian d td dudi kip doan tau. e) Lap phuang trinh chuyin ddng cua tau va eiia d td k l tur lue dtd bat ddu chay va tim vi tri, thdi dilm d td dudi kip tau. So sanh vdi kit qua tim dugc 6 cdu a va b.
1.7. Luc 7 h, mdt d td chay tii Hai Phdng vl Ha Ndi vdi van tdc 60 km/h: Ciing luc, mdt d td chay tur Ha Ndi di Hai Phdng vdi van tdc 75 km/h. Bilt Hai Phdng each Ha Ndi 105 km va coi chuyin ddng la thang.
a) Lap phuang trinh chuyin ddng eua hai xe trfin cung mdt true toa dd, ldy gd'c tai Ha Ndi va chilu duang la ehilu tur Ha Ndi di Hai Phdng, va ldy luc 7 h lam gdc thdi gian. b) Tinh vi tri va thdi dilm hai xe gap nhau.
c) Ve dd thi hai xe ti&n ciing mdt hinh. Dura vao dd thi, xae dinh vi tri va thdi dilm hai xe gap nhau. So sanh vdi kit qua tinh duge d cau b.
1.8. Mdt d td chay trdn mdt dudng thang vdi van tdc 25 m/s. Hai gidy sau, vdn td'e eiia xe la 20 m/s. Hdi gia tdc trung binh ciia xe trong khoang thdi gian dd bang bao nhidu ?
10
1.9. Mdt chdt dilm chuyin ddng trfen mdt dudng thang. Liic t = 0, van td'e ciia nd la 5 m/s ; liic t.= 4 s, van td'e eua nd la 21 m/s. Hdi: a) Gia tdc trung binh cua nd trong khoang thdi gian dd bang bao nhieu ? b) Ta ed thi tinh dugc van td'e trung binh ciia nd trong khoang thdi gian dd nhd eae sd lidu tr6n dugc khdng ? Giai thich.
1.10. Mdt electron chuyin ddng trong dng den hinh eua mdt may thu hinh. Nd tang td'e diu dan tur van tdc 3.10 m/s din van tdc 5.10 m/s trtn mdt doan dudng thang bang 2 cm. Hay tinh :
a) Gia tdc cua dlectron trong chuyin ddng dd. b) Thdi gian Electron di hit quang dudng dd.
~1.11. Mdt d td chay diu tr6n dudng thang vdi van td'e 30 m/s vugt qua tdc do cho phep va bi canh sat giao thdng phat hien. Chi sau 1 s khi d td di ngang qua
mdt eanh sat, anh nay phdng xe dudi theo vdi gia tde khdng ddi bang 3 m/s .
a) Hdi sau bao lau thi anh eanh sat dudi kip d td ? b) Quang dudng anh di dugc la bao nhidu ?
1.12. Mdt tau thuy tang tdc diu dan tii 15 m/s din 27 m/s tren mdt quang dudng thang dai 70 m. Hay xac dinh : d) Gia tdc eiia tau. b) Thdi gian tau chay.
1.13. Mdt d td chay trSn mdt con dudng thang vdi van tdc khdng doi la 40 km/h. Sau mdt gid, mdt d td khac dudi theo voi van td'e khdng ddi tir ciing dilm xudt phat va dudi kip d td thu" nhdt sau quang dudng 200 km. a) Tinh vdn tde eua d td thii hai. b) Giai bai toan bang dd thi.
1.14. Mdt vdt chuyin ddng thang cd van tdc la 5,2 m/s. Hdi van tdc ciia nd sau 2,5 s bang bao nhi6u, nlu :
a) Gia tdc cua nd bang 3 m/s ?
b) Gia td'e cua nd bang -3 m/s ?
1.15. Vdn td'e ban ddu cua mdt vat chuyin ddng dge theo true Ox la -6 cm/s khi
nd d gd'c toa dd. Bilt gia tdc ciia nd khdng ddi la 8 cm/s , hay tfnh :
a) Vi tri ciia nd sau 2 s. b) Vdn tdc ciia nd sau 3 s.
11
1.16. Mdt electron ed vdn tdc ban ddu la 3.10^ m/s. Ndu nd chiu mdt gia tdc bang
8.10^'^m/s2thi:
a) Sau bao ldu nd dat duge vdn tdc 5,4.10^ m/s ? b) Quang dudng nd di dugc la bao nhidu trong khoang thdi gian dd ?•
1.17. Mdt may bay phan luc khi ha canh cd vdn tdc tilp ddt la 100 m/s. Bilt rang
dl giam td'e dd, gia tde cue dai cua may bay cd thi dat dugc bang -5 m/s .
a) Tfnh thdi gian nhd nhdt cdn dl may bay diing han lai kl tuf luc tilp ddt. b) Hdi may bay nay ed thi ha eanh an toan trdn mdt dudng bang dai 0,8 km dugc khdng ?
1.18*. Mdt ban hge sinh tung mdt qua bdng eho mdt ban khae d trdn tdng hai cao 4 m. Qua bdng di ldn theo phuang thang dung va ban nay gia tay ra bat duge qua bdng sau 1,5 s. a) Hdi vdn td'e ban ddu cua qua bdng la bao nhidu ? b) Hdi vdn tde eua qua bdng liic ban nay bat duge la bao nhidu ?
1.19. Mdt ngudi nem mdt qua bdng tuf mat ddt ldn cao theo phuang thing diing vdi van tdc 4 m/s. a) Hdi khoang thdi gian giiJa hai thdi dilm ma van tdc cua'qua bdng cd cung dd ldn bang 2,5 m/s la bao nhidu ? b) Dd cao liic dd bang bao nhidu ?
1.20*. Mdt vat rod tu do, trong giay cudi cung rod duge 34,3 m. Tfnh thdi gian tur liic bat ddu red dd'n luc cham ddt.
1.21. Ngudi ta tha mdt hdn da tur mdt cita s6 d dd cao 8 m so vdd mat ddt (vdn td'e ban ddu bang khdng) vao dung liic mdt hdn bi thep rod tuf trdn mai nha xud'ng di ngang qua vdd vdn tde 15 m/s. Hdi hai vdt cham ddt each nhau mdt khoang thdi gian bang bao nhidu ? Bd qua stie can ciia khdng khf.
1.22*. Dl bid't dd sau ciia mdt cai hang, nhiing ngudi tham hilm tha mdt hdn da tut midng hang va do thdi gian tur liic tha din liic nghe thdy tilng vgng cua hdn da khi cham ddt. Gia sit ngudi ta do dugc thdi gian la 13,66 s. Tfnh dd sdu eua hang. Ld'y gia tdc trgng trudng g = 10 m/s^ va van tde am trong khdng khflavam = 340m/s.
1.23*. Mdt hdn bi dugc tha red tu do, van tdc ban ddu bang 0. Ggi Si la dd ddi ciia hdn bi sau giay ddu tien.
a) Hay tfnh dd ddi cua hdn bi theo Sj trong nhiing khoang thdi gian bang nhau lidn tilp va bang 1 s.
12
b) Hay tinh hidu cua cae dd ddi thue hidn trong nhihig khoang thdi gian bang nhau lidn tilp, bang 1 s va nghidm lai rang hidu dd bang mdt sd' khdng ddi va
bdng 2si.
1.24. Luc trdi khdng cd gid, mdt may bay bay tii dia dilm A dd'n dia dilm B theo mdt dudng thing vdd vdn tde khdng ddi 100 m/s hit 2 h 20 min. Khi bay trd lai, gap gid ndn tii B vl A may bay bay hit 2 h 30 min. Xac dinh van td'e cua gid.
1.25. Trdn mdt con sdng chay vdd van tdc khdng ddi 0,5 m/s, mdt ngudi bod ngugc ddng 1 km rdi ngay lap tiic bed quay trd lai vl vi trf ban ddu. Hdi thdi gian bod eua ngudi dd la bao nhidu ? Bid't ring, trong nudc lang ngudi dd boi vdd van tdc 1,2 m/s. Hay so sanh vdd thdi gian ngudi dd ed thi bod dugc trong ddng sdng lang ydn (khdng chay).
1.26. Mdt phi edng mudn may bay cua minh bay vl hudng Tay trong khi gid thdi vl hudng Nam vdd van tde 50 km/h. Bilt rang khi khdng ed gid, van td'e cua may bay la 200 km/h.
a) Hdi phi edng dd phai lai may bay theo hudng nao ?
b) Khi dd vdn td'e eua may bay so vdd mat ddt la bao nhidu ?
1.27. Mdt d td chay vdi vdn tde 50 km/h trong trdi mua. Mua roi theo phuofng thing diing. Trdn cita kfnh bdn cua xe, cdc vdt mua roi lam vdi phuang thing
dung mdt gdc 60°
a) Xac dinh van tdc ciia gigt mua ddi vdi xe d td.
b) Xac dinh van td'e cua gigt mua dd'i vdi mat ddt.
1.28. 6 td A chay thing vl hudng Tdy vdi vdn tdc 40 km/h. 6 td B chay thing vl hudng Bdc vdd van tdc 60 km/h. Hay xae dinh van tdc ciia d td B ddi vdi ngudi ngdi trdn d td A.
1.29. Mdt nhdm hgc sinh lam thf nghidm chuyin ddng eua mdt xe trugt trdn mdt mang nghidng ddm khf. Mang nghidng mdt gdc so vdi mat nam ngang. Van tdc tlie thdi cua xe duge ghi nhd mdt cam biln quang didn ndi vdi mdt may hiln thi. Trong mdt ldn thf nghidm, nhdm hge sinh nay da ghi dugc kit qua sau:
Toa dd (cm)
van tdc (m/s)
20
0,386
40
0,560
60
0,687
80
0,791
100
0,884
Hay tfnh gia tdc ciia xe vdd gia thilt xe chuyin ddng nhanh ddn diu.
1.30. Ngudi ta lam thf nghidm do gia td'e rod tu do cua mdt hdn bi thep. Sii dung mdt bd phdn do vdn tdc ndi d bai tdp 1.29 dl do van tdc hdn bi rod d eudi
13
nhung quang dudng khac nhau. Cac kit qua thf nghiem dugc. ghi trong bang sau :
Toa do (em)
van td'e (m/s)
20
1,980
40
2,803
60
3,433
80
3,964
100
4,432
120
4,848
140
5,238
Gia tri cua gia td'e rod tu do g do dugc trong thf nghiem nay bang bao nhidu ? Quy luat vl rod tu do cd duge nghidm diing khdng ?
1.31. Mdt chdt dilm chuyin ddng trdn true Ox. Phuang trinh chuyin ddng eua nd ed dang sau :
X = - 1 + lOt + 8, t tfnh bang giay, x tfnh bang met. Chgn eau dung trong eac cau sau : Chat dilm chuyin ddng
A. nhanh ddn diu rdi cham ddn diu theo ehilu duang cua true Ox. B. nhanh ddn diu rdi cham dan diu theo ehilu dm eua true Ox. C. cham ddn diu rdi nhanh ddn diu theo chilu duong cua true Ox. D. chdm ddn diu rdi nhanh ddn diu theo chieu am eua true Ox. E. cham dan diu theo ehilu duang rdi nhanh ddn diu theo ehilu am eua true Ox.
1.32. Hai xe A va B chuyin ddng trdn ciing mdt dudng thing, xudt phat tii hai vi tri each nhau mdt khoang bang /. Dd thi van tdc theo thdi gian eua chiing duge bilu diln trdn mdt he true toa dd la hai dudng song song (Hinh 1.3). cau nao sau day la diing ?
A. Trong khoang thdi gian tii 0 - ti,
hai xe chuyin ddng diu.
B. Trong khoang thdi gian tuf 0 - ti,
hai xe chuyin ddng cham ddn diu.
C. Trong khoang thdi gian tii 0 - t],
hai xe chuyin ddng nhanh ddn diu.
V (m/s)' I
Hinh 1.3
14
D. Hai xe cd cung mdt gia tdc.
E. Hai xe ludn ludn each nhau mdt khoang cd dinh, bang /.
1.33. Mdt thang may chuyin ddng khdng van tdc ban ddu tur mat ddt di xud'ng mdt gilng sau 150 m. Trong 2/3 quang dudng dau tien, thang cd gia tdc 0,5 m/s ; trong 1/3 quang dudng sau, thang chuyin ddng cham ddn diu cho din khi dtmg hin d day gilng.
van tdc cue dai ma thang may dat dugc la gia tri nao sau day ?
A. 5 m/s. B. 10 m/s. C. 30 m/s. D. 25 m/s. E. 40 m/s.
1.34. Ciing bai tap trdn, hdi gia tri nao eua gia td'e trong giai doan sau la diing ? (Chgn chilu duong true Ox hudng xudng dudi).
A. 0,5 m/s^ D. -1 m/s^
B. - 0,5 m/s E. - 2 m/s^
C. 1 m/s'
1.35. Trong mdt thf nghidm xe lan tren mang nghieng, ngudi ta da ghi duge vi tri cua xe tai cac thdi dilm khac nhau trong bang sau day :
Vitri
• t(s)
x(cm)
A
0
1,5
B
0,4
12,0
C
0,8
21,0
D
1,2
28,5
E
1,6
34,5
G
2,0
39,0
H
2,4
42,0
a) Hay xac dinh gdn diing van tdc tiie thdi eiia xe tai eac vi trf B, C, D, E va G. b) Tfnh gia td'e trung binh trong nhung khoang thdi gian 0,4 s. Em ed nhan xet gi vl chuyin ddng nay ?
1.36. Trong mdt thf nghidm trdn mang nghieng eua dem khf, vi tri eiia xe trugt dugc ghi lai sau cac khoang thdi gian diu dan 20 ms (1 ms la 1 miligiay, bang 0,001 s) trong bang sau :
Vitri
x(mm)
A
0
B
20
C
35
D
45
E
50
Hay xac dinh gdn diing vdn tde tiic thdi tai cac vi tri B, C, D.
15
1.37. Mdt chat dilm chuyin ddng trdn mdt dudng trdn ban kfnh 5 em. Tdc dd gdc eua nd khdng ddi, bang 4,7 rad/s.
a) Ve quy dao eua nd. b) Tfnh tdn sd va chu ki quay cua nd. e) Tfnh td'e dd dai va bilu diln vecta vdn tdc tai hai dilm trdn quy dao each nhau 1/4 chu ki.
1.38. Mdt ehdt dilm chuyin ddng diu trdn mdt quy dao trdn, ban kfnh 0,4 m. Bilt rang nd di dugc 5 vdng trong mdt gidy. Hay xac dinh tde dd dai va gia tdc hudng tdm eua nd.
1.39. Xac dinh gia tdc hudng tdm cua mdt ehdt dilm chuyin ddng trdn mdt dudng trdn ban kfnh 3 m, tde dd dai khdng ddi bang 6 m/s.
1.40. Dl chudn bi bay trdn cac con tau vii tru, cac nha du hanh phai luydn tdp trdn may quay li tam. Gia sit ghi ngdi d each tdm cua may quay mdt khoang 5 m va nha du hanh chiu mdt gia tdc hudng tdm bang 7 ldn gia tdc trgng trudng g. Hdi:
a) Td'e dd dai cua nha du hanh bang bao nhidu ? b) Td'e dd gdc bang bao nhidu (tfnh ra vdng/phut) ?
1.41. Tii trudng cd thi budc mdt hat mang didn chuyin ddng theo mdt quy dao trdn.
Gia sit trong tur trudng, mdt dlectron cd gia tdc hudng tdm la 3,5.10 m/s . Hdi
td'e dd dai cua nd bang bao nhidu nlu ban kfnh quy dao bang 15 em ?
1.42. Trong hd quy chid'u gin vdd tdm Trai Ddt, Trai Ddt quay mdt vdng xung
quanh true Bdc - Nam hd't mdt ngay ddm. Coi Trai Ddt la mdt qua edu bdn
kfnhRj) = 6400km.
a) Tfnh td'e dd dai eua mdt dilm nam d xfeh dao, va cua mdt dilm d vi dd
45° Bdc.
b) Trung tam phdng tdn l&a vu tru eua chau Au ddt d Ku-ru, Guy-an (thudc Phap) nam gdn xfeh dao. Hdi vdd If do vdt If nao, ngudi ta lai chon vi tri dd? c) Phai phdng tdn lita vii tru theo hudng nao dl ed lgi nhdt vl vdn tdc ?
1.43. Khi lam thf nghidm vl ddng hgc, ban Vdn da ghi dugc bang sd lidu va d6 thi dudi ddy (Hinh 1.4). Hay trinh bay va giai thich hai each xac dinh gdn dung vdn td'e tiic thdi cua vdt chuyin ddng tai thdi dilm t = 0,2 s.
16
t(s)
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
x(cm)
0
2,2
5,6
10,2
15,8
23,0
31,4
40,8 *
51,5
x(cm)
50
45
40
35
30
25
20
15
10
5
,
M
•
0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 t(s)
Hinh 1.4
1.44. Mdt ban da lam thf nghidm chuyin ddng cua bgt khf trong d'ng thing va ghi duge sd lidu rdi ve dd thi nhu Hinh 1.5. Mdi dudng thing trdn dd thi ung vdd mdt gdc nghidng ciia dng.
Hay phdn tfch va xdc dinh tinh chdt cua chuyin ddng cua bot khf.
X (cm)
Hinh 1.5
2-BTVL 10(NC)-A 17
DONG LUC HOC CHAT D I € M
I - BAI TAP VI DU
Bail
Mdt vdt cd khd'i lugng m = 2 kg, chuyin ddng dudi tae dung cua mdt luc keo F]j biln ddi theo thdi gian, va mdt
lue can Fj, ed dd ldn khdng ddi la 2 N. Dd thi van td'e eua vat nhu trdn
Hinh 2.1. " Hay ve dd thi bilu didn su bid'n
thidn eua dd ldn luc keo theo thdi gian.
Bdi gidi Theo dinh luat II Niu-tan :
dodd F,,-ma + Fc (1)
Trong 2 giay ddu, dd thi van tde la mdt doan thing dd'c ldn, vat chuyin ddng nhanh ddn diu vdd gia tdc :
Av 2 . .2 a = — = — = 1 m/s
At 2
Thay vao (1) : F^ = 2.1 + 2 = 4 N
F(N)|
4
10 t(s)
8 10t (s )
Hinh 2.2
Trong 4 gidy tilp theo, dd thi van tdc la doan thing song song vdd true hoanh, vat chuyin ddng diu, gia tde a = 0. Theo cdng thiic (1), ta ed :
Fk = Fc = 2N
Khi dd lue keo can bang vdi lue can.
18 2-BTVL 10(NC)-B
Trong 4 giay cudi, dd thi van tdc la doan thing ddc xud'ng, vat chuyin ddng chdm ddn diu vdi gia tde :
a = Av 0 -= -0,5 m/s At 4
Theo edng thiic (1), ta ed:
Fk = 2.(-0,5) + 2 = 1 N
Dd thi cua luc keo F^ theo thdi gian dugc bilu didn nhu trdn Hinh 2.2.
m2 Bai 2 (Bdi tap trdc nghidm) Vo ?X:
^7777 / / / / / / / / / / / / / / / A
mi
Hinh 2.3
Trong Hinh 2.3, mi = 0,5 kg ;
m2 = 0,8 kg ; hd sd' ma sat nghi va hd sd
ma sdt trugt giiia vdt m2 va mat ban diu
la |u = 0,2. Ngudi ta giii cho hd ddng ydn,
rdi truyin cho rh2 mdt van tdc ban ddu
VQ cd hudng nhuhinh ve. Hay chgn cau
md ta dung vl chuyin ddng eiia vat 1 :
A. vat 1 chuyin ddng chdm ddn diu ldn trdn, dd'n mdt dd cao nhdt dinh, rdi chuyin ddng nhanh ddn diu xud'ng dudd.
B. Vdt 1 chuyin ddng diu ldn phfa trdn. C. Vdt 1 chuyin ddng cham ddn diu ldn trdn din mdt dd cao nhdt dinh rdi
dumg lai.
D. Cd thi xay ra mdt trong 3 kha nang ndi trdn, tuy thudc vao dd ldn cua Vg.
Ggi y:
Khi lam loai bai trac nghidm, cdn vdn dung kiln thiic da hgc dl nhanh chdng loai trii nhiing phuang an tra ldi sai va lua chgn phuang dn dung. Trong bai nay :
Sau khi vdt 2 duge truyin vdn tdc VQ, trgng luc Pj (hudng xud'ng dudi) va
Fms (hudng sang phai) diu cd tdc dung can trd chuyin ddng eua hd. Vdy hd khdng thi chuyin ddng diu dugc. Ta loai ngay cdu B.
Cdu A va cdu C diu cd y ddu diing (hd chuyin ddng chdm ddn diu). Sau khi
hd diing lai, trgng luc Pi cd xu hudng keo vdt 1 di xud'ng va keo vat 2 di sang bdn
19
phai. Lue ma sat lue nay se hudng sang trai dl can trd chuyin ddng eua hd. Di lua
chgn giiia eac kha nang A va C ta phai so sdnh Pi vdd gia tri cue dai F j cua lUc
ma sdt nghi:
Pl = mig = 0,5.9,8 = 4,9 N
F^, = nm2g = 0,2.0,8.9,8 = 1,57 N
Vdd sd lidu cua bai nay ta dd dang thdy Pi > F^,^. Vdy, sau giai doan chuyin ddng cham ddn diu, hd khdng dumg lai ma se chuyin ddng nhanh ddn diu theo ehilu ngugc lai, A dung.
(Ne'u sd lidu trong ddu bai ddn dd'n Pi < Fn, thi C diing).
Trong cdc ldp ludn tren, ta thdy dd ldn cua VQ khdng anh hudng ddn chilu hudng didn biln cua hidn tugng, vay ta loai D.
Bai 3 Mdt chid'c ban trdn ban kfnh
R = 35 cm, quay quanh true thing diing vdi vdn tdc gdc co = 3 rad/s.
Hdi ta cd thi dat mdt vat nhd trdn vung nao cua ban ma vat khdng bi vang ra xa tam ban ? Hd sd ma sat nghi giiia
vdt va mat ban la |J.„ = 0,25. Hinh 2.4
Bdi gidi
Vdt se khdng bi vang di nd'u luc ma sat nghi cua mat ban du dl ddng vai trd cua
luc hudng tdm : F^^^ = F t
ma F^sn ^ ^^mg ; F t = m o ^
d ddy r la khoang each tii vat din tam ban, Hinh 2.4.
Tuf dd : m(o\ < |a„mg
^„g _ 0,25.9,8 ^ 0 ^ -
(o 3 vay, dl vat khdng bi vang, ta cdn dat nd trong pham vi hinh trdn ddng tdm vdd
ban, bdn kfnh 27 em.
(Dap sd nay chdp nhdn dugc vi r < R).
20
II - Bi BAI
2.1
2.2
Hay xac dinh luc do vdt nang lam cang cac ddy AC, AB. Cac sd lidu eho trdn Hinh 2.5.
Chgn edu dung. Khi dang di xe dap trdn dudng ndm
J ngang, nlu ta ngumg dap, xe vdn di tilp chii chua ditng ngay. Dd la nhd A. trgng lugng cua xe. B. luc ma sat. C. qudn tfnh eua xe. D. phan luc cua mat dudng.
2.3. Giai thfch tac dung cua day an toan trdn xe d td.
2.4. Giai thfch tdc dung cua cae dudng bang trdn san bay dd'i vdi vide cdt eanh va ha canh cua may bay.
2.5. Rdt khd ddng dinh vao mdt tdm van mdng va nhe. Nhung nlu ta dp mdt vdt na,o dd vao phfa bdn kia tdm van thi lai ed thi dl dang ddng dugc dinh. Vi sao ?
2.6. Chgn cdu phat bilu dung. A. Nd'u khdng ed lue tde dung vao vdt thi vdt khdng chuyin ddng dugc. B. Nd'u thdi khdng tdc dimg luc vao vat thi vat dang chuyin ddng se dumg lai. C. vat nhdt thid't phai chuyin ddng thso hudng ciia lue tac dung. D. Nd'u cd luc tde dung ldn vat thi van td'e cua vat bi thay ddi.
2.7. Mdt qua bdng cd khd'i lugng 0,2 kg bay vdi van tdc 25 m/s din dap vudng gdc vdi mdt biic tudng rdi bi bat trd lai theo phuang cii vdi van tdc 15 m/s. Khoang thdi gian va cham bang 0,05 s. Tfnh luc cua tudng tac dung ldn qua bdng, coi lue nay la khdng ddi trong sud't thdi gian tae dung.
2.8. Luc Fl tac dung ldn mdt vat trong khoang thdi gian 0,8 s lam van tdc ciia nd
thay ddi tit 0,4 m/s din 0,8 m/s. Luc khac F2 tde dung ldn nd trong khoang
thdi gian 2 s lam vdn td'e cua nd thay ddi tur 0,8 m/s din 1 m/s (Fi va Fj ludn ciing phuang vdd chuyin ddng).
p a) Tinh ti sd —, bilt rang eae luc nay khdng ddi trong sudt thdi gian tae dung.
F2 b) Nd'u luc F2 tde dung ldn vdt trong khoang thdi gian 1,1 s thi vdn tdc eua vdt thay ddi thi nao ?
21
2.9. isidt lue tac diing vao mdt vdt trong khoang thdi gian 0,6 s lam vdn tdc cua nd thay ddi tur 8 cm/s din 5 cm/s (luc ciing phuong vdi chuyen ddng). T i ^ dd, tang dd ldn cua lue ldn gdp ddi trong khoang thdi gian 2,2 s nhung vdn giii nguydn hudng eua lue. Hay xae dinh vdn tde cua vdt tai thdi dilm cudi.
2.10. Mdt lue F truyin eho vdt ed khdi lugng mi mdt gia tdc bang 8 m/s , truyin
cho mdt vdt khac ed khdi lugng m2 mdt gia tde bang 4 m/s .Nlu dem ghep
hai vdt dd lai thanh mdt vdt thi lue dd truyin cho vdt ghep mdt gia tdc bang
bao nhidu ?
2.11. Mdt vdt cd khdi lugng 3 kg dang chuyin ddng thing diu vdi vdn tdc VQ = 2 m/s
thi chiu tde dung eua mdt luc 9 N ciing chilu vdi VQ. Hdi vdt se chuyin ddng
10 m tilp theo trong thdi gian la bao nhidu ?
2.12. Mdt vdt khdi lugng m = 0,5 kg chuyin ddng nhanh ddn diu vdd vdn tde ban
ddu VQ = 2 m/s. Sau thdi gian t = 4 s, nd di duge quang dudng s = 24 m. Bilt
rang vdt ludn chiu tac dung cua lue keo Fk va luc can FJ. = 0,5 N.
a) Tfnh dd ldn cua luc keo.
b) Nd'u sau thdi gian 4 s dd, luc keo ngiing tac dung thi sau bao ldu vdt se dumg lai ?
2.13. Mdt vdt nhd khdi lugng 2 kg, luc ddu dting ydn. Nd bat ddu chiu tac dung
ddng thdi eua hai luc Fi = 4 N va F2 = 3 N. Gdc giiia Fi va F2 la 30°.
Tfnh quang dudng vat di dugc sau 1,2 s.
2.14. Hgp lue tae dung ldn mdt xe d td bid'n thidn theo dd thi d Hinh 2.6. Bilt xe cd khdi lugng 2 tdn, van td'e ban ddu bang 0. Ve dd thi vdn tdc cua xe.
-200 f
Hinh 2.6 2.15. Hai ngudi keo mdt sgi ddy
theo hai hudng ngugc nhau, mdi ngudi keo mdt lue 50 N. Hdi sgi ddy cd diit hay khdng nlu nd chi chiu duge luc cang tdi da l a80N?
22
2.16. Tfnh gia tde rod tu do d dd cao 5 km va d dd cao bang nita ban kfnh Trai Ddt. Cho gia tdc rod tu do d mat ddt la g = 9,80 m/s^, ban kfnh Trdi Ddt la R = 6400km.
2.17. Hay tra cliu cdc bang dii lidu d phu luc 2 cua SGK dl tfnh dd ldn cua lue hdp ddn giiia Mat Trdi va Trdi Ddt.
2.18. Nlu bdn kfnh cua hai qua cdu ddng chdt va khoang each giiia tam cua ehung cung giam di 2 ldn, thi lue hdp ddn giiia chung thay ddi nhu thd' nao ?
4 ^ (Qua cdu ban kfnh r cd thi tfch la V = - nr).
3 A. Giam 8 ldn. B. Giam 16 ldn. C. Tang 2 ldn. D. Khdng thay ddi.
2.19*. Lue hut cua Trai Ddt da^vao mdt vat khi vat d mat ddt la 45 N, khi vdt d dd cao h la 5 N. Chgn gia tri diing cua h :
A. 3R. B. 2R. C. 9R. D. ^R.
(R la ban kfnh Trdi Ddt).
2.20. Cdc gigt mua rod dugc xud'ng ddt la do nguydn nhan nao sau day ?
A. Qudn tfnh. B. Luc hdp ddn ciia Trai Ddt.
' C. Gid: D. Luc ddy Ae-si-met eiia khdng khf.
2.21. Khoang each trung binh giiia tam Trdi Ddt va tdm Mat Trang bang 60 Idh ban kfnh Trai Ddt. Khdi lugng Mat Trang nhd hon khdi lugng Trai Ddt 81 ldn. Tai dilm nao trdn dudng thing ndi tam eua chiing, lue hut cua Trai Ddt va eua Mat Trang tac dung vao mdt vat can bang nhau ?
2.22. Mdt tdn lura vu tru dang d each tam Trai Ddt 1,5.10^ km. Luc hdp ddn cua Trdi Ddt tdc dung ldn nd d vi tri dd nhd hon so vdd d mat ddt bao nhieu ldn ? Cho ban kfnh Trai Ddt R = 6 400 km.
2.23. Mdt qua bdng nem theo phuang ngang vdd vdn td'e ddu vg = 25 m/s va rod xudng ddt sau t = 3 s. Hdi qua bdng da dugc nem tur dd cao nao va tdm nem xa eua qua bdng la bao nhidu ? Bd qua luc can eua khdng khf.
2.24. Mdt may bay bay vdd vdn tdc khdng ddi VQ theo phuang ndm ngang d dd cao h so vdd mdt ddt va tha mdt vdt.
a) Nlu h = 2,5 km ; VQ = 120 m/s ; hay :
+ Ldp phuong trinh quy dao cua vat.
23
+ Xac dinh thdi gian tii liic tha vat din luc vat cham ddt. Tim quang dudng / vat di duge theo phuang nam ngang ke tii liic dugc tha cho tdi khi cham ddt.
b) Khi h = 1000 m, hay tfnh VQ dl / = 1500 m.
Bd qua anh hudng cua khdng khf.
Vo
J ^ Hinh 2.7
a
2.25*. Tit mdt dilm d dd cao h = 18 m so vdd mat ddt va each tudng nha mdt khoang / = 3 m, ngudi ta nem mdt hdn sdi theo phuang
nam ngang vdi vdn td'e ban ddu Vg. Trdn tudng ed mdt ciia sd ehilu cao a = 1 m, mep dudd eua cita each mat ddt mdt khoang b = 2 m (Hinh 2.7).
Hdi gid tri cua VQ phai nam trong gidd han nao dl hdn sdi lgt qua cita sd ? Bd qua bl day eua biic tudng.
2.26. Tii mdt dinh thdp cao 12 m so vdd mat ddt, ngudi ta nem mdt hdn da vdi vdn
tdc ban ddu Vg = 15 m/s, theo phuang hgp vdd phuang nam ngang mdt gdc
a = 45° Xae dinh phuang, chilu, dd ldn eua vdn tdc hdn da khi nd cham
ddt. Bd qua luc can cua khdng khf.
2.27. Hai Id xo A va B cd chilu dai tu nhidn bang nhau duge bd tri nhu Hinh 2.8.
Dd cung cua Id xo A la 100 N/m. Khi Hinh 2.8 keo ddu tu do eiia Id xo B ra. Id xo A dan 5 em. Id xo B dan 1 em. Tfnh dd cung cua Id xo B.
2.28. Hai Id xo Li, L2 ed dd ciing ki, k2 dugc mdc vao nhau
(Hinh 2.9).
Nlu keo ddu C ra bdng mdt luc F, hd Id xo dan mdt doan Al. Ngudi ta ggi Id xo ma khi bi keo ra vdd luc F ciing bi dan mdt doan A/ nhu hd tren la Id xo tuang duang vdi hd trdn. Tfnh dd ciing k cua Id xo dd.
2.29. Mdt Id xo ed cdc vdng gidng hdt nhau, ed chilu dai tu
nhidn la /g = 24 em, dd ciing la k = 100 N/m. Ngudi ta cat
B
A /w/ / /
24
Id xo ndy thanh hai Id xo cd chilu dai tu nhidn /i = 8 cm, /2 = 16 cm. Tfah
dd Cling kl, k2 eua mdi Id xo tao thanh.
2.30. Theo dinh luat UI Niu-tan, luc va phan luc cd dd 1< bang nhau. Vay ma khi hai ngudi thi keo eo, vdn cd ngudi thang va ngudi thua. Vi sao vay ?
2.31. Mdt xe tai chd mdt edi hdm, chay trdn mat dudng nam ngang. Trong mdi trudng hgp sau day, hay chi rd san xe ed tde dung luc ma sat nghi ldn hdm khdng ? Nlu cd, thi lue dd phu thudc vao nhiing gi va cd chilu thi nao ? - X e dung ydn.
- Xe chuyin ddng nhanh ddn diu.
- Xe chuyin ddng cham ddn diu.
- Xe chuyin ddng thing diu.
2.32. Mdt cai hdm khdi lugng m = 20 kg dat trdn san"
nha. Ngudi ta keo hdm bdng mdt lue F hudng chlch ldn trdn va hgp vdd phuang nam ngang
mdt gdc a = 20? nhu tren Hinh 2.10. Hdm _ _ , „ „ „ , _ _ _ _ ^ ° , /777777777777777777777
chuyin ddng diu trdn san nha. Tinh dd ldn cua - • Hinh 2.10
luc F . Hd sd ma sat trugt gifia hom va san nha la ^t = 0,3.
2.33. Mdt mdu gd ed khdi lugng m = 250 g dat trdn san nha ndm ngang. Ngudi ta
truyin cho nd mdt van td'e tiic thdi Vg = 5 m/s.
Tfnh thdi gian dl mdu gd diing lai va quang dudng nd di dugc cho tdd liic dd.
Hd sd ma sat trugt gifla mdu gd va san nha la |Xt = 0,25.
Cdc ddp sd nay cd phu thudc m khdng ?
2.34*. Mdt doan tdu dang chuyin ddng vdd van tdc khdng ddi Vg thi mdt sd toa
cud'i (chiim — khdi luong doan tau) bi cdt khdi doan tau. Hdi khi cac toa dd 4 . •
dfing lai thi vdn td'e cua cdc toa d phdn ddu la bao nhidu ? Bid't ring luc keo doan tdu khdng ddi; hd sd ma sat lan H; gifia dudng ray vdd mgi phdn eua doan tau la nhu nhau va khdng ddi.
2.35. Mdt mdu gd (vat 1) dat trdn ddu B cua mdt tdm van AB (vdt 2). Liic ddu, chiing dfing ydn trdn mat ban nam ngang (Hinh 2.11).
25
JMMIi l l l \rT77777777777777777
a) Nlu keo tdm vdn bang mdt luc F khdng ldn ldm, mdu gd se chuyin ddng cung vdd tdin vdn.
- Luc nao da lam cho mdu gd chuyin '" ' tfi trang thai dfing ydn sang trang thdi chuyin ddng so vdi mat ban ?
- Vi sao mdu gd vdn dfing ydn so vdd tdm van ?
b) Nlu lue F du ldn, mdu gd se chuyin ddng so vdd tdin van va so vdi mat ban. Em hay lam thf nghidm nhu d Hinh 2.11 rdi rfit ra nhdn xet:
- Mdu gd chuyin ddng so vdi mat ban theo ehilu nao ? Lue nao lam cho mdu gd chuyin ddng theo ehilu dd ?
- Mdu gd chuyin ddng so vdd tdm van theo chilu nao ? Vi sao mdu gd chuyin ddng theo chilu dd ?
2.36. Mdt qua edu nhd budc vao mdt ddu ddy treo vao trdn eua mdt toa tau kfn. Ngudi d trong toa tau thdy : d trang thai cdn bang, day treo nghieng so vdd phuang thing dfing (Hinh 2.12). Dua vao chilu lech eua day treo, ta bilt dugc dilu gi sau day ?
A. Tau chuyin ddng vl phfa nao.
B. Tau chuyin ddng nhanh ddn hay chdm ddn.
C. Tau chuyin ddng nhanh hay cham.
D. Gia tdc cua tau hudng vl phfa nao.
2.37. Mdt may bay thue hidn mdt vdng bay trong mat phing thing dfing. Bdn kfnh vdng bay la R = 500 m, vdn tde may bay ed dd ldn khdng ddi v = 360 km/h. Khdi lugng cua ngudi phi cdng la m = 75 kg. Xac dinh lure nen eua ngudi phi edng idn ghi ngdi tai dilm cao nhdt va dilm thdp nhdt eua vdng bay (d dilm cao nhdt, ddu eua ngudi phi cdng hudng xudng ddt, ghi d bdn trdn).
2.38. Mdt vdt duge dat d mep mdt chile ban xoay. Hdi sd vdng quay trong 1 s eua
ban bang bao nhidu thi vat se vang ra khdi ban ? Cho bilt ban hinh trdn ed
ban kfnh r = 0,4 m, hd sd ma sat nghi bdng 0,4 vd g = 10 m/s^.
3^ ^ r77T77?777777777777777777777
Hinh 2.12
26
2.39. Trong thilt bi b Hinh 2.13, binh Mnh tru cd bdn kfnh r = 10 em. Ta dl mdt vdt nhd dp vao thanh trong cfia binh. Hd sd ma sdt nghi gifia thanh binh va
vdt la Jin = 0,3. Hdi sd vdng quay trong mdt phut cua binh hinh tru phai nhu thi nao dl vdt bam dugc vao thanh binh ma khdng bi rod.
Hinh 2.13
2.40. Dudd tdc dung cua mdt luc cd dd ldn khdng ddi, mdt vdt cd thi chuyin ddng diu duge khdng ?
2.41. Mdt vat nhd dat trdn mdt mdng nghidng MN khd dai hgp vdd mat phing nam
ngang mdt gdc a = 20°. Hd sd ma sdt nghi va ma sat trugt gifia vdt va mdng
nghidng diu cd tri sd la ^ = 0,2. ,
Ta truyin cho vdt mdt vdn tdc ban ddu Vg nhu trdn Hinh 2.14. Trong eac edu sau ddy, cau nao la dfing ?
A. vat chuyin ddng diu do quan tfnh.
B. vat chuyin ddng cham ddn diu ldn phfa N din mdt dd cao nhdt dinh rdi chuyin ddng nhanh ddn diu vl M.
C. vat chuyin ddng cham ddn diu ldn phfa N dd'n mdt dd cao nhdt dinh rdi dumg lai.
D. Cd thi xay ra mdt trong cac kha nang trdn
ddy, tuy thudc vao dd ldn cua Vg.
2.42*. Trong thf nghidni d Hinh 2.15a, ta dung bd rung do thdi gian dl ghi lai
nhiing quang dudng vdt di dugc sau nhiing khbang thdi gian x = 0,04 s.
Khi a = 20°, ta cd cdc chdm trdn bang gidy nhfi Hinh 2.15b. (Con sd dudd
mdi chfl chi vach chia theo milimet, khi ta dp vach sd 0 cua thudc do vao A).
Khi a = 42°, ldm tuong tu nhu trdn, ta dugc kit qua ehi ra trdn Hinh 2.15e.
Tim hd sd ma sdt trugt ^ gifia mat phang nghidng va vdt.
Hinh 2.14
27
Oau but da
Bang giay
A B C D E • • • • • •
0 5 12,5 22,5 35
a) b)
M N • • •
0 10
p a «. • 28 54
c) Hinh 2.15
R V
88
2.43. Trong ea hd d Hinh 2.16, khdi lugng eua hai vdt la mi = 200 g, m2 = 300 g, he sd ma sdt trugt gifla vat 1 va mat ban la jij = 0,2. Hai vat dugc tha ra cho chuyin ddng vao Ific vat 2 each mat dat mdt doan h = 50 em. a) Tfnh gia tdc cua mdi vat.
Q / / / / / / /
777777777777777777777777777777777777777:^rrrr7777:777777>
Hinh 2.16
Is.
b) Tfnh lue cang cua day khi hai vat dang chuyen ddng. c) Kl tfi Ific vat 2 cham ddt, vdt 1 cdn chuyin ddng thdm dugc mdt doan dai bao nhieu ?
2.44. Trong hd d Hinh 2.17, khd'i lugng cua hai vdt la mi = 1 kg ; m2 = 2 kg. Dd cao lue ddu cua hai vdt chdnh nhau h = 1 m. Hdi sau bao nhidu lau kl tfi khi bat ddu chuyin ddng thi hai vat d vi tri ngang nhau ?
2.45. Trong hd d Hinh 2.18, ta cd :
mi = 500 g; a = 30° ; eac he sd ma sat trugt va ma sat nghi gifla vdt 1 va mat phing nghidng la |it = | ^ = 0,2. Mat phing nghidng duge gifl ed dinh. Hay tfnh gia tdc cua mdi vat mi, m2 vd luc ma sat gifla vdt 1 vdd mat phing nghidng trong cae trudng hgp-:
a) m2 = 500 g ; b) m2 = 200 g.
mg
^
|mi
Hinh 2.17
28
2.46. Vdt khdi lugng m dat trdn mdt mat phing nghidng mdt gdc a so vdd phuang nam ngang (Hinh 2.19). Hd sd ma sat nghi gifla vat va mat phing nghidng la ^„. Khi dugc tha ra nhe nhang, vat cd thi trugt xudng hay khdng la do nhiing yd'u td nao sau day quylt dinh ?
A. m va jijj. B. a va (i -
C. a va m. D. a, m va |j,jj.
2.47*. Trdn Hinh 2.20, vat ed khd'i lugng m = 500 g ; a = 45°, day AB song song vdd mat phing nghidng ; hd sd ma sat nghi gifla vdt vd mat phing nghidng la |j,„ = 0,5. Hay tfnh :
a) Ap luc do vat tdc dung ldn mat phing nghidng.
b) Luc ma sat gifla vdt va mat phing nghidng
c) Luc cang eua day.
2.48*. Ngudi ta bd trf mdt ca hd nhu d Hinh 2.21a. Vat m2 cd gan mdt bang gidy ludn qua bd rung do thdi gian.
Khi tha eho hd chuyin ddng, bd rung ldn lugt ghi lai trdn bdng gidy nhiing chdin den sau tfing khoang thdi gian x = 0,04 s nhu Hinh 2.21b.
(3 Wt'
Hinh 2.19
Hinh 2.20
mg / but d9
Bang giSy
V7777777777777777777777777777777777777777777Z7777?.
a)
A B C D G H I K L
b) Hinh 2.21
29
Ta do duge:
Doan thing
Chilu dai (mm)
AB
17
BC
28
CD DE EF
39 50 61
FG
59
GH
54
HI
49
IK
44
KL
39
a) Giai thfch su bid'n thidn cua ehilu dai cae doan trdn.
b) Dua vao eac chdm tfi G din L dl xac dinh hd sd ma sat tnigt gifla ban va vdt 2.
c) I>ua vao cac eh&i tfi A din E dl xac dinh m2, nd'u bid't mi = 400 g.
2.49. Trong thf nghiem vl lue dan hdi, vi khdng cd Id xo ndn ban Thang da lam thf nghidm vdi mdt ddy cao su.
- Ldn lugt treo thdm eac qua nang 1, 2, 3... 8 lam ddy cao su dan ra.
- Lam ngugc lai, bdt ddn cae qua nang 8, 7, 6... 1 ddy cao su co lai.
Sau khi ldy sd lieu nhilu ldn trong qud trinh dan ra vd eo lai cua ddy, ban da ve dugc dd thi F(x) (Hinh 2.22), trong dd dudng 1 fing vdi qua trinh ddy cao su dan ra, dudng 2 fing vdi qua trinh ddy cao su eo lai.
Hay phdn tfch dd thi dl rut ra tfnh
chdt dan hdi cua ddy cao su nay. So
sanh vdi tfnh chd't dan hdi cua Id xo
trong bai da hgc. " ^.^^2.22
Ff
30
TINH HOC VRT R AN I
I - BAI TAP VI DU
Mdt vdn ddng vidn boi ldi diing trdn van nhay (xem Hinh 3.1). A la mdt d true cd phuong ndm ngang va vudng gdc vdd mat phing hinh ve, B la tru dd. Cac khoang each dugc cho trdn hinh ve. Trgng lugng eua ngudi bang 600 N, cua tdm vdn bang 100 N. ^
1. Lap mdt bang lidt kd cdc luc tac dung ldn ngudi va ldn t£m van.
2. Tfnh cac luc chua bilt.
Hinh 3.1
Bdi gidi
1. Phdn tfch cac luc dat ldn tumg vat trong hd
Tdin van (1) chiu bd'n lue tdc dung dat d A, B, C vd Gi (trgng tdm cua tdin
van), kf hidu la Agi, Bgi, C21 va Pi (trgng luc dat ldn tdm van).
Ngudi (2) chiu tdc dung cua hai luc la trgng luc P2 ddt tai G2 va phan lue cua
tdm vdn C12 tac dung ldn chdn ngudi dfing tai C.
Theo dinh ludt III Niu-tan : C21 = -C12.
31
Bang eae lue dat ldn tdm van va ngudi nhu sau :
- Ddi vdd tdrn van :
F / ^ van
— •
^ 01
—* Pl
^ 2 1
Dilm dat
A
B
Gl
C
Phuang, chilu
Thing dfing
Thing dfing t
Thing dfing X
Thing dfing i
Ddldn
7
7
100 N
7
- Dd'i vdi ngudi —•
ngir&i
P2
^12
Dilm ddt
G2
C
Phuang, chilu
Thing diing -l
Thing dfing t
Dd ldn
600 N
7
Chu y : 6 true va tru dd kf hidu bang chi sd 0, tdm van kf hidu bang chi sd 1, ngudi kf hidu bang chi sd 2. •
2. Vilt dilu kidn cdn bang ddi vdi tfing vdt
- Ddi vdd tdm vdn :
a) Dilu kidn vl luc :
Agi + Bgi + C21 + Pl = 0
b) Dilu kidn vl momen luc ddi vdd 6 true O tai A
0 + AB.B, '01 AGi.PJ AC.|C2i| = 0
- Dd'i vdd ngudi (ehi cd dilu kidn vl luc):
P 2 + C i 2 = 6
3. Giai bai toan, tim ede dai lugng chua bilt
Tfi cdng thfie (3), ta cd : - —» - P2 ^ ~Gi2 = C21
(1)
(2)
(3)
32
Nhu vdy, gia tri cua cac luc C12 va C21, bang trgng lugng P2 cua ngudi.
Cdc luc trong cdng thfic (1) cung phuong, vi thi ta cd :
Aoi + B o i - P i - C 2 i = 0
hay la Api+ B01 = Pi+ C21 = Pi+ P2 (4)
Cdng thfic (2) cho :
2.Boi-2,5.Pi-5.P2 = 0
hay Id ^01 -2,5.100 + 5.600
= 1625N (5)
Thay (5) vao (4) ta dfige gid tri cua Agi:
Aoi=-925N
Ddu - cd nghia la lue Agi hudng xudng dudd.
Kit qua:
- Cac luc tdc dung ldn t ^ van dugc chd d bang dudd ddy •—•
•''^01
^01
—» Pl
C21
Dilm dat
A
B
Gl
C
Riuang, chilu
Thing dfing 4'
Thing dfing t
Thing dfing -l -
Thing dfing -l
Ddldn
925 N
1625N
100 N
600 N
- Cdc luc tdc dung ldn ngudi dugc cho d bang dudd ddy :
—•
' ngudi
P2
G12
Dilm dat
G2
C
Phuong, chilu
Thing dfing -l
Thing dfing .t
Ddldn
600 N
600 N
n-D^BAI
3.1. Mdt hdn bi bdng sdt khdi Ifiong 0,2 kg dfige treo vao mdc C nhd mdt sgi ddy mim cd khdi lugng khdng ddng kl (xem Hinh 3.2),
3-BTVb 10(NC)-A 33
I Hinh 3.2
1. a) Xac dinh nhitng luc dat ldn hdn bi. ^ ^ ^
b) Phat bilu dilu kidn can bang cua hdn bi.
c) Tfnh gid tri cua nhfing luc dd va bilu didn eac luc dd vdi ti Id 0,5 em tuang fing 1 N.
2. a) Ngudi ta treo mdt luc k l gifia mdc C va sgi ddy. Luc k l chi lue nao ?
b) Dat d phfa dudi hdn bi mdt nam cham. Sod day treo vdn gifl thing dung va lue k l ehi 2,2 N. Hay phat bilu dilu kidn can bdng eua hdn bi va bilu diln cac Ific dat ldn hdn bi vdi cfing ti Id nhu cau trdn.
3.2. Hai quyln sdch dat chdng ldn nhau trdn mdt mat ban ndm ngang. Khdi tam
Gl va G2 eua chfing ciing ndm tren mdt dfidng thang dfing. Trgng lugng cua
quyln sdch nam trdn la 10 N, cua quyln dudd la 18 N.
1. a) Ve sa dd cac lue tde dung ldn tiing quyln sach.
b) Xac dinh eac luc tac dung ldn ttog quyln sach. Tfnh ede luc dd va phat bilu dinh ludt da sfi dung dl tfnh.
2. Bay gid xet hd gdm ea hai quyln sach.
a) Xac dinh cac ngoai lue dat ldn hd.
b) Cho bid't gid tri eua cac luc dd.
c) Luc do hd tde dung ldn mat ban bang bao nhidu ?
3.3. Mdt vat cd trgng lugng P = 10 N duge treo vao mdt ddu Id xo R. Ddu kia cua Id xo dugc gdn cd dinh trdn mdt gia dd. Khdi lugng Id xo cd thi bo qua dugc.
1. Xet hd Id xo - vat nam can bang. Lidt kd cac ngoai luc dat ldn hd. Xac dinh va bilu didn cac luc do gia dd tac dung ldn Id xo va do Id xo tdc dung, ldn vat.
2. Xet rieng vat ndm can bang. Xac dinh cae luc dat ldn vat.
3.4. Mdt hinh tru bang nhdm cd ehilu cao 20 em, ban kfnh 1 cm, dugc treo vao
ddu mdt luc k l R. Khd'i lugng ridng cua nhdm la 2,7 gjcm Bd qua luc
Ae-si-met cua khdng khf.
1. Khi cdn bang, luc k l chi bao nhieu ?
34 3-BTVL 10(NCHl
2. Nhung hinh tru chim hoan toan trong nudc (Hinh 3.3).
a) Hay ve so dd thf nghidm. Lidt kd cdc luc ddt ldn hinh tru.
b) Xac dinh luc ddy Ae-si-met. Sd chi cua lue kl la bao nhidu ?
3.5. Mdt vat nhd S khdi lugng m dugc treo d ddu mdt sgi ehi manh. Vdt S bi hut bdi mdt thanh thuy tinh hflu CO nhilm didn. Luc hfit eua thanh thuy tinh cd phuang nam ngang. Vat S nam can bdng khi sgi
• chi lam mdt gdc a vdd phuang thing dfiiig.
a) Lap bang lidt kd cac luc dat ldn vat S.
b) Xdc dinh gdc a theo eac luc.
c) Tfnh luc cang cua sgi day.
3.6
Hinh 3.3
Cho bilt: m = 0,5 g ; F = 3.10 ^ N ; la'y g =10 m/s^.
Hai luc song song cung chilu each nhau mdt doan 0,2 m. Nd'u mdt trong hai luc cd gia tri 13 N va hgp luc cua chfing cd dudng tde dung cdch luc kia mdt doan 0,08 m.
a) Tfnh dd ldn cua hgp luc.
b) Tfnh dd ldn cua luc kia.
3.7. Hai luc song song cung chilu, cd dd ldn 20 N vd 30 N. Khoang each gifla dfidng tac dung eua hgp luc cua ehung din luc ldn han bang 0,8 m. Tim khoang cdch gifia hai luc dd.
3.8. Giai bai tap 3.6 vd 3.7 vdi gia thilt hai luc ngugc ehilu.
3.9. Mdt vdt khd'i lugng m = 450 g ndm ydn trdn mdt mat nghidng
mdt gdc a = 30° so vdd mat nam ngang (Hinh 3.4).
a) Bilu didn cdc luc dat ldn vat.
b) Tfnh dd ldn cua luc ma sat gifia vdt va mat nghidng. Hinh 3.4
35
e) Bilt hd sd ma sat nghi gifla vdt va mat
nghidng Hn "= 1- ^^^ S^ nghidng cue dai bdng bao nhidu dl vdt khdng bi trugt ?
3.10. Mdt Id xo cd dd cfing k = 50 N/m.
1. Chilu dai tu nhidn cua Id xo /g = 50 cm. Treo mdt vdt 2(X) g vao mdt ddu Id xo (Mnh 3.5a). Hdi chilu dai cua Id xo khi treo vdt la bao nhidu ?
2. Ddt vdt dd trdn mdt mat nghidng sao cho Id xo nam dgc theo mat nghidng. Hd ndm cdn bang. Gdc nghidng a = 30°
a) TMi ehilu dai cua Id xo (Hinh 3.5b).
b) Tfnh phan luc N cua mat nghidng ldn vat.
Bd qua khdi lugng Id xo va ma sat gifla
vdt va mat nghidng ; ldy g = 10 m/s .
3.11. Dl xid't chat mdt deu, ngudi ta tac dung
ldn mdt ddu can cdld mdt luc F lam vdi can cdld mdt gdc a (Hinh 3.6).
a) Xdc dinh ddu cua momen luc F ddi vdd true quay cua deu.
b) Vilt bilu thfic cua momen luc F ddi vdd true cua deu. c) Tfnh momen dd, bilt F = 20 N ;
OA = 0,15 m va a = 60°
3.12. Trdn mdt 6 khoa cua canh cfia cd hinh qua ddm, ngudi ta tae dung mdt ngdu luc, nhumd tad Hinh 3.7.
a) Xac dinh ddu cua momen ngdu luc, b) Ve eanh tay ddn cua ngdu luc. c) Vilt bilu thfic cua momen ngdu luc theo F, AB va gdc a.
a)
>/?f^//i/^////^////.//j>>/>^^f^f^^^^>/^f/.
b)
Hinh 3.5
Hinh 3.6
36
3.13. Mdt thudc manh cd thi quay quanh mdt true nam ngang di qua ddu O cua thudc. Ggi xx' la dudng thing dfing di qua O, gdc a la gdc gifla thanh va true xx' (Hinh 3.8). Hay tihh momen cua trgng luc cua thanh ddi vdd true ndm ngang qua O tai cdc vi trf cua
thanh img von cac goc a = —; —; Jt.
Bilt m = 0,03 kg ; OG = a = 20 cm; g = 9,8 m/s^.
3.14. Mdt thanh ddng chdt, trgng lugng P = 1 N, chilu ddi AB = /, dugc dat nam ngang. Ddu A ti ldn mdt ludi dao, ddu B treo vao ddu mdt luc k l Id xo (Hinh 3.9).
Tai dilm M cdch A mdt
Hinh 3.8
M N
lmi I m2
Hinh 3.9
doan AM = — cd treo mdt
qua nang khdi lugng mi = 500 g ; tai dilm N
4/ cdch A mdt doan AN = — ed treo mdt qua nang khdi lugng m2 = 200 g.
Hdi luc kl d ddu B ehi bao nhidu ? (Ldy g = 10 m/s^).
3.15*. Cdi cdn ddn cd dang nhu Hinh 3.10. Khi khdng treo vdt ndo vd dat qua can d vi tri O thi can nam thang bang.
a) Chfing minh rang khoang each OB ti Id vdi trgng Ifigng cua vat mdc d K. b) Hdi trgng lugng cua qua can bang bao nhidu ? Bid't rang khi treo.mdt vdt 2 kg tai K thi qua cdn phai dat d vi tri B each O la 20 cm, Cho bilt AI = 5 cm.
B
Qu4cdn t I I
Hinh 3.10
37
3.16*. Bdn vidn gach gidng hdt nhau, ed chilu dai L, dugc dat chdng ldn nhau sao cho mdt phdn cua mdi vidn nhd ra ngoai vidn ndm dudi (Hinh 3,11), Hay tfnh:
a) Cac gia tri ldn nhdt cua cac doan ai, a2, a^, a^ nhd ra cua mdi vidn sao cho chdng gach vdn cdn bang. b) Khoang each h tfi mep ban diri mep ngoai cung cua vien gach trdn cfing nhd ra.
3.17. Mdt vdt hinh hop chfl nhdt nam cdn bang trdn mdt mat nghidng. Trong cac hinh ve dudd ddy, hinh nao bilu diln dfing cac luc tde dung ldn vdt ?
Hinh 3.11
/%. B. Hinh 3.12
3.18. Mdt qua edu dugc treo trdn mdt sgi J:^ day. Trong cdc hinl; ve dudi ddy T (Hinh 3.13), hinh nao bilu didn | dfing ede luc tae dung ldn qua cdu ? \j)
'M^ •/'//.>,
T
3.19. Mdt cai gdy gd ddng ehdt, mdt ddu to, mdt ddu nhd. Dung mdt sgi ddy manh budc cdi gdy d mdt vi tri ma khi treo day ldn thi gay ndm ngang (xem Hinh 3.14) Cua ddi gay d chd budc day thdnh hai phdn. Kd't ludn nao sau ddy vl trgng Ifigng cua hai phdn gdy la dung ?
A. Trgng lugng phdn ed ddu nhd ldn han phdn kia vi dai han. B. Khdng chac chan phdn nao ed trgng lugng ldn han. Phai cdn ttog phdn.
•P
A.
t UJUi.
J 1
%
B.
P
C.
Hinh 3.13
yyy/y.
Hinh 3.14
38
C. Trgng lugng phdn cd ddu to ldn hon. D. Trgng lugng hai phdn bang nhau vi day budc dfing vi tri trgng tdm cua thanh.
Day CO dp dai 2L
o
B Ddy da gdp lai, ddu B trung vdi O
Hinh 3.15
3.20. Chgn cau dfing. Mdt sgi day thep manh, etog, ddng chdt ed dd dai AB = 2L. Gdp sod ddy sao cho ddu B trung vdd dilm gifla O cua ddy (xem Hinh 3.15). Trgng tdm cua ddy se
A. vdn nam tai O.
B. nam tai mdt dilm each O mdt
doan bang—L, vl phfa A. o
C. nam tai mdt dilm cdch O mdt doan bang — L, vl phfa A.
3 ,D. nam tai mdt dilm cdch O, mdt doan bdng ^L, d phdn bi gdp.
8 3.21. Mdt em be ddt mdt cdy gdy nam
ngang trdn hai ngdn tay trd, sau dd dich ngdn tay bdn phai tid'n ddn vl bdn trdi (Hinh 3.16).
Hay du dodn va giai thfch su dich chuyin cua cdy gdy, lam thf nghidm kilm chtog. Nd'u sau dd lai dich ngdn tay phai theo ehilu nguge lai thi su dich chuyin cua cay gay cd ngugc lai so vdd trudc khdng ?
B
D
Hinh 3.16
3.22. Cho cdc dung cu sau :
- Mdt khd'i gd hinh hdp chfl nhat cd tilt didn la ABCD, khdi lugng m (Hinh 3.^). - Mdt thudc thing cd dd chia nhd nhdt dd'n mm. Hay tnnh bdy vd giai thfch mdt phuang an thf nghidm dl xdc dinh gdn dfing luc F cdn thid't tac dung vao A theo phuang song song vdd CD dl lam Idt khdi gd quanh D.
B a A F
C D Hinh 3.17
39
CRC DINH LURT BflO TORN
I -BAITAP VIDU
Bail
Hai xe lan dugc ndi vdi nhau bing mdt sgi d% 6i ep chat m ^ 16 xo dat giOa
hai xe. Thoat ddu ca hai xe nam ydn trdn mat ddt. Khi ddt day, 16 xo bung ra, ddy
hai xe chuyin ddng theo hai hudng ngugc nhau. Xe 1 co khffi lucng m| = 100 g
chuyin ddng dugc 18 m thi dfing lai. Hdi xe 2 co khfi luoag m2 = 300 g di datK
quang dudng bdng bao nhidu ? Hd sd ma sat trugt giiia xe va mat ddt la fif
Bai gim
Khi 16 xo bung ra, thdi gian tuong tac la rdt ngdn, do dd t ^ g ddng lucng cua ca hai xe dugc coi la bao toan (bdng kfadng) :
miVi + m2V2 = 0, do do :
^ 2 mi
(1)
Khi hai xe chuyin ddng, chi cd luc ma sat thuc hidn cdng lam ddng nang ciia
mdi Xe giam dih khdng. Ap dung dinh U ddng nang, ta cd :
- M t ^ i g s i =
-Htm2gS2 =
Tfi(l)va(2),tadugc:
Sj m 2
2 m?
mivf 2
"12^1
2 J
suy ra —*- = —^ So V?
(2)
Vdy M-(iJ--m.
40
Ghi chii: Cd thi giai bang phuong phap ddng luc hgc dl tim dugc ding thfic (2) 6 trdn nhfi sau :
Chuyin ddng cua hai xe la biln ddi diu (chdm ddn diu):
Vl = 7 2 ^ = J2 ;^ s i = V2HtgSi
V2 = V2a2S2 = J 2 - ^ S 2 = V2MtgS2 m j
Suyra — = j — chfnh la (2). V2 VS2
Bai 2
Mdt d td cd khd'i Ifigng 1,5 tdn bdt ddu md may chuyin ddng vdi gia tdc khdng ddi va dat vdn tdc 18 m/s sau thdi gian 12 s. Gia sfi lue can la khdng ddi vd bang 400 N. Hay tim :
a) Dd ddi cua d td va cdng cua luc keo thitc hidn trdn dd ddi dd.
b) Cdng sudt trung binh cua ddng co trdn ca dd ddi.
c) Cdng sudt tfic thdi cua ddng co tai thdi dilm cudi.
Bdi gidi
a) Ggi F la luc klo eua ddng ca d td va F^ la luc can. Theo dinh ludt n Niu-tan :
F - FJ, = ma
Chuyin ddng la nhanh ddn diu tfi trang thai nghi vdd a = —, do dd :
F - F . = m— *= t
. Luc keo cua d td bang : '•
F = F + — = 400 + 1500.1,5 = 2650 N t
Dd ddi cua d td bdng :
at^ 1,5,144 s = — = ^ ^ = 108m
Cdng cua luc keo thuc hidn bang :
A = Fs = 2 650,108 = 286 200 J
41
b) Cdng sudt trung binh cua ddng CO d td trdn ca dd ddi
A. _ 286200 t ~
SJ. -=23 850 W tb . . 12
c) Cdng sudt tfic thdi cua ddng co d td tai thdi dilm cudi
9 = Fv = 2 650.18 = 47 700 W
Bai 3
Hinh 4.1
Mdt chile vaii cd khd'i lugng lO kg trugt khdng ma sat tfi trang thai nghi tren mdt mat phang nhan, nghidng mdt gdc
30° so vdd mat san ndm ngang (Hinh 4.1). Sau khi di hit dd ddi Si = 3 m trdn mat nghieng, vat trugt tilp tren mat san mdt dd ddi S2 = 5 m thi dtog hin. Hay xdc dinh :
a) van tdc cua vaii d cud'i mat phing nghidng. b) He sd ma sat trugt gifla vaii va san.
c) Dd giam ca nang cua vaii do ma sat.
Ldy g = 10 m/s^.
Bdi gidi a) Chuyin ddng cua vaii trdn mat phing nghieng la nhanh ddn diu vdd gia tdc
khdng ddi a = gsina vi lue tdc dung la thanh phdn trgng luc Psina (Hinh 4.1). Do dd, van td'e eua vaii d cudi mat phing nghidng la :
V = yflasi = -y/2gsina.Si
= ^/2.10.0,5.3 =yl30= 5,48 m/s
b) Theo dinh If ddng nang, khi vaii trugt trdn mat san nam ngang tfi van tdc v dd'n khi dtog, cdng cua luc ma sat trugt thuc Men trdn dd ddi S2 bang dd giam ddng nang eua vaii:
-FmstS2 = -^itPs2 = mv
Suy ra:
^t v^ _ 30
2gS2 ~ 2.10.5 = 0,3
42
c) Trdn mat san ndm ngang, thi nang trgng trudng cua vaU khdng thay ddi, do dd dd giam co nang AW cua vaii cung bang dd giam ddng nang cua nd. Ta cd :
,2
AW = mv 10.30 = -150 J
Hinh 4.2
2 2
Vdy CO nang cua vaii giam mdt lugng bang 150 J
Bai 4
Hai vat cd khdi lugng mi = 1 kg vd m2 = 2 kg
dugc ndi vdd nhau bang mdt sgi day vat qua rdng
rgc nhu Hinh 4.2. Day khdng dan va cd khd'i lugng
khdng dang kl. Ban ddu vat m2 dugc gifl d dd cao
1 m. Tha tu do cho nd rod xudng phfa dudi thi
ddng thdi lam vat mi chuyin ddng ldn phfa trdn
theo mat phing nghidng. Bilt gdc nghidng a = 30°
va hd sd ma sat trugt [iy = 0,2.
a) Dung dinh luat biln thidn ca nang tfnh van tdc eua vat m2 khi nd vfia cham da't.
b) Tim gia tdc cua hd va luc cang T cua day. Kilm lai gia tri van tdc cua vat
m2 da tfnh d cau a).
Bd qua khd'i lugng rdng rgc yd ma sdt gifla ddy va rdng rgc.
Bdi gidi
a) Do sgi ddy khdng dan ndn tai mdi thdi dilm hai vdt mi va m2 cd cung dd ddi va
cung vdn tdc. Do mat phing nghidng mdt gdc 30° ndn khi vat m2 rod dugc mdt doan
s = h2 = 1 m (cham ddt) thi vat mi nang thdm dugc dd cao hi = s.sin30°= — = 0,5 m,
tfic la thi nang trgng trudng cua vat m2 giam, cdn eua vat mi tang.
Ngoai lite tac dung ldn hd hai vat la luc ma sat trugt. Vdn dung dinh ludt bid'n thidn CO nang khi hd vdt dich chuyin dugc mdt dd ddi s, ta cd :
Anst = -FmstS = W ' - W = (W; + W,') - (W, + W,)
43
vdi W va W la co nang (tdng ddng nang va thi nang) cua hd hai v|t tai cac vi tr ddu va cudi trong chuyin ddng.
Nhdn xet: W^ va W diu bdng kfadng vi ban ddu hd nam y ^ va ta chrai mik
thd nang bang khdng tai cac vi tri dd. Do dd :
- F ^ = w ; + w;
(m,+m2)v^ . , -Htmig cos a.s = —J——^ +mighi - m2gh2
TTiay sd ta lim dugc V = 2,94 m/s.
b) Giai bai toan bang phuong jMp ddng luc hoc
Ta phdn tfch luc va vilt phuong tnnh dinh ludt n Niu-ton cho tfing vdt (Hinh 4.3):
Tj - mjgsina - (Atmigcosa = mia
™2g - T2 = m2a
Vi ddy khdng dan ndn Ti = T2, Cdng tfing vd hai phuong trinh, ta thu dugc :
mj - m,(sina + u, cosa) a = —i i i-i i g mi + m2 Hinh 4.3
2-1(0,5 + 0 , 2 . ^ .9,8
= 4,33m/s^ .
Luc cang cua day T2 = m2 (g - a) = 2(9,8 - 4,33) = 10,9 N.
van tdc cua mdi vdt tai dilm cudi bang :
v = ^(2a&=y|2A^Ki = 2,94 m/s
Kit qua nay gidng kit qua da thu dugc 6 cdu a),
Bai 5
Mdt con Idc gdm mdt qua cdu nhd khdi lugng m treo d ddu mdt sgi day c6 chilu dai /, Ddy khdng dan va cd khdi lugng khdng dang kl. Ddu kia ciia ddy dugc gifi chat tai mdt dilm cd dinh O.
44
Thoat ddu, gifi vdt d vi tri ddy cang va ndm ngang, sau dd tha cho vdt chuyin ddng tfi do. Khi qua vi tri cdn bdng (trdn phuong thing dtog) thi ddy bi vudng vao mdt dinh tai dilm C d
khoang cdch OC = - (Hmh 4.4).
Hay md ta va phdn tfch chuyin ddng tilp theo cua con lde va xac dinh con lie se dat tdi dd cao nao so vdd vi tri can bdng. Hinh 4.4
Baigiai
Sau khi day vudng dinh, vat chuyin ddng theo mdt quy dao trdn tam C, ban
kfnh r = —. Vdt se rdi quy dao trdn tai dilm B khi thoa man dilu kidn :
mgcos a = mv a)
trong dd a la gdc chilu cfia trgng luc P ldn ban kfnh, cung bdng gdc hgp bdi vdn tdc ciia vdt tai dilm B vdd phuong ngang (Hinh 4.4). Ta cd dilu kidn (1) khi khdng cdn luc cang cua ddy (T = 0, vi thi vdt cd thi rdi khdi quy dao trdn) va thanh phdn mgcosa cua trgng luc chfnh Id luc hudng tdm.
Ddng thdi, theo dinh ludt bao toan co nang, xet tai hai vi tri ddu va cudi (A va B) ta cd ding thfic :
,1 mg.2r = mv + mgr(l + cosa) (2)
vdi quy udc chgn mfic khdng cua thi nang d vi tri cdn bang cua con lde (dilm D).
Tfi (1), suyra:
V =grcosa
Thi vdo (2), ta dugc:
(3)
vd rfit ggn:
mg,2r = — mgr cos a + mgr(l + cos a)
cosa 2 = —r— + l + cosa
45
2 hay cos oc = — (4)
Khi rdi quy dao trdn, vdt cd vdn tdc xac dinh bdi (3) va cd hudng hgp v^ phuang nam ngang gdc a xdc dinh bdi (4), Ta thdy gidng nhu trudng hgp mdt vdt dugc nem xidn gdc a vdi vdn tdc ban ddu Vg, Theo kit qua da bid't trong chujang Dgng hgc chdt diem, vdt se ldn tdd dd cao cue dai so vdi vi tri xudt phdt la
2 - 2
Vg sm a 2 g • ; ^ • •
Do dd, do cao md con lac dat dugc so vdd vi tri cdn bang la :
^ v^sin a ., , ,-. , H = +r(l + eosa) (5)
2g
Thi (3) va (4) vao (5), cudi cung ta dugc : .
" - 2 7 ' - 2 7 ^
II-DEBAI.
4.1. Hai vdt cd cfing ddng lugng nhung cd khdi lugng khac nhau, etog bat ddu chuyin ddng trdn mdt mat phing va bi dtog lai do ma sat. Hd sd ma sat la nhu nhau. Hay so sanh thdi gian chuyin ddng cua mdi vdt cho tdd khi bi dtog. A. Thdi gian chuyin ddng cua vat cd khd'i lugng ldn dai han. B. Thdi gian chuyin ddng cua vat cd khd'i lugng nhd dai han. C. Thdi gian chuyin ddng cua hai vat bang nhau. D. Thid'u dfi kidn, khdng kit luto dugc.
4.2. Mdt qua bdng cd khdi lugng m = 300 g va cham vao tudng va nay ngugc trd lai vdi cung tdc dd. Van tdc cua bdng trudc va cham la +5 m/s. Dd bid'n thien ddng lugng nao cua qua bdng sau day la dung ?
A. -1,5 kg.m/s. B. 1,5 kg.m/s. C. 3 kg.m/s. D. -3 kg,m/s,'
4.3. Ddng lugng ban ddu cua mdt vdt la pi. Sau dd, dudi tdc dung cua m6t
luc khdng ddi F, vdt cd ddng lugng la P2. Hudng va dd ldn cua Pi va
P2 cho trdn Hinh 4.5a. Trong nhiing vecto ve d Hinh 4.5b, vecto nao chi
hudng cua luc F ?
46: .
B
b)
Hinh 4.5
4.4. Mdt con chim bi nhdt va dang ddu trdn mdt thanh ngang trong ldng. Ldng dugc treo vao mdc cua mdt luc kl Id xo. Hdi sd chi tfic thod cua luc kl thay ddi nhu thi nao khi chim. bay ldn hoac bay xudng trong ldng ?
4.5. Giai thfch nguydn tac chuyin ddng cua may bay (hoac tau thuy) nhd luc keo tao bdi canh quat (hoac chan vit).
4.6. Mdt dia ddng chdt quay vdi van tdc gdc co quanh mdt true cd dinh vu6ng gdc vdi mat (fia vd di qua tam cua dia. Tim ddng lugng cua dia.
4.7. Mdt prdtdn cd khdi lugng irip = 1,67.10 kg chuyin ddng vdi van td'e
Vp = 1.10 m/s tdd va cham vao hat nhan heh (thudng ggi la hat a) dang
ndm ydn. Sau va cham, prdtdn giat Ifii vdd van tdc v'p = 6.10 m/s cdn hat a
bay vl phfa trudc vdd van tdc Va = 4.10 m/s. Tim khd'i lugng cua hat a.
Hinh 4.6
4.8. Mdt xe cat cd khd'i Ifigng M dang chuyin ddng vdd vdn td'e V trdn mat nam ngang. Ngudi ta bin mdt vidn dan cd khdi lugng m vao xe vdd vdn tdc V hgp vdi phuong ngang mdt gdc a va ngugc hudng chuyin ddng cfia xe (Hinh 4.6). " Bd qua ma sat gifia xe vd mat dudng.
a) Tim vdn tdc u cua xe sau khi dan da nam ydn trong cat.
b) Tfnh ngoai luc (hudng va dd ldn) tdc dung ldn hd dan - xe trong
thdi gian At xay ra va cham.
4.9. Mdt tdn Ifia vu tru khi bdt ddu rdi bd phdng trong gidy ddu tidn da phut ra mdt lugng khf ddt 1300 kg vdi van tdc v = 2 500 m/s.
47
a) Tim biln thidn ddng lugng cua lugng khf phut ra trong 1 s. b) Tfnh luc ddy cua tdn Ifia tai thdi dilm dd.
c) Tim luc tdng hgp (phuong, chilu, dd ldn) tac dung ldn tdn Ifia, bilt khdi
lugng ban ddu cua tdn Ifia bang 3.10 kg.
4.10*. Mdt con Ich khdi lugng m ngdi d ddu mdt tdm van cd khdi lugng M va chilu dai L ndi ndm ydn trdn mat nUdc. Ech bdt ddu nhay ldn theo hudng dgc chilu dai tdm vdn, Hdi nd phai nhay vdi vdn tdc ban ddu Vg bang bao nhidu dl vdi mdt budc nhay nd tdd dugc mep cudi tdm van, nlu gdc nhay hgp vdi phuang ngang mdt gdc a ? Bd qua luc can cua nudc,
4.11. Trdn hd cd mdt con thuyin, mui thuyin hudng thing gdc vdi bd. Luc ddu thuyin nam ydn, khoang cdch tfi mui thuyin tdi bd la 0,75 m, Mdt ngudi bdt ddu di tfi mui din dudi thuyin, Hdi mui thuyin cd cdp bd dugc khdng, nlu ehilu dai cua thuyin / = 2 m, Khdi lugng cua thuyin la M = 140 kg, cua ngudi la m = 60 kg, Bd qua ma sat gifla thuyin va nudc.
4.12. Cdu nao sau ddy la dfing ? Cdng sudt dugc xac dinh bdng A. gid tri cdng cd kha ndng thuc hidn, B. cdng thuc hidn trong don vi thdi gian, C, cdng thue hidn trdn don vi dd dai, D, tfch cua cdng va thdi gian thuc hidn cdng.
4.13. Chgn cau dfing.
Mdt ngfidi nhdc mdt vdt cd khdi Ifigng 6 kg ldn dd cao 1 m rdi mang vdt di ngang dugc mdt dd ddi 30 m. Cdng tdng cdng ma ngudi da thuc hidn la A, 1860 J, B. 1800 J. C. 180J, D,60J.
4.14. Cdng cfia mdt Ific khdng ddi dl dua mdt hdm nang khdi lugng m ldn mdt dd cao h cd phu thudc vao van tdc nang hay khdng ?
4.15. So sanh cdng tuong tog cfia cac luc F,, F2
va F3 khi dilm dat cua cdc luc nay dich chuyin cung mdt quang dudng tfi A din B (Hinh 4,7),
4.16. Mdt ngfidi ndng mdt vdt nang 300 N ldn dd cao 2 m trong 6 s, Trong khi dd, mdt thang may dfia mdt khd'i lugng nang 3 000 N ldn dd cao 10 m trong 4 s. Hay so sanh cdng, cdng sudt cua ngudi va may da thuc hidn.
48
4.17. Ngudi ta mudn ndng mdt hdm 200 kg ldn cao 7,5 m vdd vdn tdc khdng ddi trong khoang thdi gian 5 s. Cd ba ddng cO vdd cdng sudt khdc nhau : 1 kW, 3,5 kW va 6 kW. Hdi dfing ddng co nao la thfch hgp ?
4.18. Mdt thang mdy khdi Ifigng 1 tdn cd thi chiu tai tdi da la 800 kg. Khi chuyin ddng, thang may cdn chiu mdt luc can khdng ddi bang 4.10^ N. Hdi dl dua thang may ldn cao (cd tai trgng tdi da) vdi vdn tdc khdng ddi 3 m/s thi cdng sudt cua ddng co phai bang bao nhidu ?
4.19. Mdt cdn cdu ndng mdt vat nang cd khdi Ifigng m = 5 tail. a) Luc nang cua cdn cdu phai bang bao nhidu dl vat cd gia tdc khdng ddi bang 0,5 m/s . b) Cdng sudt cua cdn cdu biln ddi theo thdi gian ra sao ? c) Tfiih cdng ma cdn cdu thuc hidn dugc sau thdi gian 3 s.
4.20. Mdt d td chay trdn dutog nam ngang vdd van tdc 72 km/h. Cdng sudt cua ddng CO g '= 60 kW.
a) Tim luc phat ddng cua ddng co. b) Tfnh cdng cua luc phdt ddng khi d td chay dugc quang dudng d = 6 km.
4.21. Mdt vdt cd trgng lugng P = 10 N dat trdn mat phing ngang, Tac dung ldn vat mdt luc F = 15 N theo phuang ngang, ldn thfi nhdt trdn mat nhdn, ldn thfi hai trdn mat nhdm vdd cfing dd ddi 0,5 m, Bid't ring cdng toan phdn trong ldn thfi hai giam cdn 2/3 so vdd ldn thfi nhdt (khdng cd ma sat). Hay tim luc ma sat va hd sd ma sdt trugt gifla vdt va mat phing.
4.22. Mdt cdn cdu ndng mdt conteno 2,5 tdQ theo phuang thing dtog tfi vi tri nam ydn vdi gia tdc khdng ddi. Sau 2 s, conteno dat van tdc 4 m/s. Bd qua mgi
luc can. Ldy g = 10 m/s .
a) Xac dinh cdng sudt trung binh cua luc ndng cua cdn cdu trong thdi gian 2 s. b) Tim cdng sudt tfic thdi tai thdi dilm t = 2 s.
4.23. Mdt vdn ddng vidn cfi ta trong khi thi ddu da ndng mdt ta cd khdi lugng m = 230 kg. O ddng tac thfi nhdt, ngudi dd ndng ta ldn vai lam trgng tdm Cua ta chuyin tfi dd cao hi = 30 cm ldn dd cao h2 = 1,4 m (so vdi mat ddt) trong thdi gian x =1,2 s. O ddng tdc tid'p theo, ta dugc nang bdng len dd cao h3 = 1,8 m trong thdi gian x'= 2 s. a) Tim cdng cua trgng luc thuc hidn trong hai ddng tdc cfi ta ndi trdn.
b) Cdng sudt cua luc co bdp ma van ddng vidn da san ra trong ttog giai doan cfi ta la bao nhidu ?
4-BTVL 10(NC)-A 49
4.24. Mdt em be dd mdt qua bdng trdn mdt toa tau dang chuyin ddng. Ddng nan| cua qua bdng phu thudc vao vdn tdc cua tau nhfi thi nao ? Khi dd, ddng nang nay cd cdn la dai Ifigng vd hudng khdng ?
4.25. Mdt ngudi cheo thuyin ngugc ddng chay nhung thuyin vdn ndm ydn so vdi bd sdng. Hdi ngudi cd thue hidn edng hay khdng ? Nd'u ngudi dd ngumg cheo va dl thuyin trdi theo ddng nudc thi da cd cdng nao dugc thue hidn ? Gia thilt nudc chay vdi vdn tdc khdng ddi.
4.26. Tdc dung mdt luc F khdng ddi lam mdt vdt dich chuyin dugc mdt dd ddi s tfi trang thai nghi din luc dat van tdc v. Nd'u tang luc tac dung ldn n ldn thi vdi etog dd ddi s, van tdc cua vat da tdng thdm bao nhidu ?
A. n ldn. B. n^ ldn. C. Vn ldn. D. 2n ldn.
4.27. Mdt vat ban ddu nam ydn, sau dd vd thanh hai manh cd khdi lugng M va 2M. Bilt tdng ddng nang cua hai manh la W^. Ddng nang cua manh nhd la bao nhidu ?
3 2 3 4 4.28. Mdt d td cd khdi lugng 1000 kg dang chay vdd van tdc 30 m/s.
a) Tim ddng nang cua d td. b) Dd biln thiin ddng nang cfia d td bang bao nhidu khi nd bi ham tdd vdn tde 10 m/s ? e) Tfnh luc ham trung binh, bilt quang dudng ma d td da chay trong thdi gian ham la 80 m.
4.29. Mdt ddu tau khd'i lugng 200 tdn dang chay vdd vdn td'e 72 km/h trdn mdt doan dudng thing nam ngang. Tau ham phanh ddt ngdt va bi trugt trdn quang dutog dai 160 m trong 2 phut trudc khi dtog hin. a) Trong qua tnnh ham, ddng ndng cua tau da giam bao nhidu ? b) Lue ham tau dugc coi nhu khdng ddi. Tim luc ham va cdng sudt trung binh cua luc ham nay.
4.30. Tfnh cdc gid tri ddng nang cua
a) mdt dlectron cd khdi lugng m^ = 9,1.10"^' kg chuyin ddng trong dng phdng didn tfi cfia may thu hinh vdd vdn tdc 7.10^ m/s. b) mdt thidn thach cd khd'i Ifigng 1 tSm bay vdd vdn tdc 100 km/s.
c) Trai Ddt, dugc coi nhu mdt chdt dilm cd khd'i lugng M^ = 5,98.10^ kg chuyen ddng quanh Mat Trdi vdd td'e dd trung binh (ddi vdd hd quy chilu nhdt tam) v = 30 km/s.
50 4-BTVL 10(NC)-B
4.31*. Mdt chile xe chuyin ddng trdp mdt dutog nam ngang vdd vdn tdc v. Ta ggi khoang ham d Id quang dudng xe chay dugc tfi luc bat ddu ham tdi khi dtog han. Bang dudi ddy thi hidn chuyin ddng cua mdt d td chay trdn dutog nam ngang trong dd ghi lai nhtog khoang ham tuong tog vdi cdc vdn tdc v cua d td trudc khi bi ham vdi cfing mdt luc ham khdng ddi.
v(m/s)
d(m)
8
6
16
24
24
54
32
96
36
121,5
a) Ve dd thi bilu didn khoang ham d la ham cua van tdc v. Khoang ham cd ti Id thudn vdi vdn tdc khdng ?
b) Ve dd thi thfi hai bilu didn khoang ham la ham cua binh phuong vto td'e fy ^
va xdc nhdn ham nay cd dang d = Kv vdi K la mdt hdng sd. Tim gia tri cua K tfi dd thi. Hay cho bilt y nghia vat If va don vi eua K trong he SI.
4.32. cau nao sau day la dung ? Mdt ngudi di ldn gdc cao theo cae bac thang.
A. Thi nahg trgng trutog cua ngudi (hoac thi nang cua hd ngudi - Trai Ddt) da tang.
B. Thi ndng trgng trutog khdng ddi vi ngudi da cung cdp mdt cdng dl thdng cdng cua trgng luc.
C. Di tihh dd bid'n thidn cua thi nang trgng trutog, bat budc phai ldy mfic khdng cua thi nang d mat ddt.
D. Nlu mfic khdng cua thi nang dugc chgn d tdng cao nhdt thi khi ngudi cdng ldn cao, thi nang trgng trutog se giam ddn din cue tiiu va bang khdng.
4.33. Nudc tfi mat dap nha may thuy didn cao 80 m chay qua d'ng ddn vao tuabin vdi luu lugng 20 m^/s. Bid't hidu sudt eua tuabin X = 0,6, tim edng sudt phdt didn cfia tuabin.
4.34. Mdt vdt cd khd'i Ifigng m = 3 kg dfige dat d mdt vi tri trong trgng trutog va cd thi nang tai vi tri dd bang Wt = 500 J. Tha tu do eho vat rci tdi mat ddt,
tai dd thi nang cfia vat bang Wj = -900 J.
a) Hdi vat da rod tfi dd cao nao so vdd mat ddt ?
b) Hay xac dinh vi tri tog vdd mfic khdng cua. thi nang da chgn.
c) Tim vdn tdc cua vdt khi di qua vi tri nay.
51
4.35. Mdt vanh kim loai hinh trdn dugc treo ldn tudng vao mdt thanh dd T (Hinh 4.8). Vanh duge coi la ddng nhdt va ed khdi lugng m = 800 g vdi dutog kfnh D = 40 cm.
a) Tim the' nang trgng trutog cfia vdnh, nlu chgn mfic khdng cua thi nang tai dilm treo.
b) Xae dinh do biln thidn thi ndng khi quay
vanh mdt gdc 30° quanh dilm treo. Vanh
ludn d trong mat phing thing dfing.
4.36. Mdt ngudi nang mdt cdi thang dang ddt nam dudd ddt va dung nd vao mdt bfic tutog theo
gdc nghidng 60° so vdd mat ddt,(Hinh 4.9). Tim bid'n thidn thi nang trgng trutog eua thang. Cho bilt thang dai 5 m va cd khdi
lugng 8 kg. Ldy g = 10 m/s^.
4.37. Mdt tdm gd hinh hop cd kfch thudc nhu sau : dai L = 1,8 m, rdng / = 0,5 m, day d = 4 cm.
a) Bid't khdi lugng ridng cua gd p = 0,8 g/cm .
Tfnh khd'i lugng eua tdm gd.
b) Mdt ngudi/thg nhdc tdm gd dang d vi tri dung thing dtog va nang nd ldn tdi dd cao h = 2 m d tu the' nam ngang (Hinh 4.10). Thi nang trgng trutog cua tdm gd tang hay giam mdt lugng bang bao nhidu ?
Hinh 4.8
Hinh 4.10
4.38. Mdt khdu sung dd chod cd mdt Id xo dai 10 cm, luc bi nen chi cdn dai 4 cm thi cd thi bdn thing dtog mdt vidn dan cd khdi lugng 30 g ldn cao 6 m. Tim dd etog cua Id xo.
4.39. Mdt loai dd chod dugc thid't k l nhu sau : trong hdp kfn cd mdt ddu bup bd gdn trdn mdt Id xo da bi nen. Khi md nap hdp. Id xo bi dan va ddu bup bd bdt ngd bdt ldn theo phuong thing dfing (lam ngudi md gidt minh !). Gia sfi ban
52
ddu Id xo bi nin mdt doan / = 8 cm, hd sd etog cua Id xo k = 80 N/m va khdi lugng cua ddu bup bd m = 50 g. Tim ddng nang cua ddu bup be khi Id xo trd vl trang thai hit bid'n dang. Bd qua khdi lugng Id xo.
4.40. Mdt Id xo cd dd etog k = 10 N/m va ehilu ddi tu nhidn /g = 10 em. Treo vao nd mdt qua cdn khd'i lugng m = 100 g. Chgn mfic khdng cua thi nang tai vi trf cua qua can tog vdd trang thai Id xo ehfia bid'n dang. Tfnh thi nang tdng cdng eua hd Id xo - qua can khi qua can dugc gifl d cac vi tri sao cho Id xo cd chilu ddi bdng 5, 10, 20, 25 cm. Ldy g = 10 m/s va bd qua khdi lugng cua Id xo.
4.41. Mdt qua dan phao dang chuyin ddng thi nd vd bdn ra thanh hai manh. Cho bilt dap an nao sau day la dfing ? A. Ddng Ifidng va co nang toan phdn diu khdng bao toan. * B. Ddng lugng vd ddng nang dugc bao toan. C. Chi CO nang dugc bao toan. D. Chi ddng lugng dugc bao toan.
4.42. Tfi dd cao h, nem mdt vat khdi lugng m vdd van tdc ban ddu Vg hgp vdd phuang ngang gdc a. Vdn tdc cua vdt khi cham ddt phu thudc nhtog yd'u td nao ? A. Chi phu thudc h va m. B. Phu thudc Vg, h va a.
C. Chi phu thudc Vg vd h. D. Phu thudc ca 4 yiu td h, m, Vg va a.
4.43. Nim mdt vat khdi lugng m tfi dd cao h theo hutog thing dtog xud'ng dudd. 3
Khi cham dat, vat nay trd ldn tdd dg cao h' = — h. Bd qua mdt mat nang
lugng khi vat cham ddt. Van tdc nem ban ddu phai ed gia tri ndo dudi day ?
B # D. 7^.
4.44. Mdt con chim cd khd'i lugng 52 g dau trdn mdt edi gia treo khd'i lugng 150 g (Hinh 4.11). Chim bat ddu vd canh bay ngang vdd vdn td'e 2 m/s. Hdi gid treo chuyin ddng nhu thi ndo vd dugc ndng ldn thdm mdt dd cao bao nhidu
» 2
SO vdi vi tri ban ddu ? Ldy g = 10 m/s . Hinh 4.11
53
Hinh 4.12
4.45. 'Mdt con lac don chilu dai / dugc gifi mdt ddu cd dinh tai O. Ndng con lac ldn tdi dilm A d dd cao h so vdd vi tri cdn bang rdi tha tit do, Sau khi qua vi tri cdn bdng, ddy vutog vao mdt dinh d dilm B cd dd cao h' > h (Hinh 4,12), Hdi con Idc se tid'p tue chuyin ddng va dtog d dd cao bang bao nhidu ? Bd qua mgi luc can.
4.46. Dung mdt luc F = 30 N ed phuang thing dtog dl dua mdt vdt nang P = 10 N ldn
t
cao. Hdi edng eua luc F cd gia tri bang bao nhidu va da chuyin thanh nhitng dang nang lugng nao khi vat ldn tdd dd cao h = 5 m ?
4.47. Nudc di vao tuabin vdd van tdc Vi = 6 m/s va di ra vdd van tdc V2 = 2 m/s 6 -3
dd cao thdp hon 1,5 m. Luu lugng nudc la 3 m /s. Hidu sudt cua tuabin la
3C= 0,8. Tfnh cdng sudt cd fch cua tuabin. ,
4.48. Nim ngang mdt hdn da khd'i lugng 2 kg vdi van td'e 5 m/s tfi tdng gdc cd d6 cao 12 m so vdd ddt. Bd qua luc can cua khdng khf.
a) Xac dinh co nang cua vat d thdi dilm nem. b) Khi vat rod tdd dd cao cdch mat ddt 2 m, vdn td'e cua nd bdng bao nhidu ?
4.49. Mdt ngudi nhay du cd khdi lugng m = 60 kg, tha minh rod tfi mdt may bay true thang dfing ydn d dd cao 1000 m. Khi tilp ddt, vdn tdc cua ngfidi la V = 8 m/s. Tfnh cdng do luc can cfia khdng khf thuc hidn trong qud trinh red sau khi dfi md. Gia thilt dfi md ngay sau khi ngudi rdi khdi may bay va liic can cua khdng khf ldn ngudi va dfi la khdng ddi.
4.50. Mdt hdn da cd khdi lugng 250 g red tu do va cd ddng nang bang 12,5 J khi cham ddt. Bd qua luc can cua khdng khf.
a) Tim vdn tdc cfia hdn da khi cham ddt.
b) Nd dfige tha rod tfi dd cao bao nhidu ? c) Ddt mim ndn da lun sdu dugc 8 cm vao trong ddt. Tim luc can trung binh cua ddt.
54
///////M////////////////////////////A'/'/////A'//M//////
Hinh 4.13
4.51. Mdt vat bat ddu chuyin ddng trdn mdt mat ddc cd hinh dang bdt ki tfi dd cao 1 m so vdd mat ndm ngang (Hinh 4.13). Tun van tde cua vat khi nd tdd chan ddc. Bd qua ma sat gifla vdt va mat ddc.
4.52. Mdt bua may khdi lugng 400 kg ed trgng tam nam each mat ddt 3 m. a) Xac dinh thi nang trgng trutog cua bfia, nlu chgn gdc toa dd d mat ddt.
b) Khi bua ddng cgc, trgng tdm cua nd ha xudng tdd dd cao 0,8 m. Tun do giam thi nang cua bfia va van tdc cua bua khi cham cgc, bid't rang bfia dugc tha tu do tfi dd cao ban ddu. Bd qua mgi luc can.
4.53. Mdt vat trugt khdng ma sat trdn mdt ranh cd dang nhfi Hinh 4.14, tfi dd cao h so vdd mat nam ngang va khdng ed vdn td'e ban ddu, Hdi dd cao h ft nhdt phai bang bao nhidu dl vdt khdng rdi khdi quy dao tai dilm B cua vdng trdn ban kfnh r ?
4.54. Mdt xe lan cd thi chuyin ddng trdn mdt dutog ranh cd dang nhu Hinh 4.15. Chilu cao hai dinh so
vdd mat ddt la h^ = hg = 0,52 m va chilu cao dilm C la h^ = 0,30 m. Xe dugc tha tu do tfi A.
a) Bd qua ma sat. Hay xdc dinh cac vdn tdc tai cac dilm B, C, D, E.
b) Xe cd bi rdi khdi vdng trdn d dinh C hay khdng ? Tai sao ? Sau khi tdi E, xe tilp tuc chuyin ddng nhu thi nao ?
4.55. Mdt vdt khd'i Ifigng mi Va cham true didn vdd vdt m2 = - j - dang ndm ydn.
Trudc va cham, vat 1 cd van tdc la v. Sau va cham hoan toan khdng dan hdi, ca hai vdt chuyin ddng vdd cfing vdn tdc v'. Ti sd gifla tdng ddng ndng cua hai vdt trudc vd sau va cham cd gia tri ndo dudd ddy ?
Hinh 4.14
55
^ • 5 2 r v ^
v V y
^ • 4 i T v ^
v ^ y
4.56. Mdt sd qua cdu ran va hoto toan ddng nhdt dugc treo thanh day sat nhau bang nhiing sgi ddy dai bang nhau (Hinh 4.16). Khoang each gifia hai qua edu eanh nhau la rdt nhd (kfch thudc mdi qua cdu la khdng dang kl). Dilu gi se xay ra khi:
a) Keo qua cdu d ngoai etog Idch mdt Hinh 4.16 gdc nao dd rdi tha cho va cham vao qua cdu tid'p theo ?
b) Keo lech ttog nhdm 2 qua, 3 qua... va tha tu do chtog ddng thdi ? Bd qua mgi ma sat va mdt mat nang lugng.
4.57. Bdn mdt vidn dan cd khd'i lugng 10 g vao mdt mdu gd ed khd'i lugng 390 g dat trdn mdt mat phing nhdn. Dan mac vao gd vd cung chuyin ddng Vdi van tdc 10 m/s.
a) Tim van tdc cua dan luc bin.
b) Tfnh lugng ddng nang eua dan da chuyin sang dang kfadc.
4.58. Mdt bua may cd khd'i lugng M = 400 kg tha tu do tfi dd cao 5 m xudng, ddng vao mdt cgc cd khdi lugng m = 100 kg trdn mat ddt lam cgc Ito sdu xudng ddt 5 em. Tim luc can cua ddt (dugc coi la khdng ddi).
4.59. Mdt xe khd'i lugng mi = 1,5 kg chuyin ddng vdd vdn tdc Vi = 0,5 m/s din va cham vao mdt xe khdc khd'i lugng m2 = 2,5 kg dang chuyin ddng ciing chilu. Sau va cham, hai xe dfnh vao nhau va cfing chuyin ddng vdd vdn tdc V = 0,3 m/s. Tim vdn tde ban ddu cua xe thfi 2 va dd giam ddng ndng cua hd hai xe. , '
4.60. Hai vdt cd khd'i lugng m va 2m cd ddng lugng tuong iing la p va —, chuyin
ddng theo cung phuong din va cham vdd nhau. Sau va cham, hai vdt trao ddi
56
ddng lugng cho nhau, vdt nay cd ddng lugng Ific trudc cua vdt kia. Tim lugng ddng nang tidu hao sau va cham da chuyin thanh nhidt.
4.61. Chgn cdu dtog.
Bdn kfnh cua Trai Ddt la Rp, cua Mat Trang la Rj. Nlu khdi lugng ridng cua ca hai la nhu nhau thi ti sd cfia gia tdc trgng trutog trdn bl mat Trai Ddt va bl mat Mat Trang la :
A. | a . B. rv ^2 Ar. 3
R f RD
Rxy
4.62. Thidn Vuong tinh cd khd'i lugng Ito hon khdi lugng cua Trai Ddt 15 ldn va dutog kfnh thi Ito hon 4 ldn. Gia td'e trgng trutog tren bl mat Thien Vuong tinh gdn dfing bang gid tri nao sau ddy ?
A. 5 m/s^. B. 9 m/s^. C. 36 m/s^. D. 150 m/s^.
4.63. Mdt vd tinh nhan tao chuyin ddng diu theo quy dao trdn quanh Trdi Ddt d dd
cao h = 670 km. Tmh tdc dd dai cua vd tinh. Cho R^ = 6 370 km.
4.64. Khi ha thdp quy dao chuyin ddng va di vao ldp khf quyln tren cao, vdn td'e cua vd tinh nhdn tao se thay ddi nhu thi nao ?
4.65. Ngoai chuyin ddng trdn quy dao quanh Mat Trdi, Trdi Ddt tu quay diu quanh true cfia nd hutog dgc theo hai cue Bdc va Nam (cdn ggi la chuyin
. ddng ridng). Gdn hd quy chid'u vdi true quay cua Trdi Ddt. Hay xdc dinh :
a) Chu ki cua chuyin ddng ridng tfnh bang gidy.
b) Tdc dd dai cua mdt dilm trdn xfeh dao cua Trdi Ddt. c) Tdc dd dai cua hai cue cua Trai Ddt.
4.66. Mdt don vi thutog dugt dfing dl do khoang each gifia eac thidn thi trong vfl tru (vd etog Ito so vdi nhtog khoang each gifla cac vdt thi trdn Trai Ddt), ggi la don vi thidn van (kf hidu U.A), dugc dinh nghia 1 U.A = 150.10 km la khoang cdch trung binh gifla Trdi Da't va Mat Trdi. Hay dp dung dl tfnh :
a) Khoang each Mat Trdi - Mdc tinh bang km bilt Mdc tmh each Mat Trdi 5,2U.A.
b) Khoang cdch Mat Trdi - Hoa tinh bang U.A, bilt Hoa tinh each Mat Trdi
228.10^ km.
57
4.67*. Mdt ngudi 60 kg dfing trdn mdt ehilc thuyin nam gdn bd mdt hi nudc. Chi vdi mdt sgi ddy thiing, ngudi dd da xac dinh dugc gdn dung khdi lugng cua chid'c thuyin.
Hay du doan va giai thfch each lam eua ngudi dd.
4.68. Cho cac dung cu sau (Hinh 4.17): - Mdt mat phing nghieng.
- Mdt khd'i gd cd khdi lugng m da bilt.
- Mdt thudc cd do chia tdi mm.
- Mdt ddng hd cd kim giay. Hay trinh bay va giai thfch mdt phuang an thf nghidm dl xdc dinh nhiet lugng toa ra khi khdi gd trugt trdn mat nghidng (khdng cd van tdc ban ddu)
Hinh 4.17
4.69. Cho cac dung cu sau (Hinh 4.18):
- Mdt vidn bi sdt dac, dutog kfnh khoang 2 - 3 em.
- Mdt vidn bi sap dac, to bang bi sdt,
khd'i lugng ridng khoang 1,2 g/cm .
- Mdt thudc do cd dd chia tdd mm.
- Mdt gia dd va day treo. Hay trinh bay va giai thfch mdt phuang an thf nghiem dl xae dinh tl Id tidu hao CO nang trong va cham khdng dan hdi cua hai vidn bi
Hinh 4.18
58
CO HOC CHAT LUU
I - B A I TAP VIDU
Bai 1
Tfnh dp lue tdc dung ldn mat kfnh cfia sd nhd cua mdt tau ngdm d dd sau 1000 m. Cita sd hinh trdn ban kfnh 15 cm. Bid't khd'i lugng ridng cua nude la 1,0.10^ kg/m^va dp sudt khf quyln p^ = 1,01.10^ N/m^.
Bdi gidi
Ap sudt d dd sau 1 000 m bang : p = Pa + Pgh
= 1,01.10^ + (1,0.10^).(9,8.10^) N/m^
= 9,9.10^ N/m^.
' Do kfch thudc cfia sd nhd so vdi dd sau ndn ta coi dp sudt tai mgi dilm eua cfia sd la bang nhau va bang dp sudt cua nudc d dd sau 1000 m.
Ap lue ldn cfia sd bdng : F = pS = (9,9.10^).(7i. 0,15^)
F = 7,0.10^ N.
Bai 2
Mdt binh dfing mdt chdt ldng cd khdi lugng ridng la p. Thanh binh cd mdt Id nhd (Hinh 5.1). Phia trdn mat thoang cua chdt long cd dp sudt la p, Tfnh vdn tdc cua chdt long chay ra khdi Id, Ggi khoang each tfi mat thoang din Id la h,
Bdi gidi
Theo ddu bai, tilt didn cua Id la nhd sg vdd tilt
didn cua mat thoang (A2 « Ai), Nhu thi, chilu cao cua mure chdt long coi nhu
khdng ddi, vdn tdc cua chdt long d mat thoang bang khdng, Ap dung dinh luat BIc-nu-li cho hai dilm d mat thodng va d tilt didn Id, ta cd :
p — • _ - _ - _ -
rs^^
J
Ai r L-J
h - _ - _ - _ - j
, - - - V r
-;
r -
'JS
,----
r -
_Pa
A2
Hinh 5.1
59
1 2 Pa+^PV =P + Pgh (1)
Ta thdm vao vl phai sd hang pgh vi mat thoang ndm cao hon mfic Id mdt doan bang h, Tfi dd ta cd :
v= / ? ( P _ P ^ . 2 g h (2)
Trutog hgp binh hd, tfic la p = p^, ta cd :
v= V2gh nghia la, van tdc cua ddng nudc thodt khdi Id each mat thoang mdt doan bang h dung bang vto tdc mdt vat rod tu do tur do cao h so vdi Id xudng din Id,
I I - D ^ B A I
5.1. vat nao dudd day gdy ra dp sudt Ito nhdt xudng san nam ngang khi ddt nam ydn trdn san ?
A. Hinh hop vudng nang 25 N, ed canh 15 em. '
B. Hinh tru nang 25 N, cd ban kfnh day 10 cm.
C. Hinh hdp vudng nang 25 N, ed eanh 10 cm.
D. Hinh tru nang 25 N, cd bdn kfnh day 15 cm.
5.2. Tfnh khdi lugng cua mdt qua cdu sdt ed dutog kfnh 3,0 cm.
5.3. Mdt khd'i hinh hdp lap phuong ddng chdt cd canh 5,0 cm, khd'i lugng 1,31 kg. Hdi khd'i dd lam bang chdt gi ? (Tham khao Bdng khdi lugng rieng cua mgt so chdt trong SGK).
5.4. Mdt ngudi 50 kg dfing thang bang trdn gdt mdt d l giay. Grid sfi tid't didn dl giay hinh trdn, bdng phang, ed ban kfnh 2 cm. Tfnh dp sudt cua ngucd dat ldn san.
5.5. Tinh dp sudt thuy tinh d day mdt hd sdu 30 m.
5.6. Tilt didn eua pit-tdng nhd trong mdt cai kfch thuy luc bang 3 cm , cua pit-tdng Ito bang 200 em . Hdi cdn mdt lue bang bao nhidu tdc dung ldn pit-tdng nhd dl du ndng mgt d td nang 15 000 N ldn ?
5.7. Tilt dien ngang tai mdt vi tri cua mdt dng nude ndm ngang bdng 10 cm , tai 2 mdt vi tri thfi hai bang 5 cm . Van tdc nudc tai vi tri ddu la 5 m/s, dp sudt tai
vi tri sau bang 2.10^ N/m^. Hay tfnh :
60
a) van tdc nudc tai vi tri thfi hai. b) Ap sudt nudc tai vi tri ddu.
c) Luu lugng nudc di qua mdt tilt didn dng (tfnh ra m^/min).
5.8. Mdt binh hinh tru dutog kfnh 0,1 m ; cao 0,20 m. Mat day binh cd khoet
mdt Id tilt didn 1 cm . Ngudi ta cho nude chay qua binh vdi luu lugng
1,4,10 " " m^/s. Hay xac dinh :
a) Vdn tdc cua ddng nude tai mat thodng cua binh vd tai mat Id, b) Chilu cao cua muc nude dugc dua vao trong binh. Chilu cao cua binh cd du dl binh ehfia lugng nudc sad eho nudc chay vdi luu lugng nhu vdy khdng ?
5.9. Nha bdc hgc Pa-xcan (Blaise Pascal) da lam mdt khf dp k l kilu Td-ri-xe-U (Torricelli) dfing rugu vang lam ehdt Idifg thay eho thuy ngan. Hdi chilu cao h cua cdt rugu vang la bao nhidu tog vdd ap sudt khf quyln d dilu kidn tidu chudn, tfic la 1,013.10^ Pa ? Bilt khdi lugng ridng cua rugu vang la 0,984.10^ kg/ml
5.10. Ap sudt khf quyln d dilu kidn tidu chudn bdng 1,013.10^ Pa. Mdt con bao dd'n gdn, chilu cao cua cdt thuy ngdn trdn phong vu bilu (khi ap kl) giam di 20 mm so vdi luc binh thutog. Ap sudt khf quyln luc dd bang bao nhidu ? Cho bilt khdi lugng ridng cua thuy ngdn la 13,59 g/cm^.
5.11*. Trong mdt dng ddn kfn cd mdt luu lugng nudc khdng ddi. Tai mdt dilm cua dng cd dutog kfnh tilt didn ngang 8,0 cm, dp sudt la 2,5.lO" Pa. Tai mdt dilm khdc cao hon dilm nay 0,5 m cd dutog kfnh tilt didn ngang 4,0 em, dp sudt la 1,5. lO"* Pa. Ldy g = lOm/s . a) Xac dinh vdn tdc ddng nudc tai hai vi tri trdn. b) Tuih luu lugng cua ddng nudc trong dng.
5.12. Mdt mdy bay cd khd'i lugng 16 000 kg va mdi eanh cd didn tfch bang 40 m . Khi may bay bay theo phucmg nam ngang, dp sudt tac dung ldn phfa trdn canh bang 7,0.10 Pa. Tfnh dp sudt tac dung lin phfa dudi cdnh. ^ ^/•^~* ~
5.13. Ong Pi-td dung dd xae dinh vdn tdc cua ddng khdng khf bdng cdch do dd chdnh gifla dp sudt toan phdn vd dp sudt finh | | - - J ^ cua ddng khdng khf (Hinh 5.2). Nd'u d'ng ^ ^ chfl U ehfia thuy ngdn (khd'i Ifigng ridng Hinh 5.2
61
13,6.10^ kg/m^) cd do chdnh gifia hai cdt la Ah = 5 cm, hay tfnh vdn tdc •3
ddng khdng khf (khd'i lugng ridng cua khdng khf bang 1,25 kg/m ).-
5.14*. Ong xiphdng la mdt dung cu don gian dung dl dua chdt long tfi mdt nod sang mdt noi khae ma khdng tdn cdng. Hinh 5.3 cho ta mdt vf du vl d'ng xiphdng. Nudc trong binh dugc rut ra nhd d'ng xiphdng. Luc ddu ddng chay phai dugc mdi bang each hut chdn khdng trong d'ng (tuong tu d'ng mut cua cdc hop dd udng). Sau dd nudc tu ddng chay qua d'ng. Hay chtog rninh rang vdn tdc ddng chay ra khdi
dng cd van tde v = yl2gh, trong dd h la
-f-
'.-Z
-
h
Hinh 5.3
dd chenh gifla muc nudc trong binh va midng dng.
5.15*. Nam 1654, nha phdt minh bom khdng khf 6t-t6-vdn Ghd-rich (Dfic) da hut chdn khdng hai ban cdu bang ddng thau up sdt nhau. Ong eho 8 con ngua chia thanh hai tdp keo hai nfia bdn cdu theo hai phfa dd'i didn. Tdm con ngua khoe da khdng thi keo tach dugc hai nfia ban cdu ra. Thf nghidm dugc lam vdi su chtog kiln cua Hdi ddng thanh phd Mac-do-budc. Do do cdn cd ten ggi la bdn edu Mac-do-bude. Ngudi ta cd thi tfnh dugc dp luc
ldn nfia ban cdu bang cdng thfic tir^(Tp^-p), trong dd r la ban kfnh qua
cdu, Pa la dp sudt khf quyln bdn ngoai, p la dp sudt khdng khf bdn trong
qua cdu (vi khdng thi rut hit khdng khi dl ed dp sud't bdn trong qua cdu
bang khdng), p «; p^. Gia sfi p = 0,1 p^ ; r = 0,3 m. Hay tfnh lue dfi dl tach
hai nfia ban cdu ra.
5.16. Mdt d'ng Pi-td trdn may bay dang bay d tdm cao, do dugc dd chdnh dp sudt gifla hai nhdnh la 180 Pa. Hdi vdn tde may bay lue dd bang bao nhidu ? Cho bid't khd'i lugng ridng cua khf quyln d dd cao dd la 0,031 kg/m^.
5.17. Mud'n xac dinh luu lugng nude di qua tilt didn ngang cua dng ddng, ngudi ta
dung dng Ven-tu-ri dl do hidu dp sudt tinh Ap = p2 - Pi gitta hai tilt didn
ngang Si va S2. Bilt Si = 0,2'm^ ; S2 = 0,1 m^ ; Ap = 1 500 N/m^ ; hay tfnh luu lugng the tfch eua nudc trong d'ng.
62
5.18. Chgn cdu dung.
Dat mdt dng thing, hai ddu hd, theo phuong thing dtog trdn mdt ddng nudc chay. Ap sudt khf quyln la p^. Muc nudc trong d'ng ddng ldn din dilm C. Dilm A' nam trdn cung mat ngang vdi dilm A va cd cung van td'e v cua ddng chay (Hinh 5.4). Ap sudt tinh tai A' bang :
A. pg(AC) + Pa. B.p^.
C. pg(AC - BC) + Pa. D. pg(BC) + Pa.
5.19. Chgn cau dung.
Dl do. van tdc ddng chay eua mdt eon sdng, ngudi ta dung mdt dng thuy tinh hai ddu hd, mdt ddu dugc udn cong hinh thudc thg. Ong dugc dat sao cho tid't didn ddu A vudng gdc Vdd ddng chay (Hinh 5.5). Dai lugng pgh bdng
A. dp sudt khf quyln.
B. dp sudt tinh tai dilm B trong dng. C. ap sudt ddng tai A. D. dp sudt toan phdn eua ddng chay.
./d. .A^
Hinh 5.4
B h
- ^h - -
Hinh 5.5
5.20. Chgn cdu dung.
Tfi mdt vdi nfidc chay xud'ng thanh ddng. Tilt
didn ddng chay tai A la SA, tai B la Sg = ^ K. '^'SA - ^
'^S,
Hinh 5.6
(Hinh 5.6). Htog nudc vao mdt chdu thi A. dat chdu tai A htog dugc nhanh hon tai B hai ldn.
B. dat chau tai A htog dugc nhilu hon nhumg tai B lai htog dugc nhanh hon.
C. dat chau tai B htog dugc nhanh hon tai A hai ldn.
D. dat chdu d bdt ki dilm ndo trdn ddng chay trong cung thdi gian, diu htog dugc lugng nudc nhu nhau.
63
5.21. Cho cac dung cu saU (Hinh 5.7):
- Mdt dng thuy tinh hinh chfi U hd hai ddu.
- Mdt thudc cd dd chia nhd nhdt dd'n mm.
- Mdt Ig nudc.
-Mdt Ig ddu.
Hay trinh bay va giai thfch mdt phuang an thf nghiem di xae djnh gdn dung khdi lugng ridng cua ddu. Hinh 5.7
5.22. Cho cac dung cu sau (Hinh 5.8a): .
- Mdt cdc hinh tru.
- Mdt thudc day cd dd chia nhd nhdt din mm.
- Mdt ddng hd bdm giay hidn sd.
Hay tnnh bay va giai thfch mdt phuong an thf nghidm dl xac dinh gdn dung van tdc chay cua nudc khi ra khdi vdi cua may nudc trong nha (Hinh 5.8b).
a) Hinh 5.8
b)
64
CHAT KHI mmmmmmmmmmmmi^mm^^m^m^^
I-BAITAPVIDU
Ball
Mdt vat cd didn tich bl mat la 20 cm^ dugc ma mdt ldp bac day 1 ^m. Cd bao nhidu nguydn tfi bae ehfia trong ldp bac dd ?
Bdi gidi
Khdi lugng ridng cua bac la 10,5 g/cm ; khd'i lugng mol cua bac la 108 g/mol. vay sd nguydn tfi cd trong 1 g bac la :
6,023.10 «c'7/:oin20 . ^^^ -r--—=55,768.10 nguyen tu. lOo
Ldp bac ma cd thi tfch la : 20 cm^. 0,000 1 cm = 0,002 cm^. Khd'i lugng cua ldp bac nay la : 0,002.10,5 = 0,021 g. Vay sd nguydn tfi bae cd trong ldp bac ma la :
55,768.10^°. 0,021 = 1,17.10 ° nguydn tfi bac.
Bai 2
Nung ndng mdt lugng khdng khf trong dilu kidn ding dp, ngfidi ta tha'y nhidt dd cua nd tang thdm 3 K, cdn thi tfch tang thdm 1% thi tich ban ddu. Hay tinh nhidt dd ban ddu cua lugng khdng khf.
Bdi gidi
Ggi Vl, Tl vd V2, T2 la thi tfch; nhidt do mydt dd'i cua lugng khdng khi d trang thdi ddu vd cud'i; dp dung dinh luat Gay Luy-xdc ta cd thi vilt:
^ = ^ (1) • ^2 1
Tiln htoh nhtog phep biln ddi ti Id thfic, ta cd :
5-BTVL 10(NC)-A 65
^ = ^ (3)
Theo dl bai thi: ^^ ~ ^^ = 0,01 va T2 - Ti = 3 K. Do dd phuong trinh (3) trd
thanh : ^ = 0,01 hay : Tj = - ^ = 300 K. l l U,U1
Dl chuyin ddi tfi nhidt giai Ken-vin sang nhidt giai Xen-xi-fit, ta dp dung he thfie :
T = t + 273 hoac t = T -273
vay: ti = T i - 2 7 3 = 30D-273 = 27°C.
Bai 3
Mdt qua cdu cd thi tfch V = 0,1 m dugc lam bang gid'y mdng. Qua cdu co mdt Id hd nhd ben dudd va qua Id hd nay ngudi ta cd thi dd't ndng khdng khf trong qua cdu din nhidt do T2 = 340 K, cdn nhidt dd cua khdng khf xung quanln la
Tl = 290 K. Ap sudt cua khdng khf ben trong va bdn ngoai qua cdu bang nhau va cd gia tri la p = 100 kPa.
Hdi vd bang gidy eua qua cdu phai cd khd'i lugng nhu thi nao dl qua cdu co thi bay len ? Coi khdng khf nhu mdt ehdt khf thudn nhdt cd khdi lugng ridng bang 1,29 kg/m^ d dilu kidn chudn (pg = 1,013.10^ Pa; Tg = 273 K).
Bdi gidi
Qua cdu bay ldn nhd luc ddy Ae-si-met, do Ito cua luc nay bdng trgng lugng cua khd'i khdng khf bdn ngoai bi chid'm chd. Ggi pi va P2 la khdi lugng ridng cua khdng khf d 290 K va d 340 K. ,
Nhu vdy, d day luc ddy Ae-si-met F^ cd dd Ito la F^ = PiVg, trong dd V la thi tfch cua qua cdu va g la gia tde trgng trutog.
Mat khac, tfi phuong trinh Cla-pd-rdn - Men-dd-ld-ep, ta suy ra p = — = — . V RT
vay dilu kidn dl qua cdu cd thi bay ldn dugc la : p2Vg + mg < piVg hay
m < piV - P2V, trong dd m la khdi lugng cua vd bdng gidy cua qua edu.
66 5-BtVU 10(NC)-B
Bdygidtaphaitfnhpi vapjtfigidttidachola: pg= ^ ^ = 1,29kg/m^ Tavilt: RTn
Pl p|a/RTi p Tg , p.Tg — = ^ . ' = —-Tf- ; vay Pl = P o - ^ Po POI^/RTQ PO Tl Pg.Ti
Lam tuong tu, ta ed : p2 = pg pTg
P0T2
Thay Pi va P2 vao dilu kidn cua m, ta ed
m < V p g pTg
Po vTi T2 ; = V p g P ^
Po
Thay sd ta duge : rti < 0,1.1,29 ^ 10^ 273
1,013.10^
50
340.290
T2-Ti^
V TiT2< J
= 17,6.10 ^kg.
Vdy khdi Ifigng vd qua edu khdng dugc vugt qua gia tri 0,017 6 kg.
II - DE BAI
6.1. Tha mdt hat mudi an vao mdt binh nudc, sau mdt thdi gian cac phan tfi mudi phdn bd diu trong toan thi tich nudc. Hay giai thfch hidn tugng.
6.2. Tai sao trong cha't long, su khulch tan didn ra cham hon rdt nhilu so vdi trong cha't khf ?
6.3. Chgn cau tra ldi ddy du trong cac cau sau day. Hai chdt khf ed thi trdn iSn vao nhau tao ndn mdt hdn hgp khf ddng diu la vi : A. Cdc phdn tfi khf chuyin ddng nhidt. B. Hai chdt khf da cho khdng cd phan tog hod hgc vdi nhau. C. Gifla cdc phdn tfi khi cd khoang trdng. D. Gdm ca ba cdu trdn.
6.4. Ngfidi ta ghi chep rang tai cfia sdng A-ma-ddn da tim thdy mdt thdi vang thidn nhidn cd khdi lugng 62,3 kg. Hdi lugng chd't cua thdi vang nay ?
6.5. Tim cdu sai trong cac edu sau ddy :
Sd A-vd-ga-drd la
A. sd phdn tfi (hay nguydn tfi) cd trong 22,4 Kt khf d dilu kidn chudn (0°C, 1 atm).
B. sd phan tfi (hay nguydn tfi) cd trong 1 mol khf.
C. sd phan tfi (hay nguydn tfi) ed trong 1 don vi khdi lugng khi.
D. sd nguydn tfi cd trong 12 g cacbon 12.
67
6.6. Cho bilt khdi lugng ridng cfia khdng khf d dilu kidn chudn la 1,29 kg/m. Coi khdng khf nhu mdt chdt khf thudn nhdt, hay tfnh khdi lugng mol cua khdng khi.
6.7*. Trutog hgp nao sau ddy cd lugng ehdt nhilu nhdt ?
A. 5 cm bac. 3
B. 1 em vang. 3
C. 10 cm nhdm. D. 20 cm^ graphit. (Xem Bdng khdi luctng rieng cua mgt sd chdt b phu luc 2 SGK Vdt If 10 nang cao).
6i8. Hoa tan ddu 0,003 g mudi an NaCl vao trong 10 lft nudc. Ndu ta muc ra 5 cm nudc dd thi cd bao nhieu phdn tfi mudi trong dd ?
6.9.
Hinh 6.1
Cho bilt dutog kfnh phdn tfi nude la 2,69.10"^° m. Nlu ta xip cac phdn tut nudc cd trong 1 mg nudc nam canh nhau theo mdt dutog thing thi dutog thing nay dai bao nhidu ? Hay so sanh dd dai nay vdd dutog xfeh dao cua Trai Da't (dai 4.10' m).
6.10. Mdt lugng khdng khf cd thi tfch 240 cm^
ehfia trong mdt xilanh cd pit-tdng ddng kfn,
didn tich cua pit-tdng la 24 cm (Hinh 6.1).
Ap sudt cua khdng khf trong xilanh bang dp sudt ngoai la 100 kPa. Cdn mdt luc bang bao nhidu dl dich chuyin pit-tdng sang trai 2 em ? Sang phai 2 cm ? Bd qua ma sat gifla pit-tdng va thanh xilanh. Coi cdc qua trinh xay ra la ding nhidt.
6.11*. Mdt binh hinh tru kfn hai ddu, cd dd cao la h, dugc dat nam ngang, ben trong cd mdt pit-tdng cd thi dich chuyin khdng ma sat trong binh (Hinh 6.2). Lfic ddu pit-tdng dugc gifi cd dinh d chfnh gifla binh. Hai bdn pit-tdng diu cd khf etog loai nhung dp sudt khf bdn trdi Ito gdp n ldn dp sudt khf bdn phai.
Nlu bdy gid ta dl pit-tdng tu do thi pit-tdng dich chuyin nhu thi nao ? Nhidt dd cua hd khdng ddi.
/?ff////r777
> ' . : ' • ' • . ' . ' . : ' . ' . : .- !.• •»• .-.• \--'•.'•%^ :.'•-'•
l/j/y/7//yjffA
' • • . . • . ' - 1
h Hinh 6.2
68
6.12. Trdn dd thi p - V (Hinh 6.3) ve hai dutog ding nhidt cua cung mdt khd'i Ifigng khf. Dutog ndo tog vdd nhidt dd cao hon ?
O
Hinh 6.3
6.13. Trdn dd thi V - T (Hinh 6.4) ve hai dutog ding dp cua cung mdt lugng khf. Dutog nao tog vdd dp sudt cao hon ?
6.14. Trdn dd thi p - T (Hinh 6.5) ve hai dutog dang tfch cua cung mdt lugng khf. Dutog nao tog vdi thi tich Ito hon ?
Hinh 6.4
O Hinh 6.5
6.15. Mdt lugng khdng khf ehfia trong nidt qua edu dan hdi cd thi tfch 2,5 lft, d nhidt dd 20°C va dp sua't 99,75 kPa. Khi nhung qua cdu vao nudc cd nhidt dd 5°C thi dp sud't cua khdng khf trong dd la 2.10^ Pa. Hdi thi tfch cua qiia cdu giam di bao nhidu ?
6.16. Cd mdt lugng khf dung trong binh. Hdi ap sudt cua khf se biln ddi thi nao . nd'u thi tfch cua binh tang gdp ba ldn, cdn nhidt dd thi giam di mdt nfia ?
A. Ap sudt khdng ddi. B. Ap sudt tang gdp ddi.
C. Ap sudt tang gap bdn ldn, D. Ap sudt giam di sau ldn.
6.17*. Mdt van ddng vidn leo nui cdn hft vao 2 g khdng khf d dilu kidn chudn trong mdi nhip thd. Hdi khi d trdn nui cao, tai dd khdng khf cd dp sudt la 79,8 kPa va nhidt dd - 13°C thi thi tich khdng khf ma ngudd d'y phai hit vao trong mdi nhip thd bang bao nhidu ? Bid't rang khd'i lugng ridng cua khdng khf d dilu kidn chudn la 1,29 kg/m va gia sfi khd'i lugng khdng khf hft vao trong mdi nhip thd ludn ludn nhu nhau.
6.18. Chgn cdu tra ldi ddy du. Ap sudt cua chdt khf tdc dung ldn thanh binh phu thudc vao A. thi tich cfia binh, khd'i Ifigng khf vd nhidt dd.
69
B. thi tich cua binh, loai chdt khf va nhidt dd. C. loai chdt khf, khdi lugng khf va nhidt dd. D. the tfch cua binh, so mol khf va nhidt dd.
6.19. d dd cao 10 km each mat ddt thi dp sudt khdng khf vao khoang 30,6 kPa, cdn nhidt do la 230 K. Tfnh khd'i lugng rieng va mdt dd phdn tfi cfia khdng khf tai dd cao dd ? Coi khdng khf nhu mdt khf thudn nhdt cd khdi lugng mol la 28,8 g/mol.
6.20. C) thod ki nen cua mdt ddng co dd't trong bdn ki, nhidt dd cfia hdn hgp khf tdng tfi 47°C dd'n 367°C, cdn thi tfch cua khf giam tfi 1,8 lft dd'n 0,3 Ht. Hdi dp sudt cua khf d cud'i ki nen, nd'u ap sudt cua khf luc bat ddu nen la 100 kPa ? Coi hdn hgp khf nhu mdt chdt khf thudn nhdt.
6.21. Cho bdn binh cd cung dung tfch va etog nhidt dd dung cac khf khdc nhau. Khf d binh nao cd dp sudt Ito nhdt ? A. Binh 1 dung 4 g khf hidrd. B. Binh 2 dung 22 g khf cacbonic. C. Binh 3 dung 7 g khf nito. D. Binh 4 dung 4 g khf dxi.
6.22. Tfnh khd'i lUgng khdng khf thoat ra khdi mdt can phdng cd thi tfch V = 60 m^ khi ta tang nhidt dd cua phdng tfi Tj = 280 K din T2 = 300 K d dp sudt chudn. Cho bid't khd'i lugng rieng cua khdng khf d dilu kidn chudn la 1,29 kg/ml
6.23. Mdt binh ddy khf dugc ddng kfn bang mdt nut cd tilt didn 2,5 cm^. Hdi phai dun ndng khf din nhidt dd nao de nut cd thi bdt ra nd'u luc ma sat gifi nut bang 12 N ? Bilt rang dp sudt ban ddu cua khdng khf trong binh va d ngoai bang nhau va bdng 100 kPa, cdn nhidt do ban ddu cua binh la -3°C,
6.24*. Mdt lugng khf da thuc hien lidn tilp bdn P4 qua trinh dugc bilu didn trdn dd thi p - T (Hinh 6.6). Qua trinh nao sau day la dang tfch ? A. Qua trinh 1-2. B. Qua trinh 2-3. C. Qua trinh 3-4. D. Qua trinh 4-1.
6.25*. De do do sdu cuamdt hd boi, ban Nam da cdm mdt d'ng nghiem hinh tru ed chia do rdi lan xudng day hd. Sau khi lan, ban dy da tfnh ra dd sdu cdn tim.
Theo em, ban Nam da lam each nao ? Giai thfch.
Hinh 6.6
70
CHAT RfiN vn CHA'T LONG
SV CHUV€N TH€
I -BAI TAP VIDU
Bai 1 Mdt sgi ddy kim loai dai 1 m, cd tilt didn ngang la 1 mm va dugc treo thing
dtog. Ngudi ta mdc vao ddu dudi cua day mdt vat trgng lugng 200 N thi thdy day dai thdm 1 mm. Nd'u bay gid ngudi ta dung mdt sgi day khdc cung vat lieu nhung dai 3 m, cd tilt didn la 0,5 mm va mdc vao nd mdt vat trgng lugng 300 N thi day se dai thdm bao nhidu ?
Bdi gidi Ddi vdi cac bai tap vl su biln dang cua vat rdn thutog chi dung c6ng thfic
a = — = F——. trong dd E la sua't Y-ang. Trong bai tap nay thi E chua cho bid't, S /g
song ta khdng cdn dung din gia tri cu thi cua nd.
Ggi IQ, IA/I, F va S la cac tri sd tuong tog cua sgi day thfi nhdt va ggi /gi, lA/il, Fl vd Sl la cdc tri sd tuong tog cua sgi day thfi hai, trong bai tap nay ta phai tim l,A/il cdn cac tri sd khdc diu da cho bid't.
Ap dung cdng thfic trdn cho ttog sgi ddy, ta vid't: F IA/I
- Ddi vdi soi ddy thfi nhdt — = E (a) S /g
-Ddi vdd sgi ddy thfi hai -J-= E-—!-• (b) \ 'oi
Fy_ lA/i l
S, ini , . , , F, . S . IA/I ./„, Chia (b) cho (a) ta dugc : - ^ = - j ^ . suy ra: \My\ = \ " •
"s X" Thay cac tri sd da cho vao bilu thfic eua \Aly\ (khdng cdn phai ddi cae gid tri
. . , , , , 300N.lmm^.lmm.3m . vd don vi SI) ta thu duoc : IA/il= ^ = 9mm.
200N.0,5mm2.1m
71
Bai 2
Cho mdt thudc met bang thep ldy chudn d 0°C (nghia la d 0°C thudc dai
dung 1 m theo chudn gd'c). Dung thfidc nay do mdt thanh nhdm d 0°C tM chilu dai
cua thanh nhdm la 2,5 m. Hdi d 30°C thi chilu dai cua thanh nhdm la bao nhidu
nd'u dtog thudc bang thep ndi trdn ? Cho bid't a (thep) =11,0.10 K va
a(nhdm) = 24,5.10~^K"^
Cac tri sd ldy dd'n 4 sd le va quy trdn din 0,5 mm; vf du 1,(X)7 35 m « 1,007 5 m.
Bdi gidi Ta quy ude dfing ehi sd 1 eho nhiing dai lugng lidn quan din vat lidu thep va
ehi sd 2 cho vat lidu nhdm. Trong bai tap nay ta luu y rdng : do ed dan nd dai yi nhidt ndn ca thudc do ldn thanh nhdm diu cd do dai khae di Idii d 30°C.
6 30°C (id dai cua thudc la: /i = /gi(l + OiAt) = 1.(1 + 11,0,10^.30)« 1,0005 m.
O 30°C dd dai cua thanh nhdm la :
h = 02(1 + "2^0 = 2,5.(1 + 24,5.10"^.30) « 2,5020 m.
2 5020 Lue nay chilu dai cua thanh nhdm se gdp ' = 2,5010 ldn dd dai cua thudc
bang thep. Vay dd dai cua thanh nhdm d 30°C do bang thudc thep la 2,5010 ra ; tfic la chi dai thdm 1 mm. Vl mat thue t l thi su sai khdc nay khdng dtog kl ndn ngudi ta khdng quan tdm.
Ndi chung thi khi chi tao thudc do, ngudi ta dung eac vat lidu cd hd sd dan nd dai nhd, td't nhat la dfing hgp kim inva (gdm 63,8% sat, 36% kin va 0,2% cacbon)
e d a = 16.10"^ K~\
Bai 3
Mdt mtog xa phdng dugc tao ra d mdt khung day thep hinh chfl nhat dat nam ngang cd eanh AB = 10 cm di ddng dugc. Hdi cdn thuc hidn mdt cdng bang bao nhidu dl lam ttog didn tfch mtog xa phdng btog each dich chuyin canh AB di mdt doan 5 em ? Cho bid't a (nudc xa phdng) = 0,04 N/m.
Bdi gidi
Luc etog bl mat cua mtog xa phdng dat ldn canh AB la :
F = 2a/ = 2.0,04.0,1 = 0,008 N
vay dl ttog didn tfch mtog xa phdng btog each dich chuyin canh AB di mdt doan 5 cm thi cto phai dat ldn canh AB mdt ngoai luc cfing phuong, ngugc chilu
72
vdi luc etog F va cd do Ito ft nhdt la 0,008 N (khdng kl ma sat). Cdng ma ngoai luc thuc hidn la :
A = 0,008.0,05 = 0,0004 J
Bai 4 Nhfing thing dtog hai d'ng mao ddn thuy tinh cd dutog kfnh trong ldn lugt
la 1 mm vd 2 mm vao thuy ngan. Hdi dd chdnh Idch gifla hai muc thuy ngan d bdn trong hai dng mao ddn dd bang bao nhidu ? Cho bilt a (thuy ngan) = 0,47 N/m vd p (thuy ngdn) = 13600 kg/m^
Bdi gidi 4a
Ap dung cdng thfic : h = cho hai dng mao ddn vdd cac dutog kfnh la pgd
1 mm va 2 mm. O day, h la dd tut xud'ng cua muc thuy ngan trong dng mao ddn so vdi muc, thuy ngan bdn ngoai dng.
Ah= hi -h2 = 4a 4a
pgdi pgd2 4a(d2-di)
pgdid2 4.47.10"^ (0,002-0,001)
13,6.10^.9,8.0,001.0,002 ., 0,00188 ____
^^= 026656 = ' ' ' ° ' " ^ -
Bai 5 Dd 1,5 lit nudc d 20°C vao mdt dm todm cd khd'i lugng 600 g va sau dd dun
btog blp didn. Sau 35 phut thi da cd 20% khd'i lugng nudc da hoa hoi d nhidt dd sdi 100°C. Tinh cdng sudt cung nhidt eua blp didn, bid't rtog 75% nhiet lugng ma blp cung cdp dugc dung vao viec dun nUdc.
Cho bilt nhidt dung rieng cua nhdm va cua nudc ldn lugt la 880 J/kg.K va 4190 J/kg.K; nhidt hod hoi ridng cua nudc d nhidt d6 sdi 100°C la L = 2,26.10^ J/kg; khd'i lugng ridng cua nudc la 1 kg/lft.
Bdi gidi Nhidt lugng ma blp da cung cdp cho dm nudc la :
Q = miCiAt + m2C2At + 0,2.m2L trong dd ehi sd 1 tog vdd dm, cdn chi sd 2 tog vdd nudc.
Thay cdc tri sd vao phuong trinh tren, ta dugc : Q = 0,6.880.80 + 1,5.4190.80 + 0,3.2,26.10^ = 1223 040 J
Goi cdng sud't cua blp la 9, thdi gian dun la t thi: — = 0,75 .S' T
W^y:S> = 1223040
x.0,75 35.60.0,75 = 776,5 W.
73
Bai 6 Trong mdt cto phdng kfch thudc 5 m x 4 m x 3 m d 20°C cd dd dm ti ddi la 70%.
a) Hay xac dinh dilm suong.
b) Cd bao nhidu hod nudc dugc tach ra khdi khdng khf dm khi nhidt dd cua phdng la 11°C? .
c) Khi dd do dm ti dd'i cua khdng khf la bao nhieu ?
Bdi gidi
a) Xdc dinh diem sucmg
Thi tfch cua cto phdng la : V = 5.4.3 = 60 m . Dl xdc dinh dilm suong cdn
phai tim dd am tuydt dd'i. Tfi cdng thfic f = — = 0,7, suy ra : a = 0,7A. A
6 20°C thi A = 17,3.10"^ kg/ml Vdy a = 0,7.17,3.10"^ kg/m^ = 12,10.10f kg/hi . Mud'n cho dd dm nay trd thanh dd dm cue dai thi nhidt dd cfia phdng phai giam dd'n nhiet do nao ? Theo Bdng dp sudt vd khdi lucmg rieng cua hcfi nUdc bdo hod d nhiet do khdc nhau (bai 56 SGK) thi gid tri 12,10.10 kg/m nam trong khoang nhidt dd tfi 10°C (tog vdi A = 9,4.10"^ kg/m^) din 15°C (tog vdi
—3 3
A = 12,8.10 kg/m ). Btog each ndi suy : ^ tz , i —y,4 Q
5 = 1 2 : 8 3 M * ^ ' ^ ' ' " ^ ^ ^ ^ = ^ ^
Vdy dilm suong la: 10°C + 4°C = 14°C. b) Tim luang hai nudc ngung tu (khi nhidt do cfia phdng la 11°C) 6 11°C thi dd dm cue dai la : A = 10.10"^ kg/m^ (tfnh btog each ndi suy).
Khdi lugng hod nudc da ngung tu la :
Am = 60 ml(12,1.10"^ kg/m^ - 10.10"^ kg/m^) = 126.10"^ kg
c) Xdc dinh do dm ti ddi (ciia khdng khf trong phdng d 11°Q
Luc dd hod nudc cd trong khdng khf cua phdng da trd nen bao hoa ndn dd dm ti ddi la 100%.
II - DE BAI
7.1. Trutog hgp nao dudd ddy thi chuyen dgng nhiet Id dao dgng cua cdc hat cdu
tgo chdt xung quanh vi tri cdn bdng xdc dinh ? A. Trong tinh thi kim cuong.
74
B. Trong thuy tinh rto. C. Trong thuy ngto ldng. D. Trong hod nudc.
7.2. Cd hai khdi ldp phuong, mdt lam ra tfi mdt don tinh thi va mdt lam ra tfi thuy tinh. Bd hai khdi nay vao nudc ndng thi chung cdn gifl dugc hinh dang hay khdng?
7.3. Hay cho bilt cac vdt sau ddy chiu eac biln dang gi ? a) Sgi day dto khi ngudi ta ldn day dto va khi chod dto. b) Cai bdp bdnh khi cdc em nhd chod bdp bdnh. c) Mui khoan khi dang khoan. d) Cdi dinh khi bi ddng vao gd.
7.4. Khi keo mdt sgi ddy ddng cd tilt didn ngang la 1,5 mm , ngudi ta thdy day bat ddu bi biln dang deo khi luc keo cd gid tri tfi 45 N trd ldn. Hdi gidd han dan hdi cfia ddng (tfnh theo don vi Pa) ?
7.5. Mdt den ehfim cd khdi Ifigng 250 kg dugc treo bang mdt sgi day todm vdd gidd han bin cfia todm la 1,1.10 Pa. Ddy treo phai cd tilt didn ngang la bao nhidu dl tog sudt keo gdy bod trgng lugng cua dto chum khdng vugt qua 25% gidd han bin cua vdt Udu lam ddy ? Dd bid'n dang ti dd'i cfia ddy la bao toidu ?
7.6. Cho mdt ddy btog ddng thau (dd Id mdt hgp kim gdm cd ddng, thilc va kem) dai 3,6 m va dutog kfnh la 1 mm. Tfto hd sd dto hdi cua ddy va sudt Y-tog cua vat lidu dfing lam day, bid't rang day da dai them 8 mm khi treo vao nd mdt vat khdi Ifigng 19 kg.
7.7*. Cto phai dat mdt luc la bao toidu vao ddu mut mdt thato sdt cd tilt didn
ngang la 10 cm dl ngto khdng eho thanh sdt dai thdm ra khi toidt dd cfia
thato ttog tfi 0°C din 30°C ?
Cho bid't a(sat) = 11,4.10"^ K"%a E(sat) = 200.10^ Pa.
7.8. Cd mdt sgi day dto lam btog vat lidu cd sudt Y-tog la 220 GPa va cd dd dai ban ddu la 88 cm. Sod ddy dto dd dugc keo etog vdd tog sudt 100 MPa. Tilp tuc ldn ddy dto, ngudi ta da klo ddy dai thdm ra 1 mm. Hdi tog sudt da lam etog ddy dto khi dd btog bao toidu ?
A. 250 MPa. B. 300 MPa.
C. 350 MPa. D. 400 MPa.
75
7.9. Cd the gdn day ddng true tilp vao thuy tinh hay khdng ?
7.10. Tai sao cai dito dc bang thep dd van vao cai dai de btog ddng khi ho ndng ca hai, cdn khi ngudi di thi lai rdt khd thao ra ?
7.11. Mdt bato xe btog gd cd dutog ldnh 1,2 m cto dugc lap mdt vanh dai sat ma
dutog kfto cua nd khi d 0°C tod hem dutog kfto cua banh xe la 6 mm. Hoi
phai ddt ndng vtoh dai sdt dd'n nhidt dd nao dl cd thi lap nd vao bato xe ?
Cho bid't a (sdt) = 11,4.10"^ K"^
7.12. Tfi tito thi thach ato ngudi ta lam ra mdt hito tru, true eua huih tiu song song vdi true cua phto Itog tru sau mat eua tinh thi thach anh (xem toh chup tinh
thi thach anh d Hito 50.1b trong SGK). 6 nhidt dd 18°C, bdn kfto day hinh
tru la 10 mm, cdn ehilu cao la 50 mm. Hay xdc dinh thi tfch cua hito tru nay
d nhiet dd 300°C, bid't rang he so dan nd dai theo true cua hito tru la
7,2.10 K , cdn theo phuong vudng gdc vdi true hito tru la 13,2.10 K .
7.13*. Mdt tdm ddng hito chfl toat cd kfch thudc 0,6 m x 0,5 m d toidt dd 20°C
dugc nung ndng dd'n 600°C. Hay tfto didn tfch tdm ddng khi nd dugc nung
ndng. Khi tfto cd thi bd qua cdc sd hang cd ehfia a^ Tfi bai tdp nay hay xdy
dung cdng thfic sau ddy vl su ddn nd dien tich cua tdm chdt rto :
S = So(l+yAt)
trong dd Sg va S la didn tfch cua tdm ehdt ran d tg°C va d t°C, cdn y = 2a. -
7.14. Tim nhidt dd cua mdt tdm todm phing, bilt rtog didn tfch eua nd da ttog thdm
3 200 mm do nungindng. Cho bilt didn tfch cua ttoi todm d 0°C la 1,5 m .
Ghi chu : Ap dung edng thfie tim dugc d bai tdp 7.13*.
7.15. Mdt bl btog bd ttog cd dung tfch la 2 m^ d 0°C. Khi d 30°C thi dung tich
cua nd ttog them 2,16 lft. Hay tim hd sd dto nd dai eua bd tdng.
7.16*. Tim edu tra ldi dung.
Khi ttog didn tfch bl mat cua khdi long d toidt dd khdng ddi thi:
A. Ldp bl mat khd'i long mdng di.
B. Khotog each gifia cae phdn tfi d bl mat khd'i long ttog ldn.
76
C. Gdm ca A va B.
D. Cd thdm cdc phto tfi chdt long di tfi trong ldng khd'i long ra ldp bl mat.
7.17. Tha ndi hai que didm nam song song trdn mat nudc. Nlu ta toung mdt mau xa phdng vdo mat nudc gifla hai que didm thi thdy chung tach xa toau hon, cdn nlu ta bd mdt ft dutog vao mat nudc dd thi thdy hai que diem xfeh lai gto toau ban. Hay giai thfch cdc hidn tugng trdn.
7.18*. Di ldm ra cae vidn dan chi hito cdu tod, ngudi ta nd'u chay chi va cho chi chay tod gigt vao nudc lato. Tai sao ?
7.19. Tai sao totog gigt ddu ndi trdn mat nudc cd dang hinh trdn ?
7.20. Dfing mdt cgng rom thdi mdt bong bdng xa phdng, sau dd dua ddu kia cgng rom lai gto nggn nin thi thdy Ifia nggn ndn bi tat di khi bong bdng xa phdng xep lai. Hay giai thfch hidn tugng.
7.21. Tai sao cd thi dfing thilc dl han ddng ma khdng dung dl hto todm ?
7.22. Tai sao tren mdt sd la cdy (tou la sen,...) suang cd thi dgng thato totog gigt hito cdu, cdn mdt sd la cay khdc thi udt suong ?
7.23. Nhtog chdt long nao ed thi rdt vao cdc ddy hon mep cdc ?
7.24*. Cung mdt d'ng nhd gigt va cung mdt lucmg nudc ngudi ta lam thi nghidm hai Ito, ldn thfi todt tod gigt vdd nudc d 8°C va Ito thfi hai nhd gigt vdd nudc d 80°C. Hdi hd sd etog bl mat cua nudc thay ddi tou thi nao theo toidt do ? Bid't rtog trong Ito thfi nhdt tod duge 40 gigt, cdn trong Ito thfi hai tod dugc 48 gigt.
7.25. Mdt vtoh khuydn mdng cd dutog kfto 34 mm, dat nim ngang va treo vao ddu dudd mdt Id xo dl thtog dtog. Nhung vanh khuydn.vao mdt cdc nudc, rdi cdm ddu kia cua Id xo keo vtoh khuydn ra khdi nudc, ta thdy Id xo dto thdm 32 mm. Tfto hd sd etog bl mat eua nudc, bilt rtog dd etog cua Id xo la 0,005 N/cm.
7.26. Nhung mdt khung hito vudng mdi canh dai 8,75 cm vao rugu rdi keo ldn. Tfto lue keo khung ldn, bid't rtog khdi lugng cfia khung la 2 g. Cho bilt
a (nigu) = 24,1.10"^ N/m.
7.27*. Ta tha ndi trdn mat nudc mdt que didm dai 4 cm. Bay gid ta tod rugu vao nudc d mdt phfa cua que didm ta thdy que didm dich chuyin vl phfa kia.
77
Hay giai thfch hidn tugng va tfto edng lam que didm dich chuyin tito tiln
2 cm. Cho bilt a (nudc) = 72,8.10"^ N/m ; a (ntgu) = 24,1.10"^ N/m.
7.28. Trong mdt d'ng mao dto bto kfto 0,5 mm muc chdt ldng dtog ldn 11 mm. Hay tim khdi lugng rieng cua chdt long nay, bilt rtog hd sd etog bl mat cua nd la 0,022 N/m.
7.29. Nhung hai d'ng mao dto thuy tinh cd dutog kfto khac toau vao nudc thi tha'y cdc mue chdt long trong hai dng dd chdto toau 2,6 cm. Nlu toung hai dng dd vao rugu thi hai muc chdt ldng chdto toau 1 cm. Tim he sd etog bl mat cua rugu nlu bilt he sd etog bl mat cua nudc la 0,072 N/m.
7.30. Trutog hgp nao muc chat ldng dtog len cao todt trong dng mao dto ?
A. Ong mao dan cd dutog kfto 2 mm toung vao nudc.
B. Ong mao dto cd dutog kfto 1 mm toung vao rugu. < > '
C. Ong mao dto cd dutog kfto 1 mm toung vao dte. -^
D. Ong mao dto cd dutog kfto 1,5 mm tofing vao xtog.
Cho bid't: Dd'i vdd nudc Oi = 0,072 N/m ; pi = 1000 kg/m^
Dd'i vdi rugu 02 = 0,022 N/m ; P2 = 790 kg/m^
Ddi vdi dte 03 = 0,017 N/m ; P3 = 710 kg/m^
Dd'i vdd xtog 04 = 0,029 N/m ; P4 = 700 kg/m^
Cac chat long nay diu dfto udt ede dng mao dto.
7.31. Tim cau sai trong eac cau dudd day.
Ta cd thi dfing hidn tugng ndng chay dl phto bidt
A. chdt rto don tinh thi vdd chdt rdn da tinh thi. B. chdt rto don tinh thi vdd chd't ran vd dito hito. C. chdt rdn da tito thi vdi chdt rto vd dinh hito. D. chdt rto kit tinh vdi chdt rto vd dinh hinh.
7.32. Nudc sdi hay nudc lato, nudc nao dap tdt Ifia toanh hon ?
7.33*. cau nao sau day la dung ?
A. Cung toidt cho mdt khdi ehdt ludn lam ttog thi tfch cua khdi chdt dd. B. Cung nhidt cho mdt khdi chdt ludn lam ttog toidt dd cfia khd'i chdt dd. C. Cung toidt cho mdt khd'i chdt la su truyin ntog lugng cho khd'i chdt do. D. Ca ba cau trdn diu dung.
78
7.34. Cd thi lam cho nudc sdi ma khdng cto dun duge khdng ?
7.35. Mudn lam nudc sdi h 27°C, ngudi ta da giam dp sudt ngoai tdc dung ldn mat thoang cua nudc trong cdc btog each dat cdc nudc vao trong mdt chudng thuy tinh kfn, rdi dung bom chan khdng hut bdt khf d trong chudng ra.
Hdi khi nudc trong cdc sdi thi dp sudt khf trong chudng la bao nhidu ?
A. 23,8 mmHg. B. 27,0 mmH. C, 29,0 mmHg. D. 31,8 mmHg.
7.36. Ngudi ta cd thi hod long khf CO2 d 25°C va d 35°C dugc khdng ?
7.37. Mdt lugng hoi nudc bao hoa d 100°C chid'm mdt thi tich nao dd. Ap sudt cua hoi nude se la bao nhidu nlu thi tfch eua hoi giam di mdt nfia khi toidt do khdng ddi ?
7.38*. Trong mdt xilanh va bdn dudi pit-tdng ed 0,4 g hoi nudc d toidt dd 290 K. Lugng hoi nay chid'm thi tfch 40 lft. Cd totog each nao lam cho hod nudc trd thato bao hod ?
7.39. Dl due cac vdt bang th^p; ngudd ta phai nau chay thep trong Id. Thep dua vao Id cd toidt dd 20°C, hidu sudt cua Id la 60%, nghia la 60% toidt lugng cung cdp cho Id dugc dung vao vide dun ndng thep cho dd'n khi thep ndng chay.
Di cung cdp toidt lugng, ngudi ta da dd't hit 200 kg than da cd ntog sud't toa
nhidt la 29.10^ J/kg. Cho bid't thep cd : ?i = 83,7.10^ J/kg ; toidt dd ndng
chay la 1400°C ; toidt dung ridng d thi rto la 0,46 kJ/kg.K. Hdi khdi lugng
cua me thep bi ndu chay la bao nhidu ?
7.40. Dl xdc dito toidt ndng chay ridng cua thilc, ngudi ta dd 350 g thilc ndng chay d nhidt dd 232°C vao 330 g nudc d 7°C dung trong mdt toidt lugng k l cd nhidt dung btog 100 J/K. Sau khi cdn btog toidt, nhidt dd cua nudc trong toidt lugng k l la 32°C. Tfto toidt ndng chay ridng cua thilc trong thi nghidm nay. Cho bid't c (nudc) = 4,19 J/g.K ; c (thilc rto) = 0,23 J/g.K.
7.41. Cto cung cdp mdt nhidt lugng btog bao nhidu dl lam cho 200 g nudc ldy d
10°C sdi d l60°C vd 10% khdi lugng cua nd da hod hod khi sdi ?
Cho bid't c(nudc) = 4190 J/kg.K va L(nudc) = 2,26.10^ J/kg.
7.42. Trong Id hoi, nude sdi d 197,4°C va cd dp sudt la 1,47.10^ Pa, Cto phai dd't hit bao nhidu than dl lam cho 50 kg nudc di vao Id hod chuyin hit thato hoi d
79
dilu kidn trdn ? Nhidt do ban ddu cua nudc la 10°C, hidu sudt cua Id la 80% vS ntog sudt toa nhidt cua tiian la ^,55.10^ J/kg. Cho bilt c(nudc) = 4190 J/kg,K, Coi hoi nudc nhu khf If tutog, tmh khdi lugng ridng cua hod nude trong Id hoi ndi trdn,
7.43. Trong 1 m^ khdng khf d 15°C cd 10 g hoi nudc. Hay xae dinh dd dm tuydt
dd'i va ti ddi cua khdng khf.
7.44. Do dm ti dd'i cfia mdt cto phdng d toidt dd 20°C la 65%. Dd toi ti ddi se thay ddi tou thi ndo nlu ta ha nhiet dd cfia phdng di 5 K, cdn dp sudt cua hod nfidc trong khdng khf eua phdng khdng thay ddi ?
7.45. Khdng khf trong mdt cto phdng d 17°C ed dd dm ti dd'i la 70%. Nhidt dd
cua phdng giam dd'n toidt do nao thi cac d kfto cfia sd bi md di ?
Cho bilt d 17°C, khd'i lugng ridng cua hod nudc bao hod la 14,5 g/m .
7.46. Trong mdt bito cd khdng khf d 25°C va dd dm ti ddi cua khdng khf nay la 63%. Sau khi dfing Caa2 hfit hit hod nude ed trong binh thi khdi lugng eua bito khf gitoi di 5,796 g. Hay tim dung tfch cua binh.
7.47. Nhidt k l udt cua dm k l khd - udt chi 16°C, cdn nhidt k l khd chi 20°C. Hoi dd dm ti dd'i cua khdng khf ?
7.48. Hieu nhidt dd gifia nhidt k l khd va nhidt k l udt cfia dm k l khd - udt la 3°C.
Hdi do am ti dd'i cua khdng khf la bao nhidu nlu toidt k l khd chi 20°G;
chi 25°C ?
7.49*. 6 15°C, nhidt k l khd vd nhidt k l udt cfia dm k l khd - udt chi nhidt d6
gid'ng toau. Hdi nhidt k l udt se chi nhidt do nao nlu nhidt dd cua khdng khf
ttog ldn din 20°C ? Cho rtog lugng hod nudc trong khdng khf vto tou eu.
7.50*. Trutog hgp nao dudi ddy ta cam tiidy dm todt (nghia la cd dd dm ti ddi cao todt) ?
A. Trong 1 m khdng khf ehfia 10 g hcd nudc d 25°C.
B. Trong 1 m khdng khf ehfia 4 g hod nudc d 5°C.
C. Trong 1 m^ khdng khf ehfia 28 g hcd nudc d 30°C.
D. Trong 1 m khdng khf ehfia 7 g hod nudc d 10°C.
80
7.51. Cho cdc dung cu sau (Hito 7.1):
- Hai tdm thuy tuih hito vudng.
- Mdt khay nudc tod.
- Hai kep.
- Cdc que didm.
- Mdt thudc cd dd chia tdd mm. Hay trito bay va giai thfch mdt phuang to thf nghidm dl xae dito gto dtog hd sd etog bl mat cua nudc.
7.52. Cho cac dung cu sau (Hito 7.2):
- Hai dng thuy tito thing, dutog kfto ngoai btog toau, dutog kfto trong khdc nhau.
- Mdt dng cao su.
- Mdt nfit cao su dl ddy dng.
- Mdt thudc cd dd chia tdi mm.
-Mdt bito nude. Hay trinh bay va giai thfch mdt phuong to thf nghidm dl xdc dinh gto dfing dp sudt khfquyln.
7.53. Cho cdc dung cu sau (Hito 7.3):
- Mdt d'ng thuy tito thtog, dai, dutog kfto trong khotog 3 mm.
- Mdt binh chdt long X.
- Mdt thfidc cd dd chia tdd mm.
Hay trito bay va giai thfch mdt phuong an thf nghidm dl xac dinh khd'i lugng ridng cuaX.
Hinh 7.1
Hinh 7.2
Hinh 7.3
6-BTVL 10(NC)-A 81
CO sd cun NHI€T DONG LUC HOC
I - BAI TAP VI DU
Bail
Thi tfch cua mdt lugng khf khi bi nung ndng da ttog thdm 0,02 m , cdn biln thidn ndi ntog cua nd la 1280 J. Hdi toidt lugng da truyin cho khi nlu qud tnnh la dang dp d dp sudt 1,5.10^ Pa ?
Bdi gidi
Ta dp dung phuang trinh Q = AU - A ddi vdi qua trito dtog dp.
Cdng trong qua trinh dtog dp nay la : A' = pAV = 1,5.10 . 0,02 = 3 000 J
Day la cdng do khf sinh ra ndn ta phai vid't: A = -A' = -3 000 J
Thay gia hi nay vdo phuang trinh trdn, ta dugc :
Q=1280 +3000 = 4280 J
Bdi 2
Mdt ddu mdy didzen xe Ifia cd cdng sudt 3.10 W va cd hidu sudt la 25%. Xac dito lugng nhidn lidu tidu thu trong mdi gid nd'u ddu mdy chay hit cdng sudt;
Cho bilt ntog sudt toa toidt cua toidn lidu la 4,2.10 J/kg.
Bdi gidi
A' A' Tfi cdng thfic H = — , suy ra Q, = —.
Qj 1 H
Trong 1 gid ddu may smh ra mdt cdng btog : 3.10^.3 600 = 108.10^ J.
108 10^ Nhiet lugng cto cung cdp cho ddu may trong 1 gid la: Q = '• = 432.10 J.
432 10^ Lugng nhidn lidu tieu thu trong 1 gid la : '—— = 1028,6 kg. 4,2.10^
° 2 6-BTVL 10{NC)-B
Bai 3
Gia sfi cd mdt may lanh cd hidu ntog cue dai hoat ddng gifla ngudn lato d nhidt dd -5°C va ngudn ndng d toidt dd 40°C. Nlu may duge cung cdp cdng tfi mdt ddng co didn cd cdng sudt 90 W thi mdi gid may lato cd thi ldy di tur ngudn lato mdt toidt lugng la bao nhidu ? Bilt rtog may ehi cdn lam vide 1/3 thdi gian tod CO ehi dilu nhidt trong may lato.
Bdi gidi
Thutog may lato khdng lam vide lidn tuc. Khi budng lato dat din toidt dd da dmh thi co ehi dilu toidt tu ddng ngat mach didn. Sau dd, do truyin nhidt tfi mdi trutog vao bdn trong may lanh ndn nhidt dd d budng lanh tang len, luc dd co chi dilu toidt lai ddng mach didn va may lato lai chay.
X Ot\Si
Dung edng thfic e ax = ^ % , ta tfto dugc E^^ = = 5,95. il — I2 DIJ —Zoo
Q9 Theo dinh nghia s = - ^ , ta suy ra Q2 = sA.
A . Do ddng CO didn chi cdn lafti vide 1/3 thdi gian ndn mdi gid ddng co
didn cung cdp mdt cdng la : A = 90.1200 = 108 000 J. Tfi dd ta tfto dugc :
Q2 = 5,95.108 000 = 642 600 J
II-D£BAI
8.1. Trfitog hgp nag dudd day lam biln ddi ndi ntog khdng do thuc hidn cdng ? A. Mai dao. B. Ddng dito. C. Khudy nudc. D. Nung sat trong Id.
8.2. Cho hai vidn bi btog thep gidng toau, rod tfi cung mdt dd cao. Vidn thfi todt rod xudng ddt mim, cdn vidn thfi hai red xud'ng sto da rdi nay ldn din dd cao nao dd va ngfidi ta bat ldy nd. Hdi vidn nao ndng ldn nhilu hon ?
8.3. Trutog hgp nao cd ndi ntog Ito hon : hdn hgp khf trong xilanh cua ddng co ddt trong d cudi ki nen (trude khi bi tia Ifia dd't chay) hay khf thai d cud'i ki thoat?
8.4. Ngudd ta eg xdt hai vdt vdi toau, toidt dung cua hai vdt btog toau va btog 800 J/K. Sau 1 phfit ngudi ta tiidy toidt dd cua mdi vdt ttog thdm 30 K. Tfto edng sudt trung bito cua vide eg xat.
83
8.5*.
8.6.
8.7.
8.8.
Cd hai qua cdu btog ehi gidng toau, chuyin ddng ddn gap nhau trite didn vdd vto tdc V va 2v. Hay tfto dd ttog nhidt dd At do va cham mim cua hai qua cdu.
Xac dmh do biln thidn nhidt dd cua nfidc rod tfi dd cao 96 m xudng va ddp vao cdto tuabin lam quay may phat didn, bid't rtog 50% thi ntog cua nudc biln thanh ndi ntog cua nudc. Cho bilt nhidt dung ridng cua nudc la 4190 J/kg.K.
Trong mdt thf nghidm, ngudi ta tha red tu do mdt manh thep tfi dd cao 5(X) m,
khi tdi mat dat nd cd vto tdc 50 m/s. Mato thep da ndng thdm bao nhidu dd
khi cham ddt, nd'u cho rtog toto bd cdng cto eua khdng khf chi dfing dl lam
ndng manh thep ? Cho bid't c (thep) = 460 J/kg,K va ldy g = 10 m/s .
Mdt vidn dan ehi phai ed tde dd tdi thilu la bao nhidu di khi nd va cfera vao vat cto etog thi ndng chay hoto toto ? Cho rtog 80% ddng ntog cua vidn dan chuyin thato ndi ntog cua nd khi va cham ; toidt dd cua vidn dan
trudc khi va cham la 127°C. Cho bilt e (ehi) = 130 J/kg.K ; nhidt dd ndng
chay eua chi la 327°C, nhidt ndng chay ridng cua chi la 25 kJ/kg.
8.9*. Bi
B A l
Hinh 8.1
8.10,
Pit-tdng dugc ddy tfi vi tri A dd'n vi tri B (Hito 8.1) dl nto khf trong dd bang hai each:
a) Ddy rdt chdm tfi A dd'n B.
b) Ddy rdt toanh tfi A din B rdi chd cho trang thai khf dn dito, i Cdc trang thdi ddu va cudi cua khf trong hai each tren la tofi toau va duge bilu thi btog
hai dilm Ai va Bi trdn dd thi p -V Hay md ta hai qud trinh nen khf ndi trdn, ve mdt each dinh tfto. trdn dd thi ede dutog bilu didn ede qud trinh dd va cto cfi vao dd thi, cho bid't cdng nen trong qud trito ndo Ito hem ?
Hay dung dd tiii p - V dl tim xem ddy cdc qud trinh ndi tiep nao ed thi kh^ kfn thato mdt chu tnnh ? A. Dto dtog dp, dto dtog nhidt, lam lanh dtog tfch.
B. D|un ndng dtog tfch, dto dtog nhidt, dto ding dp.
C. Dto dang nhidt, nen dtog dp, dun ndng dtog tfch.
D. Dto dtog dp, nen dtog nhidt, dun ndng ding tfch.
84
8.11*. Lam bid'n ddi mdt Ifigng khf tfi trang thai 1 sang trang thai 2, bilt rtog d trang thai 2 ca dp sudt va thi tfch cua lugng khf diu Ito hon d trang thai 1. Trong toiing each lam biln ddi lugng khf sau day, each nao lugng khi sinh cdng nhieu nhdt ?
A. Dun ndng khf dtog tfch rdi dun ndng dtog dp.
B. Dun ndng khf dang dp rdi dun ndng dang tfch.
C. Dun ndng khf sao cho ca toidt dd va dp sudt cua khf diu tang ddng thdi vd Udn tue tfi trang thai 1 din trang thai 2.
D. Tuong tu tou C toung theo mdt day biln ddi trang thai khdc C.
8.12. Nhidt dung ridng eua mgt ehdt dugc xac dinh bang toidt lugng cto cung cdp dl lam cho toidt do cua mdt don vi khd'i lugng chdt dd tang thdm 1 K. Ddi vdi khf, nhidt dung ridng phu thudc qua trito lam ndng khf, chtog han toiet dung ridng cua khi trong qua trito dtog ap Ito hon trong qua trito dtog tfch. Hay giai thfch dilu nay.
8.13. Nhidt dd cua khdng khi trong mdt can phdng r6ng 70 m la 10°C. Sau khi
dugc sudi dm, toidt dd cfia phdng la 26°C. Tfto cdng ma khdng khi eua cto phdng sinh ra khi dan dtog dp d dp sud't 100 kPa.
8.14*. Di nung ndng dtog dp 8(X) mol khf, ngudi ta da truyin cho khi mdt toidt
lugng 9,4.10^ J va khi dd khf da ndng thdm 500 K. Tito cdng ma khf thuc
hidn va dd tang ndi ntog cua khf.
8.15*. Cho 1 mol khf (coi la khi If tutog) thuc hidn chu trito 12341 tou da ve trdn dd thi p-V d Hito 8.2. Nd gdm hai qua trito dtog dp 12 va 34, hai qua trito dtog tfch 23 va 41. Cdc trang thai 1 va 3 nam trdn dutog dtog nhidt 13. Hay tfto cdng eua chu trito, bilt rtog nhidt dd d trang thai 4 la T4 = 300 K va toidt dd d trang thai 2 la T2 = 390 K.
O
Hinh 8.2
8.16. Tfto cdng sud't trung binh cua mdt ddng ca xe may nd'u khi nd chay vdi td'e
dd 25 km/h thi tidu thu 1,7 lft xtog eho mdi 100 km. Cho bid't hidu sudt eua
ddng CO la 20% va ntog sudt toa toidt eua xtog la 46.10 J/kg. Cho bilt khd'i
lugng ridng cua xtog la p = 700 kg/m
85
8.17. Trorig cac edu ndi sau ddy vl hidu sudt cua ddng co nhidt thi cdu nao la dtog ?
A. Hidu sudt eho bid't ti sd gifla edng hto fch vdi cdng toto phto eua ddng eo.
B. Hidu sudt cho bilt ddng co manh hay yiu.
C. Hidu sudt cho bilt phto trdm nhidt lugng cung cdp cho ddng eo duge biln ddi thato cdng ma ddng eo cung cdp. D. Hidu sudt eho bilt ti sd gifla nhidt lugng ma ddng co toa ra vdi nhidt lugng toto vao.
8.18. Mdt toa may nhidt didn tidu thu 0,35 kg nhidu lieu cho mdi kW.h didn. Nhidt do cua hcd nude trong Id hod la 250°C, nhidt dd cua budng ngung hcd la 30°C. Tfto hidu sudt thue cfia ddng co nhidt dtog trong toa may didn va so sato nd vdd hidu sudt cue dai cd thi cd dugc vdi ede nhidt dd cfia cdc ngudn nhidt trong toa may. Cho bilt ntog sudt toa nhidt eua nhidn Udu la 42.10 JAtg,
8.19. Dfing mdt may lanh, sau mdt thdi gian ngudd ta cd duge 300 g nude dd d -3°C lam tfi nudc d 10°C. Tfto toidt lugng da ldy di tfi nudc va nudc da. Nlu hidu ntog thuc cua may lato nay la 4 thi mdy lato da tidu thu mdt edng la bao nhidu ? Ldy nhidt dung ridng cua nude va nude da la 4,2 kJ/kg.K va 2,1 kJ/kg.K. Nhidt ndng chay rieng eua nudc da la 330 kJ/kg.
8.20. Ngto lato eua mdt mdy lato dugc gifl d nhiet dd thdp tod su bay hod cua mdi ehdt lanh. Tfto toidt lugng da ldy di tfi khdng khf va eac vdt khdc dl trong ngto lanh khi cd 50 g mdi chdt lato hod hod d nhidt dd cua ngto lato. Gia sfi may lanh cd hidu ntog cue dai vdd cac toidt dd cua ngudn ndng va ngudn lanh la 40°C va -5°C thi khi dd may lanh tidu thu mdt cdng la bao nhieu ? Cho bid't nhidt hoa hod ridng cua mdi chdt lanh la 1,68.10^ J/kg.
8.21. Nhidt dd cua vat nao ttog ldn toilu todt khi ta tha rod bd'n vdt dUdd ddy cd cung khd'i lugng va tfi etog mdt dd cao xud'ng ddt ?
A. vat btog todm, cd nhidt dung ridng la 880 J/kg.K.
B. vat btog ddng, cd nhidt dung ridng la 380 J/kg.K.
C. vat btog chi, ed nhidt dung ridng la 120 J/kg.K.
D. vat btog gang, cd nhidt dung ridng la 550 J/kg.K.
Coi tou toto bd do gitoti eo ntog dung dl lam ndng vdt.
8.22. Ndi ntog eua vdt nao ttog ldn nhilu todt khi ta tha rod bd'n vdt cd cung till tfch tfi etog mdt do cao xudng ddt ?
86
A. Vdt btog tiiilc.
B. Vdt btog todm.
C. Vdt btog niken.
D. Vdt btog sdt.
Coi nhu toan bd dd giam co nang chuyin hit thanh ndi nang eua vat.
8.23*. cau nao sau ddy la dung ?
A. Ndi nang cua mdt hd toat dito phai cd thi nang tuong tac gifla cac hat edu tao ndn hd.
B. Nhidt lugng truyin eho hd chi lam tang tdng ddng ntog eua chuyin ddng toidt cua cae hat edu tao ndn hd.
C. Cdng tae ddng ldn hd ed thi lam thay ddi ca tdng d6ng ntog chuyin ddng nhidt cua cae hat edu tao ndn hd va thi nang tuong tde gifla chung. D. Ndi ehung, ndi ntog la ham cua toidt dd va thi tfch, ndn trdng mgi trutog hgp nlu thi tfch-eua hd da thay ddi thi ndi ntog eua hd phai thay ddi.
8.24*. Cho cdc dung cu sau :
- Mdt bito thuy tito ed nut kfn vdi mdt dng thuy tito xuydn qua nut tdi gto ddy bito. Trong bito ehfia gto ddy nude.
- Mdt bito khae tuong tu khdng ed nude, dng thuy tito ngto each xa day.
- Mdt ndi nudc ndng.
- Mdt bito nude lato.
- Mdt d'ng cao su.
Tim cac each dl ed thi chuyin duge toilu nude tfi bito ng sang bito kia ma khdng dugc md nut cac bito.
87
^ MOT SO Bni TAP TONG HOP V€ CO Vfl NHI€T
1. Mdt con lde gdm mdt qua cdu tod, khdi lugng m = 200 g, treo vao ddu mdt sgi day ehilu dai / = 50 em. Ngucd ta keo qua cdu tdd vi tri ma ddy treo hgp vdi phuong thtog dtog mdt gdc a = 30° rdi tha ra toe totog (Hinh 1). Tfto lue etog eua day khi qua cdu xud'ng tdd vi tri thdp todt. Luc etog nay cd phu thudc gia tri cua / khdng ?
2. Trong Hito 2, khd'i hinh ndm ed dito ; a = 30° ; eac vdt A, B diu cd khdi lugng m = 2 kg. Bd qua ma sat
Tha cho cac vat A va B chuyin ddng. Tfto cdng sudt ma luc etog cua ddy dat dugc vao lue hai vdt chuyin ddng duge mdt thod gian t = 2 s.
3. Tfi vi tri A, ngudd ta truyin cho vat vto td'e Vl = 4 m/s tou trdn Hinh 3. Vat ldn dugc tdi dd cao h thi trugt xud'ng, va khi trd lai vi tri A vat cd vto tdc V2 = 3 m/s. Bid't a = 45° Hay tfto dd
cao h, va he so ma sat trugt \l^ gifla vat va mat phtog nghidng. (Giai btog phuong phdp ddng luc hgc va phuang phdp ntog lugng).
4*. Mdt vdt tod dat tai dinh A eua mdt ban cdu, ban kfto r, up cd dinh trdn mat bto tou trdn Hinh 4. Nhd mdt kfch thfch jrdt toe, vat bdt ddu trugt xudng (bd qua ma sdt gifla vat va bl mat ban edu). Hdi vdt se rdi khdi bto edu d dd cao nao so vdi mat bto ?
5. Khi thdi bong bdng xa phdng, ta quan sat thay luc ddu bong bdng bay ldn cao rdi dto dto roi xud'ng (nlu bong bdng khdng vd gifla chtog). Hay giai thfch hidn tugng va eho bid't tai sao bong bdng lai rod xudng.
Hinhl
7777777777777777777777777777777777777777777/
Hinh 2
Hinh 4
88
6. Mdt bito edu thuy tinh dung thuy ngto d dudd va nudc bdn trdn. Hito dang cua eac chd't long trong bito se ra sao nlu hd d trang thai khdng trgng lugng ?
7. Trdn mdt blp didn cd cdng sudt 1 kW, mdt din nude dang sdi. Tfto td'e dd hoi phut ra khdi vdi dm va tfto cdng sito ra do 1 g nudc hod hod khi sdi. Bilt rtog 80% nhidt lugng do bdp didn cung cdp dugc truyin cho nudc trong toi.
Cho bid't tilt didn cua vdi a'm la Icm^ Coi hcd nude la khf If tutog va bd qua thi tfch nude so vdd thi tfch hod eua nudc. Ap sudt cua khdng khf la 1 atm = 1,013.10^ Pa; nhidt hod hoi rieng cua nudc d 100°C la L = 2,26.10^ J/kg.
8*. Mdt khi cdu ed thi tfch 64 m . Khd'i lugng cua khf cdu (gdm vd va khf bdn trong) la 55 kg. Khf cdu dugc gifl dtog ydn trong kh6ng khf tod mdt sgi day thep ddi 50 m ndi khi edu vdd ddt.
Khdng khf d 20°C va dp sudt 1 atm = 10^ Pa, cd do am ti ddi la 80%. Tfto dd dan eua sgi day thep, bid't rtog tilt didn cua day la 2 mm va sudt Y-dng cua thep la : E = 2,1.10 Pa. Coi khdng khi la mdt chdt khi thuto nhdt cd khd'i lugng mol la p. = 29 g/mol. Hudng ddn : Khd'i lugng ridng eua khdng khf dm bdng khd'i lugng ridng cua khdng khf khd edng vdi lugng hcd nudc cd trong mdt don vi thi tfch khdng khi.
9. Trong mdt toidt lugng k l btog todm khdi lugng 300 g cd mdt cue nude da. . Nhidt dd cua nhidt lugng kl va nudc da la -5°C. Sau dd, ngudd ta eho hod
nude d 100°C vao nhidt lugng kl va khi da can btog toidt dd thi toiet dd
cua toidt lugng k l la 25°C. Luc dd trong toidt lugng kl cd 500 g nudc. Hdi khd'i lugng hoi nudc da ngung tu va khdi lugng cue nudc da cd trong nhidt lugng k l luc bat ddu thi nghidm. Cho bilt: c (todm) = 880 J/kg.K; c (nudc da) = 2,09 J/g.K ;
e (nudc) = 4,19 J/g.K ; L (nudc) = 2,26.10^ J/g ; % (nudc da) = 334 J/g. 10. Vao nam 1852 Tdm-xon da ndu y kiln vl each "sudi dm d6ng lue' nhu sau :
Nhidt lugng cd dugc khi dd't chdy toidn lidu khdng dung dl sudi dm ngay, ma cung cdp cho mdt ddng-co toidt dl sinh cdng. Cdng nay dung cho chay may lanh dl nd ld'y toiet lugng tfi mdi trutog xung quato va cung cdp toidt cho nudc sudi din (chay trong cac dng dto dat trong phdng cto sudi). Hdi each sudi toi ddng luc cd lgi hon khdng ? Lgi hon tou thi nao ?
Ap dung btog sd: dd't chdy 1 kg than da cung cdp nhidt lugng Qi « 6 000 kcal
d t = 210°C, hd thd'ng sudi cd toidt do ti = 60°C va mdi trutog cd toidt dd
t2 = 15°C (gid thid't rtog cac may nhidt cd hidu sudt cue dai).
89
Phan hai mJCR^G M^A!^ GlAl VA DAP s6
DONG HOC CHnt DI€M
1.1. Sit dung edng thfic tfto vto td'e trung binh :
y ^ ^2 - ^1 ^ Ax
* t2 - tj At
a) Ax = 2,3 m ; At = 1,0 s ; v = 2,3 m/s.
b) Ax = 57,5 - 9,2 = 48,3 m ; At = 3 s ; v = 16,1 m/s.
e) A X = 57,5 m ; At = 5,0 s ; Vji, = 11,5 m/s.
1.2. Chgn true Ox trung vdi dutog chay va cd gd'c la dilm xudt phat cua ngudi Vi chuyin ddng theo mdt chilu ndn dd ddi trung vdd qutog dutog chay cua ngudd dd.
a) Qutog dutog chay trong 4 min ddu la :
51 = 5.(4.60) = 1200 m
Qutog dutog chay trong 3 min sau la :
52 = 4.(3.60) = 720 m
Qutog dutog ngudd dd chay duge la :
S = Sl + S2
= 1200 + 720
= 1920 m =1,920 km
b) Vi chuyin ddng chi theo mdt chilu ndn trong ca thcd gian chay vdn tic trung bito btog tdc dd trung bito va bdng :
s 1920 , ^^ , ^ ' ^ '=1=7 :60=^ ' ^^ ' " / ^
Chd y : Khdng ldy trung binh hai vto tdc vi thod gian chay khac toau.
90
1.3. Chgn true Ox trtog vdd ehilu dgc cua bl boi, gd'c O la dilm xudt phat.
a) Ax = 50 m ; At = 40 s ; Vji, = — = 1,25 m/s ;
As = 50 m ; tde dd trung bito = -;— = -TTT = 1,25 m/s. At 40
b) Ax = - 50 m ; At = 42 s ; Vtb = = - 1,19 m/s ;
As = 50 m ; tdc dd trung bito = -r— = -rr- =1,19 m/s. ^ At 42
c) Ax = 0, Vtb = 0 ; As = 50 + 50 = 100 m ;
100 At = 40 + 42 = 82 s ; td'e dd trung bito = —— « 1,22 m/s.
82 1.4.
1,5 2,0 2,5 3,0 3,5 4,0 t(h)
Hinh 1.1 G
Theo dd thi, hai xe dudi kip toau sau 3 h 30 min, tai vi tri each Ha Ndi 210 km.
Chii y :
Cd thi giai bang tfto todn tou sau : Xe thfi hai dtog lai d vi tri.each Ha Ndi la 70.1,5 = 105 km. Khi xe nay bat ddu chang tilp theo thi xe thfi todt d vi tri each Ha Ndi 60.2 =120 km. Phuong trinh chuyin ddng cua hai xe kl tfi lue dd la :
91
Xl = 120 + 60t
X2 = 105 + 70t
Xe thfi hai dudi kip xe thfi nhdt khi Xi = X2. Tfi hai phuong tnnh trdn ta tim
dugc t = 1 h 30 min va x = Xi = X2 = 210 km. Vdy thod dilm dudi kip toau kl tfi lfic xudt phat tai Ha Ndi la 2 h + 1 h 30 min = 3 h 30 min, vi tri lfic dudi kip toau each Ha Ndi la 210 km.
1.5. a) Phuang trito chuyin ddng cua ngudd di bd va cua ngfidi di xe dap Ito lugt la: Xl = 20 + 5t (1)
X9 = lOt (2) b) Tfi dd thi ta thdy hai ngudd gap toau sau t = 4 h va tai vi tri x = 40 km. e) Giai hai phuong trinh (1) va (2), ta dugc kd't qua t = 4 h va x = 40 km,' dung tou cau b.
1.6. a) Cach giai tuong ttt bai tap 1.4. Dd thi cho trdn Hito 1.2G, dilm gd'c 0 tuong tog vdd luc 6 h. b) Nhin trdn dd thi ta thdy d td va tau gap nhau khi t = 2 h 50 min ; x = 120 km; tfic la chung gap nhau luc 8 h 50 min, cdch Thato phd Hd Chf Minh 120 km,
c) Xl = 30 + 45t
X2 = 60t
trong dd t la thdi gian kl tfi lue d td bat ddu chay.
X (km)
92
1.7. a) Chgn true Ox cd gdc tai Ha Ndi, chilu hutog vl phfa Hai Phdng.
Phuong trmh chuyin ddng cua hai xe la :
Xe di tfi Hai Phdng : Xi = 105 - 60t (1)
Xe di tfi Ha Ndi: X2 = 75t (2)
b) Hai xe gap nhau khi Xi = X2.
Giai (1) va (2), ta tim dugc t = 0,777 h « 46,2 min ; x = 58,33 km. e) Hgc sito tu ve dd thi.
1 « . - ^^2 - ^i) (20 - 25) ^ ^ , 2 , . . , , u^ -- ^ 1.0. a = — i - = = - 2,5 m/s (chuyen dgng cham dan).
1.9. a) Tuong tu bai tap trdn, ta tfnh dugc : a j = = 4 m/s^ (chuyin
ddng nhanh ddn). /
b) Khdng. Gia tdc tinh dugc la gia tdc trung binh. Nd'u gia tdc dd la khdng ddi thi chuyin ddng la biln ddi diu. Khi dd trung binh cua hai vto td'e nay dtung bang vto td'e trung bito trong khoang thdi gian dd. Tuy nhidn, ta khdng ed co sd dl ndi chuyin ddng cua chdt dilm la biln ddi diu.
1.10. a) Chgn true Ox trung vdd dutog di cua dlectron. Dung cdng thfic lidn hd gifla vdn td'e, dd ddd va gia tdc trong chuyin ddng thing biln ddi diu :
V - VQ = 2a(x - Xg) = 2as
Thay sd, ta cd :
(5.10V - (3.10V = 2a.(2.10~^)
Tfi dd suy ra gia td'e a » 6*25.10 m/s
b) Cd thi dfing cdng thfic v = Vg + at dl tfto thod gian t. Ta ed :
^ v - v g ^ 5.10^-3.10^
~ a " 6,25.10^^
t«8.10~%
Chii y : Ta todn thd'y, tuy gia tde rdt Ito toung hat chi todn gia tdc nay trong mdt thod gian rdt tod (ed phdn ti giay). Gid tri nay la gia tri diln hito cfia gia tdc cac hat tfch didn trong cdc may gia td'e hidti nay.
1.11. a) Chgn true toa dd trung vdd dutog di, gdc toa do trung vdi vi tri cua ato cato sat giao thdng, gd'c thod gian la luc ato xudt phdt. Khi dd d td da
93
d vi trf each ato cato sat 30 m. Phuong trinh chuyin ddng cua d td va eua ato cato sat ldn lugt la :
Xl = 30 + 30t (1)
3t^ x ,= ^ (2)
Khi ato cato sat dudi kip thi Xi = X2. Ta cd :
30 + 301 = — , hay la 2
l , 5 t^ -30 t -30 = 0 (3)
Giai phuong trinh nay, ta dugc ti = 20,95 s vd t2 = - 0,95 s. Vdy, sau 21 s
anh cato sat dudi kip d td.
b) Thay t = 21 s vao cdng thfic (1) hoac (2), ta tim dugc qutog dudng; di dugc.
Kit qua la : s = 661 m.
Chii. y : Cd thi giai bang ve dd thi.
'^'y2 1 c2
1.12. a) Tuong tu bai tdp 1.10, ta ed : a = = 3,6 m/s . 2.70
1 2 b) Dung edng thfie x - Xg = s = "Vgt +—at , bidt s, a, Vg, ta tfnh duge t.
Kit qua la : t = 3,3 s.
1.13. a) Phuang trinh chuyin ddng cua hai xe la
Xe thfi todt: Xl = 40 + Vit = 40 + 40t - (1)
Xe thfi ha i : X2 = V2t (2)
Lue dudi kip toau thi x"i = X2 = 200 km.
Cdng thfic (1) cho t = 4 h.
Cdng thfie (2) eho 200 = V2.4.
Tfi dd V2 = 50 km/h.
94
b) Dd thi (xem Hinh 1.3G)
X (km)
250--
200--
100--
6t (h)
1.14. Dung edng thfic v = Vg + at. 2
a) Ta cd a = 3 m/s ; t = 2,5 s ; Vg = 5,2 m/s. Thay vao cdng thfic trdn, ta dugc :
V = 12,7 m/s
b) Thay a = -3 m/s ; t = 2,5 s ; Vg = 5,2 m/s vao edng thfie tren, ta dugc :
V = -2,3 m/s
1.15. Phuang trinh chuyin ddng cua chdt dilm la :
X = -6t + 4t^
a) Thay t = 2 s vao cdng thfic trdn, ta dugc :
X = - 6.2 + 4.2^ = 4 cm
b) Vdn tdc V = -6 + 8t. Thay t = 3 s vao cdng thfie nay, ta dugc :
v= 18 cm/s
1.16. a) V = 3.10^ + 8.10^^t = 5,4.10^
10. Tfi dd suy rat = 3.10 '"s . b) Cd thi dung mdt trong hai cdng thfie sau
1 2 X = vot + 2 * (1)
95
VJ x = ^ (2) 2a
Thay sd vao cac cdng thfie trdn :
(1) cho X = 3.10^t + 4.10^V ; vdi t = 3.10"^° s.
(2) cho X = L_[(5,4.105)2 - (3.10^)2].
2.8.10^^
Kit qua la : x = 1,26.10"'* m. Quang dutog tuy nhd nhung rd't Ito so
vdd kfch thudc nguydn tu (10 m). ^ 2
1.17. a) Thdi gian nhd nhdt khi gia tdc can Ito nhdt, bang -5 m/s . Ta ed : ^ ^ v - v g ^ 0 - 1 0 0 ^ ^ ^ ^
a -5 b) Quang dutog chay tren dutog bang cung la nhd nha't. Ta cd :
s = 100.20 + - .(-5).20^ = 1000 m = 1 km 2
Nhu vay khdng thi ha eanh vdd dutog bang dai 0,8 km dugc. 1.18*. a) Chgn true Ox cd phuong thing dtog, hutog ldn trdn. Gd'c toadg d mat
ddt. Phuang trinh chuyen ddng cua qua bdng la : X = Vgt - 4,9t^
Luc t = 1,5 s thi X = 4 m. Thay cae gid tri dd vao edng thfic trdn, ta cd :
4 = vo.l,5-4,9.1,5^
Tfi dd suy ra : Vg = 10,0 m/s.
b) Ta ed V = Vg + (-9,8).t = 10,0 - 9,8.1,5 = -4,7 m/s.
Dd la vto tdc eua qua bdng khi ban nay bat duge. Ddu trfi cd nghia la qua bdng dang roi xud'ng.
1.19. a) Ta cd V = Vg - gt = Vg - 9,8t.
Thod dilm ti lue vdn tdc qua bdng bang 2,5 m/s la :
v - 4 2 , 5 - 4 ' = ^ 9 j = ^ 9 : 8 - = ^'^^^
Thod dilm t2 luc van tdc dat gia tri -2,5 m/s (khi di xudng) btog :
96
Khotog thdd gian gifla hai thod dilm dd la :
t = t2 - tl = 0,663 - 0,153 = 0,510 s
b) Dd cao lfic dd btog toa dd cfia qua bdng :
v^ - Vn 2 5^ - 4^ x-x„ = x = ^ ^ = ^ - ^ = 0,497m
1.20*. Chgn true Ox ed phuong thing dtog hutog xudng dudd, gdc O tai vi tri tha vdt. Ggi n la sd giay vat rod xudng din ddt. Toa dd cua vat sau n gidy la :
1 2 1 2
Toa dd eua vdt sau ( n - l ) giay la :
^n-l = 2^1-1 =\s(n-if
Trong gidy cudi cung (tfic la tfi luc (n - 1) giay dd'n luc n giay), vat rod duge 34,3 m, ta cd :
/„ = 34,3 = x„ - x„_i hay la:
/„= 34,3 = |.9,8[n2 - (n - 1)^] = 4,9.(2n - 1)
34 3 Tfi dd tacd: 2 n - 1 = ^ = 7, hayn = 4.
vay thdi gian rod la 4 s.
1.21. Chgn true toa dd Ox cd gd'c tai vi tri tha hdn da va chilu hutog xudng dudd. Phuong trito chuyin ddng cua hdn da va cua hdn bi thep Ito lugt la :
xi = ^gt^ = 4,9t2 (1)
X2 = V o t + | g t ^ = 1 5 t + 4,9t^ ' (2)
Khi hdn da rod din ddt, Xi = 8 m, thdd gian rod la ti btog :
.• = j i = 1,277 s
7-BTVL 10(NC)->^ 97
Khi hdn bi thep rod xud'ng din ddt, X2 = 8 m, thdi gian red t2 dugc tfnh theo edng thfic (2), tfic la :
8 = 15t2 + 4,9t^, hay la
4,9t^ + 15t2 - 8 = 0 (3)
Giai (3), ta dfige hai gid tri eua t2, ta chi ldy gia tri dfiong cua t2 btog :
t2 = 0,463 s
Hai vdt rod cdch toau khotog thdi gian la :
At = tl - t2 = 1,277 - 0,463 = 0,814 s
1.22*. Ggi h la dd sdu cua hang, ti la thdd gian hdn da red dto day, t2 la thdd gian
tid'ng vgng tfi ddy hang ldn dd'n midng hang. Ta cd :
h = Va .t2 = 340t2 (1)
h = - g t f =- .10tf =5tf (2)
Tfidd to=—I
2 ^ 2
5t ••2
^ 340
Thdd gian tfi luc tha hdn dd din lfic nghe thdy tidng vgng bang :,
t = t i+ t2= 13,66 s
Thay t2 vao bilu thfic vfia toto duge, ta cd : 5t2
^ 340 hay la
5tJ + 340 tl - 13,66.340 = 0 (3)
Giai phuong trito (3), ta duge hai gia tri cua tj, trong dd cd mdt gia tri am.
Ta chi ldy gid tri duong ti = 11,66 s.
Nhu vay thdd gian tieng vgng di tii ddy hang din midng hang la :
t2 = t - tl = 13,66 - 11,66 = 2 s
9 8 l BTVL 10(NC)*
Dd sdu cua hang la :
h = 340.t2 = 340.2 = 680 m
1.23*. Chgn true toa dd cd phuong thing dtog, gdc O trfing vdd vi tri eua hdn bi lfic t = 0. .
a) Sau 1 s, hdn bi rod dugc mdt ddan Si = /i = :j.l0.1^ = 5 m.
Sau 2 s, hdn bi rod duge mdt doan dutog la :
/ 2 = | . 10.(2)^ =4.5 = 20 m
Nhu vay trong giay thfi hai, hdn bi rod thdm dfige mdt doan la :
S2 = /2 - / i = 2 0 - 5 = 15m
Ta vilt lai tou sau :
52 = / 2 - / i = 5(2^-1^) = 15 m
Dd chinh la dd ddd eua hdn bi trong giay thfi 2.
Sau 3 giay, hdn bi rod duge mdt doan dutog la :
/3=| .10.(3)2=5.(3)V
Nhu vay trong giay thfi 3, hdn bi da red dugc thdm mdt doan dutog la :
53 = /3-/2 = 5[3^-2^] = 25m
S3 Cfing la dd ddd cua hdn bi trong giay thfi 3.
Ta tito duge dd ddd cua hdn bi trong giay thfi n :
b) Ta cd:
Sn = „ - n-1 = 5[n2 - (n - if] = 5(2n -1 ) m
52 - S l = 5[(2.2 - 1 ) - ( 2 . 1 - 1 ) ] = 2.5 = 10 m
53 - S2 = 5[(2.3 - 1) - (2.2 - 1)] = 2.5 = 10 m
Sn - s„_i = 5 { ( 2 n - l ) - [2(n - 1 ) - 1 ] } = 2.5 = 10 m
v a y hidu cac dd ddd sau 1 s lidn t i lp b t o g 10 m, b t o g hai ldn dd ddd sau gidy thfi todt.
Ghi chii : Cd t h i dp dung cdng thfic d bai 7 SGK la A/ = ax , trong dd ld'y 2
A/ = Sn - Sn_i ; a = 10 m/s ; x = 1 s.
99
1.24. Khoang cdch AB la :
s = vt = 100.(2.3 600 + 20.60) = 840 000 m = 840 km
Khi trd vl thdi gian bay la t' = 2 h 30 min, Ito hon 10 min do cd gid can.
Ggi vdn tde gid la VQ , ta cd :
S = (v-VG).t'
840 000 = (100 - VG).(2.3 600 + 30.60)
Tfi dd tfto dugc VQ :
VQ = 6,66 m/s
1.25. Thdi gian bed nguge ddng la :
1000 t, =
1000
1 (1,2-0,5) 0,7
Thdd gian boi xudi ddng la :
t-,= 1000 1000
(1,2 + 0,5) 1,7
Thdd gian bod ea di va vl la
t = t, + to = 1000 1000
= 2 016,8 s = 33,6 min ^i"^2 0,7 • 1,7
Nd'u sdng ydn lang thi thdd gian bod di va vl la :
t' = ^ ^ = 1666,67 s = 27,78 min 1,2
1.26. a) Hutog bay thoa mto cdng thfic tdng hgp cac vecto vdn tdc nhfi sau :
V = Vj + v^
trong dd v cd hutog Tdy, la ydn tde
tdng hgp ; v. la vdn tdc cfia may bay
theo hfitog cto xdc dinh (gia tri cua
Vj btog 200 km/h) ; V2la vdn tdc ^""-^^
cua gid theo hutog Nam. " " - .
So dd vdn td'e tou hito ve 1.4G. Hinh 1.4G
100
Dd dtog thd'y gdc a Idch khdi hutog Tdy cfia vdn tde Vi (tfic la hutog
Tdy - Bdc) dugc tfto bdng :
sma = ' 2 _ 50
200 = 0,25 ; a = 14,48°
b)Taed: v = vJ - v = 200^ - 50^
V = 193,65 km/h
1.27. a) So dd vto tdc cua gigt mua ddi vdd xe eho trdn Hinh 1.5G.
Theo so d6, ta cd : sin 60° = —^•, V
P-lL 2
trong dd Vi la vto tdc cua xe, btog 50 km/h ;
V2 la vto tde cfia gigt mua ddi vdi d td.
Tfi dd tfnh duge V2 = 57,73 km/h.
V,
Hinh 1.5G
b)VB = ' I _
tan 60° = 28,87 km/h.
1.28. Chgn hd true toa dd gto vdd mat ddt cd true Ox theo hutog Tay - Ddng,
true Oy theo hutog Nam - Bae. Vecto vto tdc cua xe A cd cac toa dd la
v^o = (-40 ; O) ; vecto vto td'e cua xe B cd cac toa dd la VgQ = (O ; 60).
Vto tdc VgA cua xe B dd'i'vdd xe A dugc tfnh theo cdng thfic cdng vto tdc
tou sau :
VBA = VBO + VQA
T a c d : VQA = - V A O = (40; 0)
Vay, vto tdc VgA cd cae toa dd sau :
V B A = ( 4 0 ; 6 0 )
Dl dtog tfto duge dd Ito cua VgA va phucmg, chilu cua nd.
Kit qua la:
VBA = 72,11 km/h, hutog Ddng - Bac lam mdt gdc 56,3°so vdd hutog Ddng!
101
1.29.
Khotog each (tii... din...)
2 2 ^2 - ' ^ l
a = —^ 2s
20cm + 40cm
0,412 m/s^
40 cm + 60 cm
0,396 m/s^
60 cm + 80 cm
0,384 m/s^
80cm+100em
0,389 m/s^ ,
Nhu vay, trong pham vi sai sd ed htog mm/s , ta cd thi coi gia tdc cua chuyin ddng la khdng ddi va btog gid tri trung bito cfia cac gia tdc la 0,395 ml%
1.30. Cdch tfto tuong tu bai tdp 1.29.
Kit qua tou sau :
Khotog cdch (tfi... din...)
2 2 ^2 - ^1
^ 2s
20em + 40 cm
9,84
m/s^
40cm + 60 cm
9,82
mii
60cm + 80 em
9,82
m/s^
80em + 100 em
9,82
mii
100 cm + 120 cm
9,65
m/s
120 cm + 140 cm
9,83
mii
Trung bito eua gia td'e g la 9,79 m/s Cd thi coi rod tu do theo quy luat cua chuyin ddng bid'n ddi (Jiu (gia tdc khdng ddi).
1.31. E dfing. Gia tdc cd gid tri am btog -2 mii, vto tdc ban ddu cd gia tri duong btog 10 m/s. Gia td'e va vdn td'e ban ddu ngugc ddu, ehdt dilm chuyin ddng chtoi dto diu theo chilu cua vto td'e, tfic la ehilu duong cfia true Ox. Vto tdc giam ddn dd Ito cho dd'n khi btog khdng, cdn gia
, ty
tdc ludn ludn btog -2 m/s , ehdt dilm tdng dto vdn tde theo chilu am cua true Ox.
1.32. a) Sai. D6 thi vto tdc cfia chuyin ddng thing diu la mdt dutog thing song song vdd true thdi gian.
b) Dung. Trong khotog thdd gian tfi 0 s - ti «, ca hai xe diu cd vdn tdc duong va gia tde dm, trdi ddu toau, do dd chuyin ddng la chdm dto diu. e) Sai.
d) Dung. Hai dutog bilu diln song song vdd toau, hd sd gdc btog toau ndn gia tdc cua hai xe la tou toau.
102
e) Sai. Hai xe dudi kip toau lfic t = ^OA ^OB
1.33. B dung. Ta cd v^ = 2as = 2.0,5.100 = 100 (mlsf, tii dd v = 10 m/s.
1.34. D dtog. Ta cd - v^ = 2a's', hay -100 (mlsf = 2a'.50. Tfi dd suy ra a' = -1 mii
1.35. a) Vdn tdc tfic thdd tai B duge tfto gto dfing theo cdng thfic :
Xp - X A 21-1,5
' » = 1 ^ = 0 : 8 3 0 - = 24.375 cm/s
Tfto tuong tu cho cac vi tri khac, ta cd kit qua sau : Thdi dilm (s)
Vitri
Vdn tdc (cm/s)
0,4
B
24,375
0,8
C
20,625
1,2
D
16,875
1,6
E
13,125
2,0
G
9,375
Vdn tdc giam ddn, chuyin ddng la cham ddn.
b) Gia td'e trung binh trong khotog thdd gian t = 0,4 s dd'n t = 0,8 s, tfic la tfi vi tri B din vi tri C, dugc tfnh theo cdng thfic sau :
Vc - Vg _ 20,6 - 24,4 ai = tc ~ tg
= -9,5cm/s^ 0,8 - 0,4
Tfto tuong tu cho cac khotog-khac, ta cd duge kd't qua sau
Khotog each
2 a (cm/s )
BC
- 9,375
CD
- 9,375
DE
- 9,375
EG
- 9,375
Gia tdc trung bito la khdng ddi, do dd chuyin ddng la chdm dto diu.
1.36. Dfing cdng thfie tfnh vdn tde tfic thdd. Vf du, tfto vdn tde tai vi tri B :
VB = ^C ~ ^ A
t c - t A
0,035 - 0 0 ,04-0
= 0,875 m/s
Tuong tu ta cd : Vc = 0,625 m/s ; Vp = 0,375 m/s.
103
1.37. a) Hito 1.6G.
b ) f = ^ = - M ^ . 0 , 7 5 s - l ' 2n 2.3,14
T = l = 1,33 s. f
e) V = r© = 5.4,7 = 23,5 cm/s.
1.38. Tdc dd gdc :
( 0 = 5 vdng/giay = 5.27i rad/s = IOTI rad/s.
Td'e dd dai: v = r© = 0,4.10.71 = 4n m/s = 12,56 m/s.
Gia tdc : a = Tti = 0,4.(107t)^ « 394,4 m/s^, hutog vao tdm dutog trdn.
1.39. a = — = — = 12 mii r 3
Hinh 1.6G
1.40. a) v^ = ar = 7gr = 7.9,8.5 = 343 (mlsf, tfi dd v = 18,5 m/s.
b) ro = - = 3,7 rad/s = ^f-.dO vdng/phfit = 35,4 vdng/phut. r 271
1.41. v = Vo,15.3,5.10^^^ = 7,25.10^ m/s.
1.42. a) Trong indt ngay ddm (86400 s), mdt dilm d xfeh dao ve mdt vdrtg theo chu vi cua Trdi Ddt. Tdc dd dai eua nd bdng ;
\3. Vxd =
_ 27tRp _ 271.6400.10^
^D 86400 m/s = 465,2 m/s = 1674,7 km/h
Tai vi dd 45°, ban kfnh dutog vi tuyin la :
R^ o =RD.eos45°
Tdc do dai cua mdt dilm d vi do 45° btog :
2TtR o 27iRr,.eos45° V = ^ = 86400 ' 3 2 9 m / s = 1 1 8 4 J b W h
104
b) Ta todn thdy, trong chuyin ddng quay cua Trai Ddt xung quanh true eua nd, tdc dd dai cd gia tri Ito todt d xfeh dao. Ngudd ta lgi dung dilu nay dl phdng cdc eon tau vu tru. Vi If do dd ndn Guy-an nam gto xfeh dao dugc chgn lam noi dat bd phdng tdn Ifia vu tru eua Trung tain Nghidn cto Vu tru chdu Au.
c) Hutog phdng cdc con tau la hutog Ddng vi Trdi Ddt quay theo chilu tfi Tdy sang Ddng. Nhu thi Igd dung dugc tdc dd quay cfia Trdi Ddt.
1.43. - Cdch 1 : Tinh theo bang sd lidu.
+ Ldy gid tri Ito cdn cua t = 0,2 s.
no 2 - 2 2'> + Tfnh gdn dung vdn tdc tfic thdi v = ^ .' ' ^ = 0,40 m/s.
- Cdch 2 : Tihh theo dd thi.
+ Trdn dfitog cong, ldy dilm M tog vdd t = 0,2 s.
+ Tai M, ve tilp tuyd'n vdd dutog cong, cdt true t tai t = 0,08 s.
+ Ta todn thdy la tog vdi s = 30 cm thi t « 0,78 s.
+ Tito gto dfing vdn tdc tfic thdd v = / ~ j^ = 0,43 m/s. (0,78 — 0,08)
Trong hai each tfto kd't qua cd sai khdc toau. Trong pham vi sai sd, ed thi chdp todn dugc.
1.44. - Tfi dd thi, ta cd todn xl t :
+ Cd ba dfitog bilu didn tog vdd ba chuyin ddng khac nhau cua bgt khf trong d'ng.
+ 6ng cd dd ngljidng Ito thi dutog bilu diln ddc hon, chtog td vto tdc
' cua bgt khf Ito hon.
+ Vto tde chi ddng biln vdd dd nghidng chfi khdng ti Id thuto vdd dd nghidng.
+ Tfi day cd thi tfnh vto td'e eu thi cfia mdi chuyin ddng.
105
&uMiig.Il
DONG LUC HOC CHAT DICMi
.1 . Xem m t o 2.IG. Trgng lue P dugc phto
phto f^ va f ^
lue etog eua day ve, ta cd :
T = AC ^
tfch thato hai thato
Ito lugt can btog vdd cac
ABva
mg or>0
day AC. Theo hito
~ 56,6 N
////////////////////////M
J20« K
''"*-'" „ Hinh2.1G TAB = mgtan30° « 28,3 N
2.2. C dung.
2.3. Khi xe dang chay nhanh ma dtog ddt ngdt, ngudd ngdi trdn xe se bi xd vl phfa trudc (do qudn tfto), cd thi bi lao khdi ghi hoac bi chto thuong do va cham mato vao cdc bd phdn cfia xe d phfa trudc chd ngdi eua mito. Ddy an toto cd tae dung gifi cho ngudd khdi xd vl phfa trudc khi xe dtog ddt ngdt.
2.4. Do cd quan tfto, mdy bay khdng thi tfic thdd dat tdd ydn tdc du Ito dl cdt cdto. Nd phai tang tdc dto trdn dutog btog mdd cdt canh dugc. Khi ha canh, nd dang cd vdn td'e Ito ndn phai ham dto trdn dutog btog mdd dtog lai duge.
2.5. Luc do bua tac dung truyin qua dinh tdd tdm vto. Vi tdin vto mdng va toe c6 khdi lugng tod ndn lue nay gdy cho vto mdt gia tdc dtog kl etog chilu vdi chuyin ddng cua dmh. Vi vdy ma khd ddng dugc dinh vao van.
Nhung nd'u ta dp vao bdn kia tdm vto mdt vdt khac (tiiutog la mdt tdm g6 ntog hoac mdt vidn gach...), tiii tdm vaff cfing vdd vdt nay hgp thanh mdt hd co khdi Ifigng Ito. Khi ta ddng dinh, hd nay cd gia tdc rdt tod (cd till coi gdn nhil dtog ydn) ndn ta dd ddng dugc dinh ngdp vao vto.
(Hay lidn hd vdi cdu tiiato ngfl dto gian : Dao sdc khdng btog chdc kd).
2.6. D dung.
10#
2.7. Gia tdc cfia bdng trong thdd gian va cham :
a = '^i^^ At
Chilu xudng true x (Hito 2.2G) :
F = ma = 0,2.800 = 160 N
-^o ^ T7 0,8-0,4 2.8. a) Fl = mai = m. = m.0,5
0,0 F2 = ma2 = m. — - — = m.0,1
^ = 5
Vo P Vt
Hinh 2.2G
b)
2.9.
Av = ajAt = 0,1.1,1 = 0,11 m/s.
Fi 81 A VA F2 32 B VB
Hinh 2.3G
Chgn ehilu chuyin ddng ban ddu eua vdt lam ehilu duong cua Ox. Luc FJ lam cho vdn tdc cua vdt giam, chtog td Fi nguge ehilu chuyin ddng. Gia td'e cua vdt trong giai doan ddu :
VR-VA 5-8 _ ,2 --^—A.- = _5 cm/s'' t. 0,6
2.10.
Khi vat tdd B, lue gifl hutog nhu cu va ttog dd Ito ldn gdp ddi, ndn gia tde cua vdt etog tang gdp ddi:
2 a2 = 2ai = -10 em/s
van td'e cua vat sau 2,2 s :
V = VB + a2t2 = 5 + (-10).2,2 = - I7 cm/s
Ddu am chtog td vat da ddi ehilu chuyin ddng.
(C6 ihi khai thac thdm : Vdt ddi ehilu chuyin ddng vao lfic nao, d ddu ?).
F F = miai =>mi = (1)
107
F = m2a2 > m2 = — a2
F = (mi + m2)a, suy ra : mi + m2
(2)
(3)
Tfi (1), (2), (3) tacd: 1 1
+ a2
= ^ 1 ^ = : 1 = 2,67 m/s2 ai+a2 8 + 4
F 9 9 2.11. a ± -^ = ^ = 3 mii
m 3
at^ S = Vgt + —
3t Thay sd : 10 = 2t + -—— Giai ra, ta duge : t = 2 s (loai nghidm dm).
^2 2.12. a) Thay sd vao edng thfic : s = Vgt + — , tfnh ra a = 2 m/s
Thay a vao cdng thfic : Fi - F . = ma, tfto ra Fj = 1,5 N.
b) Sau 4 s ddu, vdt dat tdi vto td'e,:
V = Vg + at = 10 m/s
Khi lite keo thdi tdc dung, luc can gdy cho vdt gia tdc :
- -0.5 , ,2 "="03"" -^'^'
Sau thdi gian t' vdt se dtog lai: v' = v + a't' = 0
Thay sd, ta dugc t' = 10 s.
2.13. Theo dito If ham sd edsui (Hinh 2.4G):
Y^^ = Ff + F | - 2F1F2 cos 150°
Tfi dd tfnh dfige : F12 « 6,8 N.
a = ^ = 3,4m/s^ m
at^ ^ ,r s = — - « 2,45m Hinh 2.4G
108
2.14. Xem Hinh 2.5G.
V (m/s)
154-
100 200
Hinti 2.5G
300 400 t (s)
2.15. Luc etog cua ddy khi dd la 50 N. Day khdng dfit.
2.16. 9,78 mii ; 4,36 mii.
2.17. 3,5.10^^ N.
2.18. Ggi khdi Ificmg mdi qua cdu lfic ddu la m^ va m j ; luc sau la mj va m2.
Khotog cdch gifla tdm cfia ehung lfic ddu la R, luc sau la R'. Khi ban kfto mdi qua cdu giam di 2 Ito, thi tfch cfia nd giam 8 Ito, do dd khdi lugng
etog giam 8 ldn : mi - - ^ \ ^2 = ~ ^ ' Ngoai ra, theo ddu bai thi
tnim2 Luc hdp dto gifla hai qua cdu luc ddu la : F = G ^ R
Luc hdp dto gifla chung lfic sau la
= 1 G ^ ^ = : ^ . Vdy B dung
p . ^ o i ^ h E i = G
mi m2 8 8 _
R
16 R^ 16
2.19*. Luc hdp dto giam 9 Ito, tfic la khoang each tfi vdt din tam Trdi Ddt ttog ldn 3 Ito. Luc ddu, vdt each tam Trai Ddt mdt doan R, thi sau dd, nd cdch tdm Trdi Ddt 3R, tfic la d dd cao 2R so vdi mat ddt. Vdy B dung (xem mto2.6G). Hinh 2.6G
109
2.20. B dfing.
2.21. Ggi X la khotog each tfi dilm phai tim din tdm Trdi Ddt (Hinh 2.7G). Luc hdp dto do Trdi Ddt tac dung ldn vdt:
_ GMim
Lue hdp dto do Mat Trang tdc dung ldn vdt:
GM2m ^ 2 = 2
(60R - x)^
Tfidd 11 .2
1
X- (60R -x)^
Giai ra ta dugc : x = 54R.
2.22. O cdch tam Trdi Ddt mdt khotog d : ^ GMm F = r—
Ml
Q-!R|
Fl m F2 M2 - « t > — 9
60R
Hinh 2.7G
6 mat ddt
Tfidd:
gt^
^ GMm
550
2.23. h = ^ = 44,1m.
L = Vgt = 75 m.
2.24. a) + Nd'u chgn he true toa dd tou d Hinh 2.8Ga (gdc toa dd d dilm tha vdt. Ox hutog theo Vg, Oy hutog thtog dtog xud'ng dudi) thi :
a, = 0 ;
ay =g- ;
Rfit t tfi bilu thfie eua x thay vao bilu thfie eua y ta dfige
X = Vgt = 120t
y = - ^ = 4,9t2
120^ Nd'u chgn hd true tou d Hito 2.8G b (gdc toa dd la hinh chilu cua dilm tha vdt trdn mat ddt. Ox song song vdd Vg, Oy hudng thing dtog ldn trdn) thi:
110
a. = 0 ; X = Vgt = 120t
g t ^ _ . a y = - g ; y = y g - V = 2 5 0 0 - 4 , 9 t
Tfidd 49 -> y = 2 5 0 0 - - ^ x 2
120^
O Vo
g
r
77T
y
Vo
a)
M$t(lSt \ Trf^rrrTrrrrTrrrrrrTTTTTTrrrTTTTTTTTT*-
X
b)
Hinh 2.8G
2h + Thdd gian tfi lue tha vat dd'n luc vat cham ddt la : t = , — « 22,6 s.
g
Tfi dd : / = Vgt = 120.22,6 = 2712 m.
b ) v g = | = / ^ « 1 0 5 m / s .
2.25*. Chgn true toa dd tou Hinh 2.9G, phuong trito quy dao
2v; 0
Khi vidn sdi di tdd vi tri cua bfic i2
tfitog (x = /) thi y =
Vidn sdi lgt qua cfia sd nlu : j2
h - a - b < ST 2v:
< h - b
0
g
////
y
Vo
\ \ \ V \ \ \
\ ""fa
///j///n///r I
X
h
•
(/////////
0 Hinh 2.9G
111
Suy ra:
/. g g ' 2 ( h - b ) ^ ' ' o ^ W 2 ( h - a - b )
Thay sdta ed: 1,66 m/s < Vg < 1,71 m/s.
2.26. Chgn hd true toa dd nhu Hito 2.10G (gdc toa dd la dinh thap). Phuong trito vdn tdc cfia vdt:
^ Vx = Vgcosa = 10,6 mis ' (1)
Vy = Vgsina - gt = 10,6 - 9,8t (2)
Phuang trinh chuyin ddng cua vat theo true y :
^ 2 y = (vosina)t - - ^
= 10,6t - 4,9t^
Khi hdn da tdd ddt:
y = -12 m. Ta cd :
10,6t-4,9t^ = -12.
Phuong ttito nay cd mdt
nghidm duong : t = 2,98 s.
Thay vao (2), ta cd :
Vy =-18,6 m/s
Dd Ito cfia van tdc khi vat cham ddt:
V = ^vJ+Vy.= ^10,6^+18,6^ = 21,4m/s
Vdn tde nay hgp vdd phfiong nam ngang mdt gdc P :
Hinh2.10G
2.27.
cosP = ^5. ~ 0,5 V
FRA = FAB
kAA/A = kBA/B
kp = - ^ - - ^ = 500 N/m
hay p « 60°
112
2.28. Ggi Al^, A/2 la dd dan cfia cac Id xo Li, L2 khi bi keo vdd luc F.
Ta cd : A/ = A/i + A/2 F
trong dd : A/ = —; r k
A/ F A/ F A/i = — ; A/2 = —.
(1)
(2)
Thay (2) vao (1) ta dugc : k = _ ^1^2 kl +,k2
2.29. Vi eac vdng Id xo gidng hdt toau ndn khi Id xo bi keo vdi mdt luc F todt dito, dd dan cfia mdi phto cua Id xo ti Id thudn vdd chilu dai ban ddu cua nd.
A/i _ /i
Nhung mat khac
Tfidd:
A/g /g
k - ^ - k -•"i - A/i ' ^ -
^1 _ ^lo_ _ }o_ k A/i /i
A/n
k, = _ k / g _
= 300 N/m
Tuong tu: k/„
k, = -2- = 150 N/m
2.30. Trong bai nay, phai chfi y tdi vai trd cua luc ma sdt do mat ddt tac dung vao mdi ngudd (Hito 2.110). Khi ngfidd 1 dap vao mat ddt, v^^^^wM^.'.'^/.>w.'.'.i^.'///y'///.'/^.^77f.>7w.>.'.'JWr^.'77.'.¥7//.
F, Fa
Hinh 2.1 IG
chto ngudi 1 tdc dung vao " 'i
da't mdt lue ma sdt Fj, mat
ddt tae dung trd lai chto ngudd
1 mdt phto luc ma sat FJ. Theo dinh ludt m Niu-ton :
F; = Fl (1)
Tuong tu, ngudd 2 tdc dung vao ddt lue ma sat F^, mat ddt tdc dung vao
chto ngudi 2 mdt phto luc F2, ta cd :
a-BTVL 10(NC)-A 113
F2=F2 (2)
Nd'u ngudi 1 dap mato hon ngudd 2 : Fi > F2, thi theo (1) va (2), Fi > F2.
Khi dd hgp luc do mat ddt tae dung ldn hd gdm hai ngudi ya ddy se hutog sang trai, va hd chuyin ddng sang trdi (ngudi 1 thtog cudc).
vay ai dap vao ddt mato hon thi se thtog cudc (mudn frd chod dugc edng btog, phai dam bao cho mat ddt d chd hai ngucd dtog ed dd rap gidng toau).
2.31. - Xe dtog ydn : khdng cd luc ma sat nghi.
- Xe chuyin ddng toato dto diu : F j n do sto xe tdc dung da gdy cho hdm gia tde a (btog gia tdc cua xe).
Fmsn = ma
(Fmsn hutog cung chilu chuyin ddng cua xe).
Nd'u a > Ung thi vat trugt vl phfa sau so vdi sto xe.
- Xe chuyin ddng chtoi dto diu : F^sn = ma.
Fmsn hutog ngugc chilu chuyin ddng cua xe. Nd'u lai > \i^g (chtog han khi xe ham gdp) thi vdt trugt vl phfa trude so vdd sto xe.
- Xe chuyin ddng thtog diu : khdng cd F^^^^.
2.32. Hdm chiu tac dung cua lue keo F,
frgng luc P, phto luc phap tuyin
N value ma sat Fmst (Hinh2.12G).
Vi hdm chuyin ddng diu ndn :
F + P + N'+Fmst = 0
Chilu xud'ng Ox :
F.cos a - F„3t = 0 (1)
Chieu xudng Oy :
F.sina - mg + N = 0 (2)
Ngoai ra : Fj t = IhJ^ (3)
N
*/77/y//////////
Hinh 2.12G
114 8-BTVL 10(NC)-i
Tfi (1), (2), (3) ta cd : F = ^^^^^.— « 56,4 N. cosa + [Xf sma
2.33. t = - 2 - « 2,04 s ; l^tg
2 s = , ^ « 5 , l m .
2Mtg
Cdc ddp sd khdng phu thudc m.
2.34*. Xem Hito 2.13G.
""ms; M
Fk
a,.,—^ M/4 * 3M/4 h *
.Hinh2.13G
Luc ddu, tau chuyin ddng diu do lue keo cdn btog vdd luc ma sdt Ito :
Ffc = ^msi = M/Mg (M la khd'i lugng ca doan tau)
Khi phdn dudi tau bi tach khdi doan tau, luc ma sat ham nd vdd gia tdc :
a, =
M
M 4
= - l A / g
Thdd gian dl phdn dudi tau dtog lai 0 - v ,
li/g
Trong khi dd, phdn ddu tau cd gia tde
^2
iv/r 3M
3 3M 3M 4 4
Sau thdd gian t, phto ddu tdu dat vto td'e :
M/g Vg 4 V2 = Vo + a2t = Vg+ ^ - - ^ = ^^0
115
TTT77TTTT77
2.35. a) Lue ma sat nghi F do
td'm van tac dung ldn mdu gd
lam cho mdu gd chuyin sang
trang.thai chuyin ddng. ^.^^ 2.14G
- Khi luc keo khdng Ito lam, gia tdc cfia tdm van va mdu gd cdn nhd, Trong hd quy chilu gto vdd tdin vdn, luc quan tfto tde dung ldn vdt 1 chua dfi thtog lfic ma sat nghi, ndn vdt 1 vto dtog ydn so vdi vdt 2 (Hinh 2.14G).
b) - Trong hd quy chid'u gto —*
vdd ban, luc ma sat F lam 21
cho vdt 1 chuyin ddng vl bdn phai (so vdd bto). - Trong hd quy chilu gan vdd
—* _, —» tdm vdn, Fqt thtog F21, vdt 1
chuyin ddng tfi B vl phfa A (Hito2.15G).
2.36. Lue qudn tfto lam cho ddy Idch sang bdn phai, chfing td gia tde cua tau hutog sang bdn trdi. Vdd gia tde hutog sang trdi, cd thi la tau chuyin ddng toato dto vl bdn trdi hodc cham ddn vl bdn phai, nhung ta khdng bilt dugc dfeh xdc la trutog hgp nao da xay ra. Vi vdy A, B diu sai. Dd nghidng cua ddy cung khdng lidn quan gi tdd vdn tdc. Vdy C cung sai, ehi ed D la dung.
2.37. Trong hd quy ehilu gto vdd mdy bay, ngudd phi cdng chiu tde dung cfia trgng lfic, luc qudn tfto li tdm (do may bay chuyin ddng frdn) va phto luc cua ghi ngdi (Hinh 2.16G).
7777777777?
Hinh 2.15G
4F„
N,
P + Fq + N = 0
Tai dilm cao nhdt A :
P + NA = Fq
NA = F q - P = m - g = 765N
Itsip
Hinhi.16G
116
Tai dilm thdp todt B :
NB = F„ + P = m ^ 2
= 2235N
Cdc tri sd NA, NB cung la tri sd cua luc nen cua ngudd phi cdng ldn ghi tai AvaB.
2.38. Nd'u dung hd quy ehilu gan vdd mat ddt, thi ta lap luto la vat vtog ra khi luc ma sat nghi cue dai khdng du dl ddng vai trd luc hutog tam (xem bai tdp vf du 3).
Nlu dung hd quy ehilu jgan vdi bto, thi ta lap luto la vat vtog ra khi luc quan tfto li tam thdng lue ma sdt nghi cue dai.
Ca hai lap luto cung ddn tdi:
; mro r > |inmg 2
m (27cn) r > ii^mg
n > 2 ^ ^ ^ « 0,5 vdng/giay «
2.39. Phan luc Ncua thato binh dat ldn vat la luc hutog tam. Do cd luc nay ma xud't hidn luc ma sat nghi gifl cho vdt khdi bi red xud'ng (Hinh2.17G):
msn
P 1— N
li •i
i
frong dd
vd
Dodd:
Tfidd
F =P * m s n "•
P = mg
Fmsn linN = ^„mro^r = n„m(27tn)^r.
mg < |J,nm (27tn) r
Hinh2.17G
1 n > -^J— « 2,88 vdng/gidy « 173 vdng/phfit. 27i\n„r
2.40. Cd thi. Ching han mdt vdt cd thi chuyin ddng trdn diu dudd tdc dung cua mdt lite hfitog tdm cd dd Ito khdng ddi.
117
2.41. B dfing.
Vdt chuyin ddng chdm dto diu ldn phfa N, tdd mdt dd cao nhdt dinh thi dat tdd vto tde v = 0. Vi tana > IJ^ ndn vdt se chuyin ddng nhato dto diu xud'ng phfa M.
2.42*. Tfi cdng thfie a = g(sina - ^tcosa)
ta rfit ra jit = tana - '• (1) geosa
Khi a = 20°, A/ = D E - C D = CD-BC = BC-AB
= 12,5 - 1 0 = 10 -7 ,5 = 7,5 - 5 = 2,5 mm.
a = ^ = l,5625m/s^
Thay vao (1) ta duge : ^j ~ 0,194.
Khi a = 42°, A/ = Q R - P Q = P Q - N P = N P - M N
= 3 4 - 2 6 = 26 - 18 = 18 - 1 0 = 8 mm
A/' ^ .2 a =;= - r - « 5 m/s^
Thay vao (1) ta dugc : ^,2 ~ 0,213.
Ta cd gid tri trung bito cfia \i:
„.'^^.a.2 2.43. a) Vdd he 2 vdt
a = " ^ i g - r ™ . 5 , l m / s ^
b) Vdi vat 2 :
mi + m2
m2g -T = m2a
T = m2(g-a) = l,41N
e) Khi vat 2 cham ddt, vdt 1 cd vdn tdc :
V = \/2ah = 2,26 m/s
Gia td'e vdt 1 sau khi vdt 2 cham ddt:
118
a- = =M^ = -1,96 mii m.
Vdt 1 cdn chuyin ddng thdm
vf - v" 0 - 2,26 . „ ^ = - ' 2 ^ = 2 : H l 9 6 y ^ ^ ' ' " ^
2.44. Dd Ito gia tdc cfia mdi vat:
(m-1 — m, )g „ ^„ , 2
i/i a = ^^-^ i ^ « 3,27 m/s^ m2 + mi .
Cho tdd lue hai vat d vi tri ngang toau, mdi vat diu di mdt doan —
h _ at^ 2 ~ 2
t = ^ - 0 , 5 5 s
2.45. a) Nhto xet: P2 > Pix + Fj g n g ^ ti vat mi chuyin ddng len trdn, vat m2 chuyin ddng xud'ng dudd (Hinh 2.18G). Gia td'e eua he bang :
a = — P — F
Ix ^mst
mi + m2
_ m2g - migsma - miHtgcosa mi + m2
= l,6m/s^
Trong dd ta da tiiay F j n max = Fmsf bing :
Fmst - mniig' osoi w 0,85 N
b) Trong frutog hgp nay ta todn thdy :
W///7y77M7//^^^//W7^7^7/y7W7^/
Hinh2.18G
Pw<Po + F„ (1) Ix '^ ^ 2 • ^ msn max
ndn hd khdng chuyin ddng (Hinh 2.19G).
Ta ed a = 0.
Luc nay luc ma sat nghi chua dat tdd gia tri cue dai:
WW///7/7/777^M^^^7777777/7^7/7^7,
Hinh2.19G
Fmsn = Pix - P2 = gCmisina - m2) = 0,49 N
119
2.46. B dung (nd'u tana > n„ thi vdt trugt xudng duge).
2.47*. Thato phto cua frgng luc song song vdd mat phing nghidng :
yl2 Px = mgsina = 0,5.9,8.-^ = 3,46 N
Gia tri cue dai cua luc ma sat nghi gifla vdt va mat phang nghidng la :
V2 Fmsnmax = ^^mgcosa = 0,5.0,5.9,8.^ = 1,73 N
Px ed xu hutog keo vdt trugt xudng. Gia tri cua nd ldn hon gia tri Ito todt
cua luc ma sat nghi. Do dd lue ma sat nghi dat tdd gid tri cue dai dd :
F = 1 73 N • m s n A , ' J i^
Vi vdt d frang thai cdn btog ndn :
fT + F = P '- ^ '•rasa ^x N = R,
Tfi dd : T = Px - F^s„ = 3,46 - 1,73 = 1,73 N
N = mgcosa = 3,46 N Hinh 2.20G
2.48*. a) Luc ddu (mj ehfia cham ddt), hd chuyin ddng nhanh dto diu, ndn
khotog each gifia cdc chtoi trong doan AF ttog ddn. Sau khi mi cham ddt,
lite ma sat trugt lam cho m2 chuyin ddng chdm dto, ndii khotog each gifla cdc chtoi trong doan FL giam dto.
b) Trong doan GL :
A/= K L - I K = I K - H I = H I - G H = - 5 mm
a = A/ ^ -5.10^^
0,04^ «-3,125 m/s^
Trong doan nay : a = ^ ^ = -\x^g m^
^t = — = 0,32 g
120
c) Trong doan AE :
A/' = DE - CD = CD - BC = BC - AB = 11 mm
a. = 4 = 11:151. 6,88 m/s' i- 0,04^
r^ A - ^ ( m i - | U t m 2 ) g Trong doan nay : a = —-—^-^—^^^. mi + m2
Rfitra: mi(g-a') ^ ^ ^^ ^ a' + ^tg
2.49. - Tfto chd't dan hdi cua day cao su thdng thutog dung trong sito hoat la khdng ddng nhdt trong qua trito dan ra va eo lai.
- Hd sd dan hdi ludn bid'n ddi theo dd dan eua day cao su.
- Mdi quan hd gifla dd dan vd lue dan hdi khdng don tri.
- Khdng thi dung day cao su nay lam luc kl.
- Trong khi dd, hd sd dan hdi cua Id xo trong bai da hgc la khdng ddi (trong gidi han dan hdi).
121
TINH HOC VflT ft AN I
t Hinh 3.1G
3.1. 1. a) Nhtog luc ddt ldn hdn bi gdm : luc \^
etog eua sgi ddy T hutog ldn frdn va
trgng luc P hutog xud'ng dudd.
b) Do hdn bi ehi chiu tac dung cua hai lue eho ndn dilu kidn cto btog cua nd la
f + P = 6, hay f = -P Hai luc tac dung cd cfing dd Ito, cung phuong toung ngugc chilu.
c) Tfi cdng thfic frdn, ta ed dd Ito cfia hai luc la T = P = 0,2.9,8 = 1,96 N.
2. a) Luc k l do gia tri cua luc do sgi ddy dat ldn mdc C. Sgi day cd khd'i lugng khdng dang kl, luc dd bilu thi lue etog eua sod day tai mgi dilm cua day. So ehi eua lue k l la 1,96 N.
b) Luc k l do gid tri cfia lue etog eua sod ddy, bdy gid btog 2i,2 N. Dilu kidn cto bang cua hdn bi bay gid la :
f + F + P = 6
frong dd, F la luc tdc dung eua nam chdm ldn hdn bi.
Tfi dd suy ra :
f = - ( F + p)
Luc etog T ttog ldn, ed gid tri Ito hon frgng luc, do dd luc F cd phuong
thtog dtog va hutog xudng dudi, cung ehilu vdi frgng luc P (Hinh 3.1G).
3.2. l.a)XemHito3.2G.
b) Cac luc dat ldn quyln frdn (1) gdm :
- Trgng luc Pi do Trdi Ddt hfit nd.
122
- Phto luc do quyln dudi (2) tdc dung N
^21-
Quyln sdch nam cto btog, vdy :
I "
' 21
' 12
tP2
Hinh 3.2G
(1)
P i + F 2 i = 0
Suyra F21 = -P,, va |F2I| = |?I|-
Lue do quyln dudd tdc dung ldn quyln frdn ed dd Ito btog frgng lugng quyln
frdn va hutog ldn frdn. Ta ed F21 = 10 N.
Cdc lue dat ldn quyln dudd gdm :
-Trgng luc P2 do Trai Ddt hut.
-Luc do quyln frdn tac dung F12.
- Phto luc do mat bto tde dung N. Quyln dudd ndm can btog, vay ta cd :
P2+Fi2+N = 6
theo dito luat III Niu-tan, tac dung tuong hd gifla hai vat (1) va (2) eho :
Fi-2 - -F21 (2)
vay luc F12 ed dd Ito btog dd Ito eua luc Fji, btog 10 N va hutog xudng dudd. Theo cdng thfic (1), ta cd :
N = -(P2+Fi2) (3)
Phto luc N hutog ldn frdn va vl do Ito thi N = P2 + F12 = P2 + Pi = = 18 + "lO = 28N.
2. a) Cac lue dat ldn hd gdm :
-Lite hut cfia Trdi Ddt P.
- Phto lite cua mat bto N. b)Taed: P = Pi + P2 ; P = Pi+P2= 10+18 = 28N
Hd ndm cto btog : P + N = 0
Suyra: N = - P
Phto luc N cua bto dat ldn hd btog va ngugc chilu vdi frgng luc P : N = 28 N.
123
e) Theo dinh luat tae dung tuong hd, hd tac dung ldn mat bto mdt lue bto§
va ngugc chilu vdd phto luc N, tfic la btog P.
(Khdng ndn todm Ito gitta lfic cfia hd ddt ldn mat bto vdd frgng luc cua hd, tuy rtog hai luc dd btog toau ea vl dd Ito Ito phuong, chilu).
3.3. Tuong tu bai tap 3.1. Luc Id xo dat ldn vat btog frgng lugng vat va cd ehilu nguge lai.
3.4. 1. Luc k l chi frgng lugng eua vdt P = mg = p7tr hg.
Thay cac gid tri vao edng thfic, ta dugc :
P = 2700.3,14.0,01^0,2.9,8 = 1,66 N
2. a) Xem Hinh 3.3.G.
b) Cdc luc dat ldn hito tru gdm :
Trgng lue P, luc ddy Ae-si-met A va luc etog T cua Id xo.
Luc ddy Ae-si-met A hudng thtog dtog ldn frdn, va cd dd Ito bdng :
A = p^nr^hg
= 1000.3,14.0,01^.0,2.9,8
= 0,615 N « 0,62 N
Hito tru nam cto bang, ta cd :
P + A + f = 6
f = -(p + A)
Do P va A ngugc chilu toau ndn gid tri eua T btog :
T = P - A = 1,66 - 0,62 = 1,04 N Vdy sd chi cua lue k l la 1,04 N.
3.5. a) Lidt kd cac luc dat ldn vat:
- Trgng lue P dat d frgng tam, hutog thing dtog xudng dudd ;
- Lue etog T cd phuong cua sod day, hutog ldn phfa trdn ;
- Luc didn F ed phuong nam ngang, keo vat lam day Idch khdi phuong thtog dtog (xem Hito 3.4G).
124
b) Do vat ndm cto btog, ta cd :
P + f + F = 0 (1)
Chgn mdt hd toa dd xOy, cd gdc trung vdd vat, true Ox nam ngang hutog
theo ehilu lue F, true Oy thtog dtog hutog ldn frdn. Phuong trinh vecto (1) cd hai thato phto la :
- Trdn true Ox : 0 + (-T.sina) + F = 0 (2)
- Trdn true Oy : - P + T.eosa + 0 = 0 (3)
Tfi hai phuong tiito (2) va (3), ta suy ra :
F tana = —
Thay cac gia tri cua P va F vao edng thfie frdn, ta duoc :
tana = 3.10"
5.10" = 0,6, hay a « 31°
c) Luc etog cua sod ddy :
F T = ^•^^" = 5,8.10-^ N
sina sm31°
3.6. Hgp hai luc song song Fi va F2 cung chilu cd gia tri btog :
F = Fi+F2 (1)
Dutog tde dung cua hgp lue F chia frong hai luc Fi va F2 theo edng thfic ti Id nghich vdd dd Ito hai luc. Ta cd :
V2 Fl _F2 F i+F , dl dl + d2
(2)
(Cdc bai tdp 3.6 va 3.7 giai' dugc tod ede cdng thfic (1) va (2)).
Cac dtt kidn cua bai tdp 3.6 la : d = di + d2 = 0,2 m ; Fi = 13 N; d2 = 0,08 m. Tfi cac cdng thfie frdn, ta cd :
F1+F2 . 13
Tfidd
0,2
F = Fi+F2 =
0,08 0,2.13 0,08
= 32,5 N
F, = F - F, = 32,5 - 13 = 19,5 N
125
3.7. Theo ddu bai, Fi + Fj = 20 + 30 = 50 N ; d2 = 0,8 m. Sfi dung edng thfie (2)
6 b M , a p t t . n , . c 6 : d = d , + d , = ( F , . F , ) ^ .
Thay sd vao, ta dugc : d = 2 m. 3.8. Cdch giai tuong tu ede bai tap 3.6 va 3.7. Chu y cac etog thfic lidn quan la :
F = i F 2 - F i |
d = ldn — dd
Fl _ F2 _ F
(1)
(2)
(3)
Theo dl bai tap 3.6, bilt d = 0,2 m ; Fi = 13 N ; d2 = 0,08 m.
Kit qua cho : F = (0,2.13): 0,08 = 32,5 N
F2 = F + Fl = 32,5 + 13 = 45,5 N
dj = d + d2 = 0,2 + 0,08 = 0,28 m
Theo dl bai tap 3.7, bilt Fi = 20 N ; F2 = 30 N ; d2 = 0,8 m.
Kit qua eho : F = 10 N ; d = 0,4 m ; di = 1,2 m.
3.9. a) Cae lue dugc bilu didn frdn hito 3.5G.
b)F^, = P s m a = | R
e) Psintti = |uinN = jA^Peosai
tantti = lOn = 1 ; ai = 45°
3.10. 1) Dd dto cua Id xo : F = kA/
A / = ^ = ^ = 0,04m = 4em k 50
/ = /n + A/ = 50 + 4 = 54 em '0 1
2)F = Psma= - P =kA/'
A / ' = i . ^ = 0 , 0 2 m = 2em
/ = /n + A/' = 50 + 2 = 52 em '0
s N = Peosa = 2 . ^ = S = 1,73 N
N \
y^
A i
; p
Hinh 3.5G
126
3.11. a) Ddu trfi (momen lue dm),
b) M = F.OA. sina.
J 3 e ) M = 3 ^ « 2 , 6 N . m .
3.12. a) Ddu cdng (momen luc duong).
b) Dutog vudng gdc cua hai gid.
c) M = F.AB. sina.
3.13. M = P.OG.sina = 0,03.9,8.0,2.sina « 0,06.sina N.m.
n . ^ n a = - , M = 0,06-^ « 0,04N.m ; a = - , M = 0,06 N.m ; a = TI, M = 0.
3.14. F = 3,1 N.
3.15*. a) Ggi Pg la trgng luc cua qua cto. Mi la momen dd'i vdd true I eua ttgng luc phto phfa AI cua cto ; M2 la momen dd'i vdd true I cfia trgng lue phto phfa BI cua can. Khi Pg treo d O thi cto thtog btog. Ta cd :
Mi = M2 + Pg.I0 (1)
Treo mdt vat frgng lugng P tai K thi phai dat Pg tai vi tri B. Can nim thang btog, ta cd :
P.AI + Ml = M2 + Pg .IB = M2 + Pg.IO + Pg.OB (2)
Chu y din (1), tacd:
RAI = Pg.OB, hay P = ^ . O B " AI
p Vdy, trgng lugng P freo d K ti Id vdd khotog each OB, hd sd ti Id bang - j -
_ R A I _ 2 a 5 _ ^ ^0 - OB " 20 ~ ^ ^-
3.16*. a) Xet vidn gach 4 nam frdn cfing. Nd chi ed thi tod ra ngoai vidn . gach 3 nhilu todt btog nfia ehilu
dai L cua gach : a^ = — L. Tilp
theoi dl hd hai vidn gach 3 va 4 nim cto btog tiii gidd han ngoai cfing cua dutog tde dung eua frgng ^,^^ ^ ^^
127
luc hd hai vidn gach 3 va 4 la mep phai eua vidn gach 2. Vi tri cua dutog do duge xae dito btog quy tde tdng hgp hai luc song song, cung chilu (btog toau, bang trgng lugng cua mdi vidn). Dutog nay ndm each mep phai cua
vidn gach 2 mdt doan a^ = J^- Tuong til, di hd ba vidn gach 2, 3, 4 nam
cto btog thi hgp luc cua ehung cd gidd han ngoai etog cua dutog tac dung ehi cd thi di qua mep phai cua vidn gach 1 dudd cung. Cung bang phip tfto hgp lue, ta cd thi xdc dinh duge khotog each nhd ra cua vidn 2 so vdi vidn 1
la a2 = 77 L. Cud'i cfing, frong tdm cfia hd 4 vidn gach each mep bto nhilu 6
todt chi cd thi ndm trdn dutog thtog dtog each mep bto mdt doan ai = ^L o
(xem Hinh 3.6G).
b) vay khotog each ^ = [ji'^'4'^'^'^ g j ^ " 24 ^ '
3.17. B dung (xem bai hge 27 SGK).
3.18. B dung. Hai lue dat vao qua edu.
3.19. C dung. Vi khi cto btog ta cd Pidi = P2d2 ; ma di < d2, do dd Pi > P2. 3.20. B dung. Cd thi tfto dugc dd dtog.
3.21. Chu y vai frd cua lue ma sdt gifla ngdn tay vdd cdy gdy va dp luc de ldn mdi ngdn. Su dich chuyin eua edy gdy phu thudc vao vi trf cud trgng tam eua nd dd'i vdi hai ngdn tay.
- Khi dich ngdn tay phai vl phfa tay trai, gia sfi ban ddu ngdn tay phai dich chuyin so vdd gay, cay gay dtog ydn so vdd ngdn frdi, thi :
+ Din mdt luc nao dd, cay gay se dtog ydn so vdd ngdn phai vd trugt ttdn ngdn ttai. + Tid'p theo, edy gdy lai dtog ydn so vdd ngdn frai va dich chuyin so vdi ngdn phai. + Qua tiinh lap lai luan phidn eho dlji khi hai ngdn tay cham nhau ma cay gay khdng rod.
- Nlu sau dd dich ngdn phai theo chilu ra xa ngdn frai thi cdy gdy ludn dtog ydn so vdd ngdn frai va se rod khi ngdn phai ra ngoai ddu gdy.
3.22. -Tai D phai ed lue ma sat du Ito dl gifl D khdng trugt. D frd thanh tdm quay cua vdt. - Dilu kidn cdn btog momen luc ddi vdd dilm D eho :
mga mga —^- = Fb, suy ra F = —2-
2 2b
- Dung thudc do a va b, tfi dd tfto duge F.
128
CAC DJNH LUAT BflO T O A N
4.1. B dung. Cfing ddng lugng, ndn vat cd khdi lugng tod thi vto tdc Ito. Khd'i lugng tod thi luc ma sat cflng tod, lai thdm vto td'e Ito ; do dd thdd gian chuyin ddng trudc khi dtog se dai hon.
4.2. D dfing.
4.3. Vecto B. Dua vdo ding thfic vecto: P2 - Pi = FAt, suy ra F cd hutog eua B.
4.4. Khi chim bay ldn, hgp luc N - P theo phuong thing dtog (N la phan luc cua thanh ngang dat ldn chan chim) tdc dung hutog ldn trdn gay ra bid'n thidn ddng lUgng. Ap luc tfi chto chim dat len thato ngang se Ito ban trgng lfic, do dd sd chi tfic thdd cua lfic k l ttog ldn. Ngugc lai, khi chim bay xudng, sd chi tfic thdd cfia luc k l giam (xem thdm bai tap 4.8).
4.5. Cdto quat cd cdu tao dang xoto, do dd khi quay tao ra mdt ludng khdng khf bi ddy vl phfa sau. Ddng lugng ma ddng khf mang theo vl phfa eudi may
, bay trong 1 s btog phto luc cua ddng khf tde dung ldn cato quat cua ddng CO gto vdd cato may bay va lam mdy bay chuyin ddng vl phfa trudc.
Nhu vdy, nguydn nhto chuyin ddng cfia mdy bay dung cdto quat la phan I luc tfi phfa ddng khdng khf bi cdnh quat ddy vl phfa sau tao thato luc keo
cfia may bay. Ddi vdi tau thuy, nguydn tic hoat ddng cua chan vit cung gidng nhu cdto quat cua mdy bay.
4.6. Chia dia thanh totog cap nguydn td cd khd'i lugng Am btog toau, nim ddi xtog qua tam frdn mdt dutog kfto bdt ki cfia dia. Vto tdc dai v = ror (r la khotog cdch tdd tdm dia) cua mdi nguydn td Am cd dd Ito btog toau, toung ed hutog nguge toau. Vi thi, tdng ddng lugng cua ttog cap nguydn td khdi lugng la btog khdng. Suy ra ddng lugng cua ca dia cung btog khdng.
4.7. Ap dung dmh ludt bao toto ddng lugng eho hd kin gdm prdtdn va hat a, ta cd :
mpVp = -nipVp + maVa
^ ^ M ! p i i > = ^>6^-lQ"\ -^-^0^ = 6,68.10- kg
MTVL10(NC)-A 129
4.8. a) Xe ehi chiu tac dung cfia frgng luc P
va phan lue N hutog vudng gdc vdi mat dudng. Chgn hd true toa dd xOy tou Hito4.1G.
Theo phuong ngang, tdng ddng lugng eua hi xe-dan duge bao toto vi khdng ed ngoai luc tac dung.
Chgn ehilu duong la chilu chuyin ddng ban ddu eua xe, ta vid't dugc :
MV - mvcosa = (M + ,m)u
MV - mv cos a u = M + m
Vdn td'e u cfia xe (cd dan ndm d frong) sau va cham ed phuong ngang va cd chilu tuy thudc ddu cua hidu MV - mvcosa. b) Gia thilt thdi gian va cham Id At. Theo phuong y, ddng lugng cua hd xe-dan se biln thidn vi cd ngoai lue tde dung. Ta cd ding thfic vl xung lugng cfia lfic :
FAt=Ap (N - P)At = 0 - (- mvsina) = mvsina Tfidd
Suyra ^ p ^ m v s m a ^ Q At
Kit qua frdn cho bilt N > P, tfic la dp luc vudng gdc cua xe ldn mat dutog Ito hon trgng lugng cfia xe. Cd thi todn xet thdm : nlu bdn vidn dan theo phuang nam ngang vao xe, tfic la sina = 0, thi ta lai cd N = P.
4.9. a) Bid'n thidn ddng lugng cfia khf phut ra frong 1 s : Ap = 1 300.2500 = 325.10"^ kg.m/s
b) Luc ddy (phto luc): - *'
Ap ^ 325.10^ ~ At ~ 1
325.10^ kg.mli = 325.10^ N
e) Sau gidy ddu tidn, trgng lugng tdn Ifia chi cdn btog :
F = (300.10^ -1,3.10^).9,8 = 292,7.10^* N Lue tdng hgp dat vao tdn Ifia tai gidy ddu tidn :
F - P' = 325. IO'*- 292,7. IO'* = 32,3.10'*N Luc nay chfnh la luc ddy tdn Ifia di ldn theo phfiong thing dfing.
130- 9-BTVL 10(NC)-B
4.10*. Ddng lugng cua hd leh - van dugc bao toan theo phuang ngang, ndn :
mvgcosa = Mu (1)
frong dd Vg la vto tdc cfia Ich va u la vto tdc cua vto diu tfto ddi vdi mat nudc ndm ydn. Dl Ich toay tdd mep eudi cua tdm van, cto thoa mto dilu kidn :
L - UT = (vgeosa)T (2)
vdd T la thdi gian tody eua Ich. Thay x = — (dung kit qua bai toan g
chuyin ddng cua vdt bi nem xidn, bai 18 SGK) vao (2) va giai hd phuong trinh (1) va (2) se duge :
Vn = gL
fm ^ — + 1
^M sin 2a
4.11. Ggi vto td'e eua thuyin dd'i vdi bd la v, vto tdc cua ngudd dd'i vdi thuyin la u. Chgn chilu duong la ehilu chuyin ddng cfia thuyin. Dinh luat bao toan ddng lugng dp dung cho hd kfn ngudi - thuyin :
Mv + m(v - u) = 0
Chfi y rang ede vdn tdc diu phai tfnh frong cung mdt hd quy chilu (bd hd), do dd vdn td'e cfia ngudd dd'i vdi bd la v + (-u) = v - u.
u M + m Suy ra : — =
V m
Ti sd cdc dd ddd eua ngudi vd thuyin cung bdng ti sd eae vto td'e : u _ / _ M + m V s m
Khi ngudd di hit chilu dai / eua tiiuyln thi tiiuyln etog dich chuyin dugc dd ddis:
m , 60.2 _ , s = / = = 0,6 m
M + m 140 + 60 Kit qua la mui thuyin chua cham dugc bd. Cd thi lap luto each khdc. Mud'n eho thuyin cap duge bd thi dd ddi cua thuyin phai dung btog 0,75 m. Suy ra :
, M + m 140 + 6 0 - „ ^_ / = s = —--—.0,75 = 2,5 m
m 60 131
tfic la, ngficd phai di dfige qutog dudng 2,5 m trdn thuyin, ttong khi eWlu dai eua thuyin chi la 2 m. Vi vay, khi ngudd da tdi dudi thuyin thi mui thuyin vto chua cap bd duge.
4.12. B dung. ^
4.13. D dung. Khi ngudd mang vat di ngang, khdng cd edng co hgc thuc hidn vi luc do tay ngudd gifl vat cd dd Ito btog ttgng luc va ed phuong vudng gdc vdd dd dcd.
4.14. Nd'u khi ntog hdm ldn dd cao h vdi vto tde biln thidn thi khdng toihig phai tdii edng dl thtog edng eua trgng luc ma cdn dl truyin cho vdt gia tdc a khdng ddi.
A = mgh + mto
Chi khi ntog vdt vdi vto td'e khdng ddi (a = 0) thi edng phai tdn mdd khdng phu thudc vto td'e.
4.15. Ba luc Fi,F2 va Fj cd cung mdt hito chilu ttdn phuang cua dd ddd AB, do
dd cdng thuc hidn diu btog toau..
4.16. Cdng eua ngudd : 600 J, eua may : 30000 J.
Cdng sudt eua ngudd : 100 W, cua may : 7 500 W.
4.17. A = mgh = 200.9,8.7,5 = 14700 J.
A 14700 9= — = —^ = 2940 W « 2,9 kW.
t 5
Dfing ddng co 3,5 kW la thfch hgp. Ddng eo 1 kW khdng dfi kha ntog ntog vdt. Ddng cd 6 kW se ntog vdt ldn qua nhanh.
4.18. Khi thang may di ldn, ddng co phai thue hidn cdng dl thtog frgng lue va luc can.
g' = Fv = (P + Fc)v = <1800.9,8 + 4 000)3 = 64 920 W « 64,9 kW
4.19. a) Ggi F la luc nang cfia cto edu. Theo dinh luat n Niu-ton :
F - P = ma
F = m(g + a) = 5 000(9,8 + 0,5) = 5 000.10,3 = 51500 N
b) Cdng sudt S'= Fv = Fat = m(g + a)at = Kt.
Thaysd: K = 5 000.0,5.(9,8 + 0,5) = 25 750 W/s
vay : 9^=25750^
132
Kit luto : Cdng sudt cfia cto cdu biln ddi vdd thdi gian t theo mdt ham bdc todt.
c) Tfi kit qua ttdn, vi cdng sudt S* biln ddi diu theo thdd gian, ndn ta cd thi tfto cdng do luc ndng cfia cdn edu thuc hidn ttong khoang thdd gian tfi 0 din t btog cdng thfie :
, ^ Kf Kt A = g ' , , . t = - . t = - ^
25 750 9 Thay sd: A = = 115 875 J.
4.20. a) F = 3000 N.
b) A =18.10^ J.
4.21. Cdng cua lite keo F la : A = Fs = 15.0,5 = 7,5 J
Trutog hgp cd ma sdt, cdng toan phdn, bing tdng cdng A cua luc keo F va 2
cdng Anjs cfia luc ma sat (cdng am), giam cdn — • Suy ra :
A _ I A I - —A ^ l^msj ~ 3 '^
, 1 75 |Ams| = ^A = A _ = 2 , 5 J
L u c m a s a t : F „ , = l ^ = g = 5 N .
F 5 Hd sd ma sat trugt: ^t = - ^ ^ Tn ^ ^'^'
V 4 2 4.22. a) Gia tdc cfia conteno: a= - = -=2mjs
Ggi F la luc ntog cfia cto cdu, ta ed :
F + P = ma F - P = ma F = P + ma = m(g + a).
_ , , . at^ 2.4 . Dd ddi s = — = - ^ = 4 m.
133
Cdng eua lite ntog thuc hidn
A = Fs = m(g + a)s
= 2,5.10l(10 + 2).4 = 120.10^ J = 120 kJ
Cdng sudt trung bito eua luc ntog eua cto edu
t 2
b) Cdng sudt tfic thdd :
9'^^= — = 120il0_ ^ 60.10^W = 60kW
Giai doan 1 : 9>i2 = / J ' = 2066 W.
tp= Fv = m(g + a)v = 2,5.10l(10 + 2).4 = 120.10^ W = 120 kW
4.23. a) Cdng cfia trgng lue :
Ai2 = mg(hi - h2) = 230.9,8.(0,3 - 1,4) = -2479,4 J
A23 = mg(h2 - hg) = 230.9,8.(1,4 - 1,8) = -901,6 J
b) Cdng sudt cua luc co bap (cdng duong):
2479,4 1,2
- Giai doan 2 : 9 23 = ^ ^ = 450,8 W.
4.24. Vto td'e eua qua bdng ddi vdd hai hd quy ehilu la khac nhau. Theo dinh If edng vdn td'e :
—* —»I —*
V = V + u
trong dd v la vdn tdc cua bdng ddi vdd mat ddt, v' la vdn tdc cfia bdng ddi
vdd toa tau, va ii la vdn tde cfia tau ddi vdd ddt. Nhu vdy, ddng ntog cua
, mv qua bdng do trong toa tau la Wj = , cdn do bod ngudi quan sat ttdn
mat ddt la W^ = va se khae toau.
Tuy nhidn, vide chgn hd quy ehilu khac nhau khdng anh hudng din tfto chd't ddng nang la dai lugng vd hutog, vi
(v'+u)^ =v '^+u^+2v ' i i
Tdt ea cdc sd hang vto diu la tfch vd hutog.
134
2 2
4.25. Theo dito If ddng ntog A12 - —;^ — - r^ . vdi A la tdng cdng cfia cdc
ngoai lite, m la khdi lugng cua ngudi va thuyin. Trong ca 2 trutog hgp Vi = V2, do dd A = 0. Tuy nhidn, cto phan bidt:
- Khi thuyin dtog ydn (so vdi bd), du khdng ed edng co hge dugc thue hidn, ngudi cheo thuyin vdn tdn cdng tidu hao ntog lugng co bap. Cdng ndy dung dl thang cdng cfia ddng chay.
- Khi thuyin ttdi diu theo ddng nudc, ngudi khdng phai cheo ndn khdng tdn mdt edng nao. Nhitng bay gid cdng co hgc dugc thue hidn vi da cd dd ddi cua thuyin, cdng cua ddng chay la edng phat ddng (cdng duong) cto bang vdd cdng cto (cdng am) do luc ma sat cua nudc ddi vdd thuyin.
4.26. C dfing.
4.27. C dung.
Ap dung dinh luat bao toto ddng lugng cho vat ban ddu nam ydn, ta cd :
Vl
0 = Mvi + 2Mv2, suy ra V2 = —^
Ddng ntog cfia
Ddng ntog cfia
Ddng ntog cfia
Suy ra:
4.28. a) 450 kJ.
4.29. a) 4.10^ J.
4.30. a) 223.10"^^ J.
vdt 1
vdt 2
2 vdt
Wdi^
dl 2
/ , , A2
2M
W d , =
• 1
2 Mv?
4
. „ , Mv? Mv? 3Mv? w , = i-+ L = L ' ' 2 4 4
_2W,
3
b) - 400 kJ.
b)-25.10'*N;333kW.
b) 5.10^^1
2
c)-5000N.
e) 27.10^^1.
4.31*. a) Dd thi d = f(v) khdng la ham bdc todt vi d khdng ti Id thudn vdd v.
135
b) Dd thi d = f(v^) la ham bdc todt tiieo v^ va ed till vilt dfidd dang d = Kv . Khi ve, chu y chgn ti Id thfch hgp trdn cac true. Tim gia tri cua K tfi dd thi:
Y nghia cfia
tacd :
Suyra
K:
K = 4- « 0,094 v^
: Tfi dito If ddng nang 2 2
^ , ^ mv , i„j | mv Fd = 0 ,hay Fd =
2 ^ ' ' 2 . m 2 1 2 v^
d = — V =——\ = — 2F 2— 2a
m
2a Ta thdy K cd y nghia la nghich dao eua gia tdc, do dd don vi cfia nd trong
S^ - 1 2 hd SI la — hay m .s
m 4.32. A dung.
20 m^ n
Thi nang trgng trutog
4.33. 20 m^ nudc cd khd'i lugng btog 201 = 2.10'* kg.
Wt = mgh = 2.10^9,8.80 = 1568.lO"^ I chuyin thato cdng trong 1 s se tuong tog vdi edng sudt:
9*= 1568.10"^ W
Hidu sudt X = 0,6, do dd edng sudt ed fch la :
9" = 0,6.1568.10^* = 9 408.10^ W = 9 408 kW
4.34. Chgn chilu duiong cfia true z hutog ldn trdn.
a) W. - W, = mg (zi - Z2) = 500 - (-900) = 1400 J
1400 ,.,^
b) Tai vi tri tog vdi mfic khdng cfia tbl ntog, z = 0. Do dd, thd ntog tai vi tri Zi la:
W =mgzi = 5 0 0 j ^ z i = | ^ = 17,0m 1 j . y , o
136
Vi tri ban ddu cao ban vi tri gdc 17 m. Cd thi kilm lai thi ntog tai mat ddt:
Wj =mgZ2 = - 9 0 0 J - > Z 2 = - | ^ =-30,6m
tiic la mat ddt thdp hon vi tii gdc 30,6 m.
c) V = 72gzi" = V2.9,8.17 = 18,25 m/s.
4.35. a)-1,57 J.
b) Thi ntog tang 0,21 J. Thi ntog cua vato dugc xdc dito btog thi ntog tai vi tri trgng tdm cfia vato.
4.36. Thi nang ttog 173,2 J.
1 c\~ 4.37. a) Ddi don vi: p = 0,8 g/cm^ = 0 , 8 - ^ = 800 kg/m^
10-^ Khdi lugng cua tdm gd :
m = pV = 800.1,8.0,5.0,04 = 28,8 kg
; b) Trgng tam duge ntog thdm dd cao :
Ah = h + - - — = 1,35 m 2 2
Dd tang thi nang :
AWt = mgAh = 28,8. 9,8. 1,35 = 381 J
4.38. Dan chi chiu tac dung cua cdc luc thi la ttgng lue va luc dto hdi, do dd co ntog cfia nd dfige bao toto.
Co ntog cua dan btog thi ntog ttgng trutog d dd cao Ito todt:
Wf = mgh
Chfnh thi nang dan hdi cua Id xo bi nen da chuyin thanh co nang nay. Ggi k la dd cfing cua Id xo, ta cd :
W,h = Wt
kx^ = mgh
2
^ ^ 2 n ^ ^ 2 A 0 3 ^ ^ 9 3 0 N / m x^ (0,06)2
4.39. Co ntog toto phto cua hd Id xo - ddu bfip bd bao toto vi hd chi chiu tae dung cfia pde lite thi la ttgng lue va lue dto hdi.
137
Chgn mfic khdng eua thd ntog ttgng trudng tai vi tri ban ddu cua Id xo bi nen. Khi Id xo da dto hit va ttd vl frang thai khdng biln dang, ih€ ntog dan hdi cua Id xo chuyin hoto toto thanh ddng ntog va thi ntog ttgng trutog eua ddu bfip bd. Ta cd dang thfic :
k/2 mv^ 2
+ mg/
.. - mv^ kf
Thay sd : W^ = ^^'^^•'^ ^ _ 0,05.9,8.8.10'^ « 0,22 J.
4.40.0,06251; OJ; -0 ,05 1; -0,0375 J.
4.41. D dfing.
4.42. C dung.
4.43. D dfing. Ggi Vg la vto tde ban ddu cfia vdt, v la vdn tdc khi cham ddt.
Ap dung dito ludt bao toto co ntog :
mvg mv^ mgh + — ^ =
^ 2 2 hay 2gh = v 2 - v J (1)
Do khdng mdt mat ntog Ifigng khi vdt cham ddt ndn vdt nay ldn vdd ciing 3
vdn tdc V va dat tdd dd cao h' = — h. Ta cd :
v^^2gh' = 3gh (2)
Thi (2) vao (1) se dfige : Vg = ^gh.
4.44. Ap dung dinh ludt bao toto ddng lugng di tiin vdn tdc cfia gia treo (cd hfitog ngfige vdd hfitog bay ngang cfia chim). Ap dung tilp dinh ludt bao toto eo ntog, ddng nang chuyin thato thi nang, tfi dd suy ra dd cao ma gia tteo dugc ntog ldn : h = 2,4 cm.
4.45. Gia thilt bd qua cac luc cto. Theo dinh luat bao toto co nang, thi ntog cue dai cfia con lie dugc gifl khdng ddi. Dg dd, sau khi vfidng ddy, con lde vdn ldn tdd dd cao btog dd cao ban ddu ma khdng phu thudc vdo sfi thay ddi chilu dai eua ddy.
4.46. Cdng : A = Fh = 30.5 = 150 J.
138
Thi ntog ttog : Ph = 10.5 = 50 J.
Ddng ntog ttog: 150-50=1001.
4.47. Lfiu lugng 3 m /s tog vdd khdi lugng nude m = 3 000 kg chay qua tuabin frong 1 s. Tuabin sinh cdng do cd biln thidn ddng ntog va thi nang cua khd'i lugng nudc nay.
Biln thidn co ntog cua nudc sau khi chay vao tuabin :
AW = W2-Wi =(W^2 + Wt2)-(W,j +Wtj)
= (Wd2-Wdj)-(Wej.-W,2)
Thay sd : W^ ' ^di = y (^2 " vJ) = ^ ^ (4 - 36) = -48 000 J
Wt - Wt2 = mg(hi - h2) = 3 000.9,8.1,5 = 44100 J
Suy ra AW = - 48 000 - 44100 = -92100 J.
Co nang cua nude gitoii dl chuyin cho tuabin sito edng, bing 92100 J (ttong 1 s). Hidu sudt cua tuabin la 0,8, vdy cdng sudt ed fch cua tuabin la :
9" = 92 100.0,8 = 73 680 W
4.48. a) 260,2 J. b) 14,87 m/s.
4.49.-586 080 J.
4.50. a) 10 m/s." • tv - b) 5,1 m. c) -158,75 N.
4.51. Vi chuyin ddng khdng cd ma sat ndn phan luc N cua mat dd'c tac dung ldn vat ludn vudng gdc vdd phuong dd ddd va do dd khdng thuc hidn cdng. Luc
duy todt thuc hidn edng la ttgng luc P ndn ta cd thi dp dung dito ludt bao toto CO ndng dl giai. Chgn mfic khdng cfia thi ntog tai mat ndm ngang.
Tai vi til xudt phdt: W^ = 0, Wj = mgh
Tai chto ddc: W. = ^ . W. = 0 02 2 2
Theo dito liidt bao toto eo ntog :
Wdi + w.j = W, + w .
139
niv^ nen : mgh =
V = .72gh = ^2.9,8.1 = 4,4 m/s
Nhdn xet: Khdng thi giai btog phuong phdp ddng luc hoc vi
- khdng bid't dang eu thi cua quy dao ;
- thato phdn luc theo phuong chuyin dcd ludn thay ddi theo tiing vi trf.
4.52. a) 11760 J.
b) 8 624 J ; 6,57 m/s.
4.53. Thid't ldp hai phuang trito tai dilm B (xem Hinh 4.14).
Theo dito ludt bao toto co nang :
mv ,,, mgh = m g . 2 r + — - (1)
Theo dito luat H Niu-ton :
mv^ mg = , (2)
Tfi(l)va(2),tacd: mgr
mgh = 2mgr + - ^
Suy ra : h = —
4.54. Lto lugt dp dung dito ludt bao toto eo ntog eho ttog vi tri.
.2
a) mgh^ = mvg 2
VB = ^2ghj^ = V2.9,8.0,52 = 3,2 m/s = v^
mghA = mghc+ -2
Vc = pgiK -r he) = V2.9,8.0,22 = 2,1 m/s
rnvg 2
m v
mghA = mghE+ ^
Vi h^ = hg, ndn suy ra Vg = 0
140
b) Vdn tde cua xe tai dilm C du dl xe khdng rdd quy dao duge xae dinh tfi dilu kidn:
•2 - ' h . mg = ^ . hay V = Vgi = ^ g ^ = ^9,8.0,15 = 1,2 m/s.
Vdy, vdd vdn tde v^ = 2,1 m/s, xe khdng bi red khdi quy dao d dito C cua vdng ttdn. Sau khi tdd E, xe dtog lai va chuyin ddng ttd xudng, tid'p tuc qua D, C, B rdi tdi A nlu tou ma sat la khdng ddng kl.
4.55. B dfing.
4.56. a) Theo If thuylt va cham dto hdi xuydn tdm, qua cdu 1 se truyin hoan toto ddng lugng va ddng nang cho qua cdu 2 va hidn tugng trao doi vto tdc xay ra : qua cdu 1 dtog lai, cdn qua edu 2 cd vto td'e dung bdng vto tde cua qua cdu 1. Dd'n lugt qua cdu 2 tilp tuc truyin ddng lugng cho qua cdu 3 va vdn tdc lai dugc trao ddi. Qua trito tilp tue tou vay eho tdd qua edu ngoai cfing, nd nhdn dugc vdn tdc dung bang vto tdc cua qua cdu ddu tidn va vi thi se dugc ndng ldn din mdt gdc Idch bang gdc lech ban ddu cfia qua cdu 1.
b) Nlu klo Idch ddng thdi ttog nhdm 2, 3,... qua cdu va tha cho va cham vdd cac qua edu cdn lai, thi ddng lugng dugc truyin tdd cdc qua cdu ngoai cung. Nhtog qua cdu nay se chuyin ddng thato nhdm 2, 3... qua va cung dugc ntog ldn vdd gdc Idch ban ddu.
4.57. a) 400 m/s. b) 780 J.
.4.58. Vto td'e cua bua khi cham cgc : v = •yJ2^ Ap dung dito luat bao toto
ddng lugng vdd va cham mim :
mv = (M + m)V. suy ra V = i H ^ L ^ (1) M + m
Cdng cua luc cto cua ddt btog dd giam co nang cfia hd bfia - cgc :
|Fs| = AW = M ± E ) Y ! + (M + m)gs (2)
Thay till (1) vao (2) va biln ddi, se dfige :
1 1 m eh . , , F = , . , ^ , + (M + m)g ' •' (M + m)s
Thay sd, ta dfige : |F | = 318500 N.
141
4.59J Tdt ea cac vdn tdc diu cfing phfiong, cfing chilu. Ap dung dinh ludt bao toan ddng Ifigng cho hd kfn hai xe :
miVi + m2V2 = (mi + m2)v Suy ra:
(mi + m2)v - miVi m2
Vo =
4.0,3 -1,5.0,5 2,5
= 0,18 m/s
f 2 2^ miVi . m2V2
\ 2' 2,
Dd giam ddng ndng toto phto :
AW, = W ^ - W ,
_ (mi + m2)v^ ~ . 2 :,
Thay sd, tim dugc :
AW4 = -0,048J
4.60.J3ivta ddng lugng va ddng ntog eua mdt vat cd cdng thfie liin hd : „2
W , = ^ ^ 2m
vat 1 cd khdi Ifigng m va ddng lugng p thi cd ddng ntog :
P vat 2 CO khdi lugng 2m va ddng lugng — thi cd ddng tidng :
W, (p/2)'
"2, 2.2m 16m Ddng ndng cua hd trudc va cham la :
w, = w.+w, = P 1 + ^ = - ^ P 1
^ •*! ^^ 2m 16m 16 m
Sau va cham, vdt 1 cd ddng lugng ^ , tfic la cd ddng ntog :
w; = (p/2)' p '
2nu 8m
142
vat 2 ed ddng lugng p, tfic la cd ddng ntog :
W' •= ^2 2.2m 4m
Ddng ndng cua hd sau va cham la : „2 „2 o „2
W d = w : + w : = - P - + - P - = l P -
Lugng ddng nang tidu hao chuyin thato nhidt:
W4-W^ = 16 m 8 m 16 m
4.61. A dfing.
4.62. B dung.
Gia tdc ttgng trutog trdn bl mat Trdi Ddt la g: GM
R2
Gia tdc ttong trutog trdn bl mat Thidn Vuong tito la g' = ——.
R va R' la bdn kfto tuong tog cua trdi Dd't va Thidn Vuong tito.
Ti sd:
g
M' r R ^ '
M R ' j = 1 5 . ^
16
4.63. Luc hdp dto ddng vai ttd luc hutog tam gifi cho vd tinh khdi lugng m chuyin ddng trdn quy dao. Ta cd :
g mMp (Rj) + h)? RD + h
mv 2 , suy ra v
GM D (RD + h)
Trdn mat ddt, ta cd :
Tfidd
g = GM D R D
2 g^D
Re+h
143
Suyra
Thaysd
v = R D , R o + h
v = 6370. 9,8.10 -3
6370 + 670 « 7,5 km/s.
4.64. Do cd luc cto cua khf quyln, vd tinh ddn dto ha thdp dd cao va ban kfto quy dao giam. Nlu vdn coi quy dao la gdn ttdn, ta ed :
.2
Tfidd
mv ~R
V =
GmM
GM R
vdd R la ban kfnh quy dao.
tfic la V tdng khi R giam.
Cdn ed thi giai thfch mdt each khac : Khi R giam thi quy dao chuyin dto thtoh dutog xoay dc. Lfic dd, hinh chid'u cua lite hdp dto ldn phfiong cua vdn tdc la khae khdng va lfic hdp dto sinh cdng lam tang vto tdc (Hinh 4.2G).
Phep tfnh cho thdy dd tdng vto tdc chtoi hon dd giam thi nang, do dd co nang toan / phdn cua vd tito vdn giam (vi ed edng cto [ cfia lue ma sat khi quyln). \
Vdn tde eua vd tito tang lidn tuc, do dd khi di vao ldp khf quyln day dae bao quato Trdi Ddt, vd tito se bi bdc chay.
Hinh 4.2G
4.65. a) 86400 s. b) 463 m/s. e)0.
4.66. a) 780.10"* km. b) 1,52 don vi thidn vto.
4.67*. Cd thi vdn dung dito ludt bao toan ddng lugng dl giai thfch. Ngudd dd di tfi ddu dd'n cud'i thuyin rdi dung ddy thtog do dd dai / eua thuyin vd khotog dich chuyin s cfia thuyin so vdd bd. Tfi dd tfnh duge khdi luOng
eua thuyin m' = 60
144
4.68. Ggi: h la ehilu cao cua mat nghidng ; / la chilu dai mat nghidng.
- Nhidt lugng toa ra khi khdi gd trugt trdn mat nghieng (khdng cd vto tdc 2 J.2
ban ddu) se la : Q = mgh . vdd v^ = 2a/; / = — 2 2
( 2e\ - Suy ra : Q = m gh — .
\ t^ ) Tha cho vat trugt tfi dinh mat nghidng dd'n chan mat nghidng. Do h va / bang thudc, do t bdng ddng hd se tito dugc Q.
4.69. -"Treo hai vidn bi vao cung mdt dilm vdi hai sgi day dai btog nhau.
- Nang vidn bi sap ldn dd cao hi (so vdd dd cao ban ddu sao cho day treo
nam ngang) rdi tha rod.
Sau khi va cham khdng dan hdi, ca hai se dfto vao toau va len tdd dd cao h2.
AE (M + m)gh2 - Suy ra : — =
E mghj trong dd : + Do hi, h2 va dutog kinh vidn bi bang thudc.
+ m la khd'i lugng vidn bi sap (tfnh dugc tfi khd'i lugng ridng da cho va dutog kfnh vidn bi da do).
+ M la khdi lugng vidn bi sit (tfnh dugc nhd tra bang khd'i lugng rieng cua sat va dutog kfnh vidn bi da do).
lO-BTVL 10(NC)-A 145
CO HOC CHnt LiAl
5.1. cauC.
4 D^ ^ 4 0 03^ 5.2. m = pV = P ^ T : ^ = 7,8.10^^.3,14.^^ = 0,11 kg.
3 2 3 2 m 131 3 3 ' ' '
5.3. p = T7 = —^—T = 10,48.10 kg/m Dd'i chid'u vdd Bdng khdi luang rieng V 0,05^
ciia mgt sd chdt (xem phu luc 2 SGK) thi dd la khdi lugng ridng cua bac (trong SGK la 10,5 g/cm^).
5.4. p = 1 1 ^ = - 5 0 : 9 ^ = 0,39.10^ N/m^ S 3,14.0,02^
5.5. p = Pa + pgh = 1,01.10^ + 1,0.10^9,8.30 = 3,95.10^ Pa.
5.6. FJ = Fl | 2 . = 15 000. - ^ = 225 N. ^ ^ Sl 200
5.7. a) Ta cd : ViSi = V2S2, hay V2 = Vi — = —— = 10 m/s. S2 5
b) Ap dung dito luat Bec-nu-li eho hai vi trf 1 va 2 :
1 2 1 2 Pl + 2"P i = P2 + -j^^i
suy ra : Pl = P2 + -p(v^ - vJ.)
= 2.10^+ -.1.10^ (100-25) = 2,375.10^N/m^
c) A = vS = ViSi = 5 m/s.0,001 m = 0,005 m^/s = 0,3 m^/min.
5.8. a) A = 1,4.10"" m^/s = SgVg = SiVi (1)
trong dd Sg, Vg, Si, Vi ldn lugt la tilt didn va vdn tdc d mat tiiodng vd d Id day bito.
Tfi cdng thfic (1), bid't tilt didn mat thoang va tilt didn Id d day bito, ta tfto dugc vdn tdc tai totog nod dd.
146 10-BTVL 10(NC)-B
Kit qua la Vg = 17,8.10 ^ m/s ; Vi = 1,4 m/s.
v^ •- v' b) vf - Vg = 2gh, suy ra h =^——2- « 0,1 m (ldn din nfia bito).
•^g
5.9. Cdt rfigu vang cao h (m) tao ra mdt dp sudt btog dp sudt khf quyln. Ta cd :
P = Pa = Pvanggh
Bilt p ang = 0,984.10^ kg/m^ ; g = 9,8 mii ; p^ = 1,013.10^ N/m^ ; ta tfto dugc h :
h = 10,50 m
5.10. Chilu cao cua cdt thuy ngan d ap sudt tidu chuto la :
_ Pa 1,013.10- pg 13,59.10^9,8
0,76 m
Chilu cao cua cdt thuy ngto luc sdp cd bao la hi = 0,760 - 0,020 = 0,740 m.
Ap suat tuong tog bang : ^ ' ^ Q I ' ] ^ -0,74 = 0,986.10^ = 9,86.10^ Pa.
5.11*. a) Ap dung dinh luat Bec-nu-li cho hai dilm :
Pl + 2P^1 = P2 + 2'^^^ + pgh ' (1)
ttong dd h = 0,5 m la dd chdnh chilu cao gifla hai dilm. Mat khae, ta cd :
ViSi = V2S2 (2)
trong dd Si va S2 la tjlt.didn ngang tai vi tri 1 va vi tri 2. Tfi (2), ta cd :
Sl 0,8 J,.-, V2 = v i - ^ = vi-—j = 4vi (3)
'=»2 0,4 Thay (3)vao(l), taduge :
- p ( v | - v f ) = P i - P 2 - p g h
^p.l5vf = (2,5 - 1,5). 10^ - 10 .10.0,5
2 (10^^-0,5.10'^). 2 v, = 15.10^
147
VJ = 0,816 m/s
V2 = 4vi = 3,264 m/s
b) Luu lugng ddng chay btog :
A = 0 , 8 1 6 . 7 r f ^ l = 4,09.10"^ m^/s
5.12. Dd eh'dto dp sudt btog :
16000.9,8 , _ „ ^ iQAin3po Pd - Pt = 2 40 " " '
Pd = Pt + 1,96.10^ = 70.10^ + 1,96.10^ = 71,96.10^ Pa
5.13. Do chdto hai mfic thuy ngdn d hai toato btog dp sudt ddng, ta cd :
2pv^ = PHggh
V- fcjlgj- 2-13,6.10l9,8.0,05^^^3^^
V P V 1.25
5.14*. Ap dung dito ludt Bec-nu-li cho mdt dilm nam trdn mat thoang va mdt dilm d mieng d'ng xiphdng, ta cd :
pgh = 2pv^
hay V = 72gh
5.15*. F = 7n-2(p - p) = 7n-2(p - 0,lpa) = 0,9pa7n-2 5 2
Thay sd : p^ = 1,013.10 N/m ; r = 0,3 m vao cdng thfic trdn, ta dugc : F = 25 765 N.
, , ^ 2Ap 2.180 ,^^^^ ,
V « 388 km/h.
5.17. Ap dung cdng thfic (43.1), bai 43 SGK, ta tfto dfige vdn tdc Vj tai tid't didn Si:
I 2S2AP ^ I 2.0,1^.1500
^ ~ "y p(Sf - S^) ~ V 1,0.10^(0,2^ -0,1^) ~ ^ ^
Luu lugng nudc trong d'ng ddng btog :
A = ViSi = 1.0,2 = 0,2m^/s
148
Hinh 5.8G
5.18. Cdu A.
5.19. Cdu D.
5.20. Cdu D.
5.21. -Di dng chfl U thing dtog.
- Dd nudc vao d'ng chfl U.
- Dd thdm ddu vao mdt toato bdn phai dng chfl U.
- Mat thoang cfia hai toato se chdto Idch, bdn cd ddu se cao hon (Hito 5J8G).
-Ldp bilu thfic tfnh dp sudt tai:
+ Dilm A (mat phto cdch ddu va nudc),
tacd:pA = Pa + Pighi.
+ Dilm B (cung dd cao d nhdnh bdn kia), ta cd : pg = Pa + P2gh2-
Vi PA = PB' suy ra : Pi = P2:j^-
Do hi va h2, bilt P2 se tfto dugc pi (khdi lugng ridng eua ddu).
5.22. -Do thcd gian t dl nudc chay ddy cdc (dung ddng hd).
- Dfing thudc do kfch thudc ede (dutog kfnh trong D va chilu cao h), tfto
dung tfch V cua cdc : V = Sih.
- Do dutog kfnh trong d cua vdi nude, tfnh didn tich tilt didn (bdn trong)
S2 cua vdi nudc.
- Ta cd V = Sih = vS2t, tii dd vdn tdc nudc chay ra dfige tfto theo edng thfic :
V = D^h
d^t'
149
CHnt KHI HM
6.1. Ddu tien mudi hod tan trong nudc. Mdt do phto tfi mudi d chd tha hat mudi cao hon chd khac ndn phto tfi mudi khulch tan din nod cd mdt dd phto tfi mudi thdp hon, cho dd'n khi mdt dd phdn tfi mudi mgi chd tou toau.
6.2. Mdt do phto tfi d trang thai long lto hon rdt toilu (khotog mdt nghin lto) mat do phto tfi d trang thdi khf. Su khulch tan ra xa cfia mdt phto tfi nao dd trong chd't long didn ra chdm chap hon la vi phto tfi nay va cham toilu ldn hon vdd ede phto tfi khdc so vdd khi nd khulch tan trong chdt khf. Mat khdc, su lidn kit gifla cdc phto tfi d ttang thai ldng cung cto trd su khulch tan.
6.3. CauD. 6.4. Khd'i lugng mol cua vtog la 197 g/mol, vay lugng ehdt eua thdi vtog nay
, . 62300 . , , . , bang : « 316 mol.
197 6.5. CauC. 6.6. «29g/moL
Huang ddn : Tfi phuang trito Cla-pd-rdn - Men-dd-ld-ep pV = —RT, ta
suy ra _ m _ p|Li
^~ V ~ RT nRT 1 2Q 8 31 273
tfi dd i = ^— = '- ' / = 0,02889 kg/mol« 0,029 kg/mol P 1,013.10^
6.7*. Trutog hgp D.
Hudng ddn : Dl tfto lugng chd't ta cto bid't hai dfl kidn, dd la khd'i lugng ridng va khd'i lugng mol. Cac dfl kidn nay tim d Bdng khdi luomg rieng cua mgt sdchdt (xem phu luc 2 ttong SGK) va d Bdng tudn hodn Men-de-le-ep. Gia su ta tfto lugng chdt cua 20 cm graphit. Lugng graphit nay cd khdi lugng la : 20 cm .1,6 g/cm = 32 g. Cto cfi vao Bdng tudn hodn Men-de-le-ep, ta bilt khd'i lugng mol cua cacbon (graphit) la 12 g/mol, vdy sd mol cua 32 g
32 graphit la — « 2,7 mol.
150
6.8. Sd phto tii mudi cd ttong 0,003 g mudi la : N = N^ ^ ^ =31.10^^ phto tfi. 58,5
Sd phto tfi mudi cd frong 5 em^ nude mudi la: 5.--f——- = 1,55.10^ phto tfi. { 10 000
6.9. 9.10^ m; 225 ldn.
6.10. 60 N ; 40 N.
Vi hai bdn pit-tdng diu ed khf ndn ta chi tfto luc gay ra bdi su chdnh Idch dp sudt. Luc dich chuyin pit-tdng dugc suy ra tfi su chdto Idch dp luc cua khf d hai bdn pit-tdng tog vdi vi trf cudi cua pit-tdng trong mdi trutog hgp. Sd dl ta phai tfnh ddi vdd vi trf cudi cua pit-tdng la vi su chdto Idch dp lue tang ddn.
6.11*. Khi dl pit-tdng tu do thi pit-tdng dich chuyin sang phai vi dp sud't cua khf bdn trai lto hon. Ggi X la khoang dich chuyin cua pit-tdng „ \l ^ (Hito 6.1G) va ap dung dito luat B6i-la-Ma-ri-dt cho mdi lugng khf d hai bdn pit-tdng, ta vid't:
/>/>//////>//^//;
Pi2S = P
P2 2^ = P (h
V
+ x
- X
(1)
(2)
' • . . . D . .'• I 1 -
.•.•'•.••.>'••.•.V.••...••|••'.•.•
////////T
W .* '
Hinh 6.1 G
frong dd Pl va P2 la dp sudt luc ddu cua khf ben frdi va khf ben phai; p la dp sud't cud'i cua cac khf, dp sudt nay gidng toau khi pit-tdng dtog cto btog.
Thay pi = np2 va giai hd phuong trito frdn ta tim dugc : x = — —.
6.12. Ta ve dutog dtog tfch bdt ki Vi (Hito 6.2G), dutog nay cat eac dutog dtog toidt tai cdc dilm 1 va 2 tog vdd cdc dp sudt pi va pj. Vi dutog dtog tfch Vl tog vdd cung mdt lugng khf ndn theo dinh ludt Sac-lo tiii T2 lto hon Tl vip2ltohonpi.
151
6.13. Ve mdt dutog ding nhidt bdt ki Ti (Hinh 6.3G),
dutog nay cdt cdc dutog dtog dp tai cdc
dilm Pl va P2. Dutog ding toidt fing vdi
cung mdt lugng khf tuto theo dinh ludt Bdi-la
- Ma-ri-d't, ndn piVi = P2V2. Vi V2 > Vi ndn
Pl > P2. Dutog 1 tog vdd dp sudt cao hon.
6.14. Dutog ndm dudd tog vdd thi tfch lto ban
(Hinh 6.4G). Ldi giai tuong tu led giai trong
bai 6.13.
6.15. AV = 1,3 lit. Vi khd'i lugng khdng khf trong qua edu khdng thay ddi ndn ta cd thi dfing
pV phuong trito frang thai ^—- = hdng sd.
6.16. cau D.
pV Hudng ddn : Dfing cdng thfic ^^ = htog sd.
6.17*. 1,871ft.
Hinh 6.3G
P2
Pi
i
e
'Vyi
Vi
• -
' 1
Hinh 6.4G
2 g khdng khf d dilu kidn chudn ed thi tfch la : « 1,55.10 m i,zy
Trong trutog hgp nay, khd'i lugng khdng khf gidng nhau ndn ta vto cd thi pV
dp dung phuang trito trang thai —— = hang sd.
6.18. Cdu D.
Hudng ddn : Tfi phuong trito pV = —RT, suy ra : p = —. trong dd p. 11 "
, , m tl sd — ggi la so mol; p dac trung cho loai chdt khf.
6.19. 0,46 kg/m^ va 9,6.10 " phto tfi /m^
pp Hudng ddn : Khd'i lugng ridng tmh theo cdng thfic p = -^-^ cdn mdt dd phto RT
tfi tfto theo cdng thfic n N,
frong dd V^ la till tfch cua 1 mol khf frong
m dilu kidn da cho, nd duoc suy ra tfi phuong trinh pVn = vRT, vdd v = —.
152
6.20.1,2.10''Pa.
m. 6.21. Bito 1. Theo phuong trito pV = — RT thi d ddy V va T gidng toau, vdy p 11
m ti Id thuto vdd sd mol —. Trong 4 bito da cho thi bito 1 cd sd mol lto
toat, do dd khf d bito 1 ed dp sudt lto todt.
^2^1
6.23.127°C.
Pl
6.24*. A. Qud trinh 1-2 la dang tfch, thi tfch khdng ddi.
B. Qua trinh 2-3 la ding dp, thi tfch tang ti Id vdi T.
Hinh 6.5G C. Trong qud trinh 3 ^ the tich cung ttog vi nlu ta ke dutog dtog tfch 0-3 thi dilm 4 nim bdn dudd dutog 0-3 (Hinh 6.5G).
Trdn dd thi p-T dutog ding tfch nim dudd tog vdd thi tfch lto hon (xem thdm bai tap 6.14).
D. Qua trito 4-1 la ding dp, tbl tfch giam ti Id vdd T.
Vdy A dung.
6.25*. Cd tbl ban Nam da vto dung dinh luat Bdi-lo - Ma-ri-d't dl do dd sau.
Ddu tidn ban up d'ng nghidm thtog dtog, sau dd lto xud'ng day hd ma vdn gifl nguydn tu thi cua d'ng nghiem. Ghi tod muc nude dang ldn trong dng nghidm khi d day hd. Ap dung dinh luat Bdi-la - Ma-ri-dt cho khdi khf trong d'ng nghidm se tfto dugc dd sau cua hd (coi tou dtog nhidt).
Po(/- / ' ) h =
pg/' frong dd da bid't:
Pg : dp sud't khf quyln ;
p : khd'i lugng ridng cua nudc ; g : gia tdc rod tu do ; /: dd dai cua dng nghidm (etog la do dai ban ddu cua khdi khf trgng dng nghidm); / ' : dd dai cua khd'i khf frong d'ng nghidm lfic d day hd.
11-BTVL 10(NC)-A 153
CHA'T RAN vn CHnt idNG sir CHUV€N ""^
7.1. Trutog hgp A, vi d tito thi thi vi tri cto btog dfige xdc dinh. Trong vdt rto vd dinh hinh (thuy tito rto) va frong chdt long (thuy ngto long) cdc vi tri cto btog khdng ed dinh. Trong ehdt khf (hod nfidc chang han) thi khdng cd vi tri cdn btog cua chuyin ddng nhidt.
7.2. Khd'i lap phuong lam ra tfi don tinh thi khdng gifl dfige dang ldp phfiong vi don tito tbl ed tfto di hutog.
7.3. a) Keo. b) Ud'n. c)Xoto. d) Nen.
7.4. 3.10^ Pa.
7.5. 89mm^;4.10"'^
Gidi ban bin cua vat lidu dugc dac trung bdi tog sudt cd thi gdy hu hdng vat lieu. Dl an toto ngudi ta thutog sfi dung vdt lidu vdd tog sudt thdp hon gidi ban bin khotog 4 hay 5 ldn.
7.6. k « 23,3.10^ N/m ; E = 1,07.10" Pa.
7.7*. 68,4 kN.
Nd'u thanh dugc dan nd nhidt tu do thi khi tang nhidt dd thanh se dai them ra mdt doan A/. Mudn ngan khdng cho thanh dto nd thi ta phai dung mdt tog sudt nen thanh sao eho thanh ngto di mdt doan dung bdng Al.
7.8. C.
7.9. Khdng, vi hd sd dto nd eua ddng gdp ddi hd sd dan nd cfia thuy tinh.
7.10. Vi hd sd dto nd nhidt cfia ddng lto ban thep. Khi ho ndng thi dai dc btog ddng nd nhilu hOn ndn dd van dinh dc btog thep vao frong dai de btog ddng, cdn khi ngudi di thi dai de btog ddng co lai nhilu hon ndn nd bd chat ldy dito de.
154 11-BTVL 10(N6)-B
7.11. 438X.
7.12. 15,856 cm^
7.13*. 0,306 m l
Dl chtog minh cdng thfie, ta gia sfi cd mdt tdm vdt rdn hinh ehfi todt cd chilu ddi cae canh d tg°C la /gi, /g2 va ta tfnh didn tfch cua hinh chfl nhdt dd d t°C :
h-h = /oi(l + aAt)./g2(l + aAt) = /gi./g2[l + 2aAt + a^(At)^]
Ta cd tbl vid't lai dudd dang : S = Sg(l + yAt), nd'u bd qua sd hang a^(At)^.
Tfi dd suy ra : y = 2a.
7.14. 43,53°C (vdi y = 2.24,5.10"^ K"^). Dung cdng thfic AS = SgyAt.
7.15. a =1,2.10"^ K"
7.16*. cau D. Giai thfch thdm : Ldp bl mat khd'i long la ldp phto tfi cd bl day xac dinh. Khoang each gifla cae phdn tfi khd'i long thay ddi khi nhidt dd khdi long thay ddi.
7.17. Xa phdng lam giam luc etog bl mat cfia phto nude gifia hai que didm, cdn dfitog lam tang luc etog bl mat.
7.18*. Khi tod gigt, cdc gigt chi thu vl dang cd mat ngoai tod nhdt, dd la dang hinh cdu. Sau dd cac gigt chi dugc lam ngudi frong nudc.
7.19. Gigt ddu thu vl dang cd didn tfch bl mat tod nha't, frong trutog hgp nay la
dang hinh trdn.
7.20. Vd bong bdng xa phdng la mdt khd'i nudc xa phdng hito cdu gidd ban bed hai bl mat hito cdu, mat trong va mat ngoai. Do ed luc cang bl mat ndn khi dl tu do cdc bl mat thu vl didn tfch tod todt (bong bdng xep di), nd ddy khdng khf ehfia frtog bong bdng thoat ra ngoai qua ddu kia cua cgng rom va thdi tat nggn Ifia cfia nin.
7.21. Thilc long dfnh udt ddng toung khdng dfto udt nhdm.
7.22. Suong khdng dfto udt mdt sd loai la cdy (tou la sen,...) nhung dfto udt mdt sd loai la cdy khac.
155
7.23. Nhung chd't long khdng dfto udt cdc.
7.24*. Giam di 1,2 lto, nghia la : ^^^^^ =1,2. a(d 80*'C)
7.25. 0,075 N/m.
7.26. 0,0365 N.
7.27*. Luc etog bl mat cua nude lto hon luc etog bl mat cua rugu. Luc etog bl
mat eua nude thuc hidn edng duong Ai =0,0728.0,04.0,02 =582,4.10"^ J.
Lue etog bl mat cfia rugu thuc hidn cdng am A2 = - 0,0241.0,04.0,02
= - 192,8.10""^ J. vay edng tdng cdng la : A = 582,4.10"'' - 192,8.10"''
= 389,6.10"^ J.
7.28. 816 kg/m^
7.29. 0,022 N/m.
7.30. Trutog hgp A, mue ehdt long dtog cao 14,7 mm.
7.31. Cdu A.
7.32. Nudc sdi, vi nhidt hod hod lto hon toilu so vdd toidt lugng lam ndng nude.
7.33*. - Cdu A khdng dung vi cd khi cung nhidt cho mdt khdi chdt ma thi tfch cua nd Midng totog khdng ttog ma cdn giam di. Chtog ban ta cung toidt dl lam ndng chay mdt cue nudc da. Vi thi tfch riing cfia nudc da lto hon thi tfch ridng cua nudc ndn khi cue nude dd tan ra thi thi tfch eua nd giam.
- Cdu B khdng dfing vi khi ta cung nhidt dl khdi chdt ehuylh thi (ndng chay chtog ban) thi toidt do cfia khdi ehdt dang ndng chay khdng ddi.
- Cdu C dung vi cung nhiet la su truyin ntog lugng dudd dang truyin nhidt.
- Cdu D khdng dfing vi frong ba cdu frdn chi cd mdt cdu dung.
7.34. Cd tbl, chi cto hfit khf dl giam dp sudt tac dung ldn mat thoang cua nfidc.
7.35. cau B.
Hudng ddn : Dung Bdng dp sudt vd khdi lugng rieng ctia hai nudc bdo hod a nhiet do khdc nhau (xem bai 56 SGK) va ndi suy ttong khotog nhidt dd 25°C-30°C.
7.36. 6 25°C thi dfige, cdn d 35°C thi khdng, vi toidt dd 35*'C cao hon nhidt dd tdd ban cua CO2.
156
7.37.1 atm ; dp sudt bed bao hoa ehi phu thudc nhidt dd, khdng phu thudc thi tfch.
7.38*. Cd toflng each sau ddy : a) Lam lato dtog tfch din 284 K. b) Nen dang nhidt dd'n 23,3 lft. e) Lam ddng thdd ca hai each trdn, nghia la vfia nen vfia giam nhidt do.
7.39. 4,8 tdn.
7.40. 60 kJ/kg.
7.41. 120,62 kJ.
7.42. 64,4 kg ; dung phuang trito Cla-pd-rdn -Men-dd-ld-ep suy ra edng thfic :
p = : ^ va tfto duge p = 6,77 kg/m^ RT
-2 o
7.43. a = 10 g/m ; A = 12,8 g/m (tra Bdng dp sudt vd khdi lugng rieng cua hai r%
nudc bdo hod d nhiet do khdc nhau trong SGK); f = — =78%.
7.44. Tang thdm 23%.
7.45. 11J[°C. Nhiet dd ma d dd d kfnh cfia sd md di la diem suang cua khdng khi dm.
7.46. 0,4 m^
7.47. 64%.
7.48. 72% va 76%.
7.49*. 17°C.
Hu&ng ddn : Hai nhidt kl ehi nhidt dd gidng toau thi dd dm ti ddi la 100%.
Luc dd, trong Im^ khdng khf dm cd 12,8 g hod nudc. 6 2b°C thi lugng hod
nude bao hoa la : 17,3 g/m (xem Bdng dp sudt vd khdi lugfng rieng cua hai nudc hdo hod 6 nhiet do khdc nhau trong SGK). Vay dd dm ti ddi la :
f = i | 4 X 100 = 74%. Nhidt k l khd chi 20°C ma dd dm ti ddi la 74% tiii theo 17,3
Bdng tra dd dm ti ddi (xem bai 56 SGK) su chdto Idch toidt dd gifla hai
nhidt k l la 3°C. Vay ddp sd la 17°C.
7.50*. Trutog hgp C, dd dm ri dd'i la 92,4%.
157
7.51. - Kep hai tdm thuy tinh song song each nhau btog cae thto que didm (trudc'dd phai lau sach hai mat ddi didn dl dam bao dfto udt).
- Nhung toe mdt canh cua hai tdm cham mat nudc cua khay, thdy nudc dang ldn d gifla hai tdm thuy tinh.
- Do do cao cfia phdn nudc dtog ldn va tfto hd sd etog bl m^t cua nudc , - , 4a pghd
theo cong thuc h = , suy ra a = ^-^— pgd 4
7.52. - Nd'i hai d'ng thuy tinh thdng vdd nhau btog d'ng cao su.
- Dd nudc vao dng, chd cto btog, do dd cao hi tfi mat thotog ddii midng dng tod.
- Dung nut bit kfn ddu dng tod, ntog dng kia cao ldn, khi dd :
+ BChd'i khf trong ddu dng tod bi giam va bi nen dtog nhidt.
+ Mat thoang hai ben chdto Idch Ah.
+ Do cao cdt khf bdn dng tod la h2. - Tfto Pa (dp sudt khf quyln) theo phuong ttinh dang nhidt se dugc :
^pghjAh ^' h i - h 2 ,^
- Dfing thudc do Ah, hi, h2 se tfto dugc dp sudt khf quyln.
7.53. - Nhung d'ng thing dtog vao chdt ldng.
- Do dd cao hi tfi mat thoang dd'n midng dng (cfia cdt kjif ban ddu).
- Gifl nguydn vi tri d'ng, bit ddu trdn cfia d'ng (giam khdi khf d ddu d'ng).
- Tfi tfi tod'c dng ldn cao theo phuong thtog dtog din khi ddu dudi dng gdn ldn din mat thodng. Do dd cao h2 Cua cdt khf bi giam d ddu trdn cua d'ng, va h la dd cao cdt chdt ldng ttong dng so vdd mat chdt long ttong binh.
- Day la qua trito dan ding toidt, ed tbl tfnh duge khdi lugng ridng theo cdng thfic :
- ^ Pa(h2 - hi) ^ ghh2
- Dung thudc do dugc cdc gid tri h^ h2, h.
158
CO sd cun NHICT DONG LlfC HOC
8.1.
8.2.
8.3.
8.4.
8.5*
8.6.
8.7.
8.8.
Trutog hgp D.
Vidn thfi todt, vi toan bd ddng nang chuyin sang ndi nang.
Hdn hgp khf d cudi ki nen. Nlu coi cac khf nhu khf If tutog thi ndi ntog cua khf chi phu thudc toidt dd. Nhidt dd cfia cac khf d.cudi ki nto cao hon nhidt dd cua cdc khf d cud'i ki thoat,
800 W.
At = 9v'
8c
0,11 K.
8,15 K.
357 m/s.
; trong dd c la toidt dung ridng cua chi.
8.9*. Theo cdch a thi qua trito AiBi la qua trito dtog nhidt. Theo each b thi do nto nhanh khf ndng ldn (vi toilt toa ra khdng
kip), dutog bilu didn la dutog AiCBi
bdn trdn dutog AiBi (Hinh 8.lG). Theo each b cdng nin lto hon vi dutog bilu diln qud trinh nay ndm ttdn dutog ding
toidt AiBi.
8.10. Day C.
8.11*. Cach A.
Hudng ddn : Dfing dd thi p - V dl bilu. thi cdng cua khf trong cac each da ndu rdi so sanh cdng d mdi cdch btog cdch so sato cdc didn tfch nam dudd cac dutog bilu didn.
159
8.12. Nhidt lugng cung cdp cho khf ttong qud trinh dtog dp, ngoai vide dfing dl
lam ndng khf cdn dung dl khf sinh edng khi dan.
8.13. 396 kJ. Tfto theo cdng thfic : A' = pAV ; AV la phdn thi tfch ttog thdm cua khdng khf trong phdng khi duge sudd ndng dtog dp. Khdng khf ndng thoat ra khdi phdng qua cac khe hd.
8.14*. 3,3.10^ J; 6,1.10^ J.
Hudng ddn : Phuong trinh cua nguydn If thfi todt ddi vdd qud trinh dtog dp la Q = AU - A. Trude hit, ta phai tfto cdng A' cfia khf dto ding dp. Ddi vdd trang thai ddu va cudi cua khf, ta vilt pVi = vRTi va pV2 = VRT2. Trfi
hai phfiong trito cho toau, ta ed p(V2 - Vi) = vR(T2 - Ti). VI phai cho phep ta tfto cdng cua khf dto dtog dp vi v l ttdi la bilu thfic tfto cdng.
vay : A' = 800.8,31.500 = 3 324000 J.
A' « 3,3.10 J. Cdng nay do khf sinh ra.
8.15*. 49 J.
Hudng ddn • Trude hit dp dung dito ludt Sde-lo dd'i vdd hai qua trito dang
tfch, ta tim dugc T^ = T2T4, ttong dd T la toidt dd cua qua trinh dtog nhidt.
Mud'n tfnh cdng ma khf thuc hidn trong chu trito, ta tfto didn tfch hinh chft nhdt i234.
Bilu thfie tfto edng cua chu tiito la A' = R[ T2+T4 - 2(T2T4) ^ ]
Xem thdm|iutog dto cua bai 8.14.
8.16. 760 W.
8.17. cau C.
8.18. 24% ; 42%.
8.19. 113,5 kJ; 28,4 kJ.
8.20. 84 kJ ; 14,1 kJ.
8.21. Cau C : vat bang chi, vi chi ed nhidt dung ridng be todt.
8.22. Cdu C : vdt bang niken, vi niken cd khdi lugng ridng lto todt.
8.23*. - Cdu A sai vi ndi nang cua hd khf If tudng khdng bao gdm thi ntog tuong tde giua cdc hat cdu tao ndn he.
160
- Cdu B sai vi toidt lugng truyin cho hd cdn cd tbl lam ttog tuong tdc gifla cdc hat edu tao ndn hd. Vf du ta cdp toidt dl lam cho hd chuyin trang thai. Lfic dd toidt dd khdng tang ma tbl ndng tang vi cd su thay ddi cdu true bdn trong bd.
- Cau C dung. Vf du ta nto khf thi ta vfia lam khf ndng len vfia giam tbl tfch khf.
- cau D sai vi nlu cho khf If tutog dan vao chan khdng thi ndi nang cua hd khdng ddi ma tbl tfch eua hd tang ldn.
8.24*. - Kf hidu binh cd nudc ban ddu la X, bito kia la Y.
- Dat X vao nudc ndng, Y vao nudc lanh, nudc se chay tfi X sang Y (do khf bi nd ra khi ndng va eo lai khi lato).
- Chd dd'n khi ngtog chay, ddi chd X vao nudc lato, Y vao nudc ndng. Do dng thuy tihh d Y ngdn ndn nude khdng chay ngugc ldn dugc ma chi cd khdng khf tran tfi binh Y sang binh X.
- Lai ddi chd hai binh, nudc lai chay thdm tfi X sang Y.
- Cd tbl lap lai nhilu lto dl ttog hidu qua.
MOT SO nni Tnp TONG HOP V€ CO vn NHICT
Ap dung dinh luat bao toto co ntog : .2
mv = mgh
trong dd v la vto tdc cua qua cdu d dilm thdp nhdtB.
h = HB = / - /cosa
Tfi dd:v^ = 2g/( l -cosa) (1)
Tai vi tri thdp todt cfia qua edu (Hito IG) :
V -* M I——
H
B
p t Hinh IG
T - P = Fh f
T = m v^
g + - (2)
Thay (1) vao (2) ta dugc :
T = mg(3 - 2cosa) = 2,49 N
Do lto cfia T khdng phu thudc gia tri cfia chilu dai / cua ddy.
Vi m^ = mg va lue ma sdt khdng dang kl, ndn chdc chto la vdt B di xudng,
keo vdt A di ldn. Ap dung dinh ludt II Niu-ton cho mdi vdt:
Vdt B : mg - T = ma
Vdt A : T - mgsina = ma
Giai he nay ta dugc :
a= - g ( l - s i n a )
T = —mg(l + sina)
(1)
(2)
Vdy cdng sudt tfic thdd cua lite etog T tai thdd dilm t la :
g'=Tv = Tat ' (3)
Thay (1) va (2) vao (3) ta dugc :
g' = -^mg^tcos^a « 7 2 W
162
3. a) Giai btog phuong phap ddng luc hgc
Dua vao phep phto tfch luc va dp dung dito ludt II Niu-tan, ta tfto duge gia tdc cua vat lfic di ldn (ehilu duong ldy theo chilu chuyin ddng):
ai = -g(sina + pjcosa)
Qutog dutog vdt di ldn :
v2
(1)
Gia tde
Quang
0-v? s= ^ ' 2ai
cua vat luc di
a2 = g(sina
V? 2g(sina + pj
L xudng :
- Ptcosa)
dutog vat di xud'ng :
v ? - 0 S = -4 :
vi
cosa)
(2) 2a2 2g(sina - PfCosa)
Giai hd phuang trinh (1), (2) vdd cac to pj va s, ta dugc :
2 _ 2
Pt = ^—^tana = 0,28 ^ (3) vf+v^ 2 2
vf + V 4gsma
2 2 vf + VT
Do dd h = s.sina = -^—- « 0,64 m. (4) 4g
b) Giai bang phuong phdp ntog lugng Chgn md'c tfto tbl nang d A. Khi vat di ldn, cdng cua luc ma sdt btog dd bid'n thidn co nang :
mv^ ^ms = Wg - W^, hay : -sptmgeosa = mgh ^^ (5)
Khi vat di xudng, edng cua luc ma sat cung btog dd biln thidn co nang :
Ams = WA - WB , hay : -sptingeosa = - ^ - mgh (6)
Giai hd (5), (6), ta cung dat dugc cdc kit qua tou (3), (4).
163
4*. Vdt chiu tac dung cua frgng lue P va phto luc phdp tuylh N cua ban cdu :
P + N = ma
Khi vdt rdi bl mat ban cdu thi N = 0 , do dd
P = ma Chid'u xud'ng phuong cfia ban kuih BO :
mgcosa mv
Hinh ehilu cfia a trdn phfiOng ban kfnh la gia tdc hutog tdm. Dp dd :
V = grcosa = gh (1)
Ap dung dinh ludt bao toto eo ntog 2
Hinh 2G
mgr = mgh + mv (2)
Thay (1) vao (2), ta thu duge :
h - - r
Luc ddu cac khf trong bong bdng xa phdng cd nhidt dd cao hon khdng khf (hod thd ra cfia ngudd cd nhidt do 37°C) va lue dd luc ddy Ac-si-met cfia khdng khf lto hon frgng lugng cfia bong bdng xa phdng, lam cho bong bdng bay ldn. Sau dd, bong bdng xa phdng giam nhidt dd do toa nhidt Ifigng ra khdng khf va thu tod tbl tfch bong bdng lai ndn luc ddy Ae-si-met tod dto di, cdn trgng lugng cfia bong bdng xa phdng thi khdng ddi. Din mdt lfic nao dd thi frgng lugng cfia bong bdng xa phdng lto hon luc ddy Ac-si-mit, kit qua la vdn tdc di ldn eua bong bdng giam dto rdi tfi tfi rod xudng.
O frang thdi khdng trgng lugng, khdi thuy ngto (khdng dfnh udt thuy tinh) CO lai thato dang hinh cdu ; cdn khdi nudc (dfto udt thuy tinh) loang ra frdn toto bd mat frong eua binh ehfia.
Mdi giay blp didn cung cdp cho nudc ttong dm mdt nhidt lugng la : Q = 0,8.1000 = 800 J
Nhidt lugng nay lam hod hod mdt lugng nudc btog :
800 m = -— =
L 2,26.10^ « 0,354 g
164
Thi tfch eua lugng bed nudc dugc tao ra ttong 1 gidy la :
- mRT 0,354 8,31.373 ^^^^^o< 3 ^nnn^ 3 I V = = ———,— - = 0,000595 m » 0,000 6 m 1 P 18 1,013.10^
Tdc dd hod phut raid : V 0,000595 . . . ,
^ = = -o;ooor = ' " / Hod nudc sdi thoat ra ngoai khdng khi trong qua trito ding dp nen ta ed tbl tfto cdng cua hod nudc (tao ra tfi Ig nudc) chid'm thi tfch V theo cdng thfic :
A = pAV = pV = - R T = ^ : ^ 4 ^ - 172,2 J p 18
8*. Ta tfnh luc ddy Ac-si-met F^ ldn khf cdu. Luc nay bing trgng lugng cua thi tfch khdng khf dm bi chid'm chd. Bdy gid ta tfto khdi lugng ridng cua khdng khf dm p', nd btog khd'i lugng
-3
ridng cua khdng khf khd p cdng vdi lugng bed nudc ed ttong 1 m khdng khi.
Theo cdng thfic f = -^ = ^'^' "^^y ^ = ^'^ ^•
Theo Bdng dp sudt vd khdi lugfng rieng cua hai nudc bdo hod d nhiet dd 3
khdc nhau (xem SGK, bai 56) thi A = 17,3 g/m vay : a = 0,8.17,3 = 13,84 gim Bay gid ta tfnh khd'i lugng ridng eua khdng khf khd. Tfi phuang trito Cla-pd-rdn - Men-dd-ld-ep, ta rfit ra :
m pp 10^29 . , „ . , 3 P=V =1^=831293=1'''^/"^
Tfi dd p' = p + a = 1191 + 13,84 = 1 204,84 givn
FA = (p'.64)g = 77,110.9,8 = 755,678 N Lfic ntog khf cdu la : F = (77,110 - 55).9,8 « 216,6 N Dd dto cua ddy thep dugc tfnh theo edng thfie cfia dinh luat Hue
F i.^^ A/ / I F cn 1 216,6 ^ ^ ^ ^ ^ _ — = E-r-, suy ra : A/ = /g—— = 50. —. z « 0,025 m S /g " E S 2,1.10" 2.10-^
vay A/« 2,5 cm. 9. Ggi mi va m2 la khdi lugng cue nudc dd va lugng hod nudc sdi dua vao
toidt lugng kl. Ta cd : mi + m2 = 500 g. Suy ra : m2 = 500 - mi
165
Ta thilt ldp phuong trito c to bang toidt lugng :
- Nhidt lugng ma cue nude da va nude ttong nhidt lugng k l todn vao la :
Qi = mic'iLO - (-5)] + miX + m^ c'l (25 - 0) + 300 C2 [25 - (-5)]
- Nhidt lugng ma lugng hoi nudc toa ra la :
Q2 = (500 - m i ) L + (500 -m^c ' i ' (100 - 2 5 )
Vi cac dd l to eua Qi va Q2 phai btog toau, ta cd :
5mici + m^X + 25miei + 30.300e2 = (500 - mi)L + 75(500 - mi)ci
trong dd c\ va Cj la nhidt dung ridng cua nudc da va nude, cdn 02 la nhidt
dung ridng cua todm.
Thay cdc gia tri da bilt vao phuong tri to frdn va giai ra, ta dugc :
Khdi lugng cue nude dd mi = 423,1 g.
Khd'i lugng hod nude m2 = 500 - 423,1 = 76,9 g.
10. Nguydn tdc sudd dm ddng lue duge bilu thi d so dd dudd ddy :
T - Tl . , T - T i h ^ H„
A^
Qi I -> A' = Qi
Q^ = Qi - A' = Qi
A
1
T1-T2
Q 2 = A vTi
= Q
T - T i ^ _ T / "
, suy ra :
(T -T i )T2
Q i | Opng CO nhift
H# Mng sudi
M&y lenh
'2 J T(Ti - T2)
T - T , Ta vilt dugc tou trdn la vi lAI = IA'I = Qi —=-^(vd i T > Ti)
He thd'ng sudi toto toidt lugng : Q = Q2 + Qi
O ' - A + O - Q ^-^^ 1 0 ^^-^i^^2_Q T i ( T - T i ) Q 1 - A + Q 2 - Q 1 J + ^ i T ( T i - T 2 ) ~ ^ i T ( T i - T 2 )
Tdm lai: Q = Q^ + Q'l = Qi ^ [ j ^ ^ •
Ap d , n g s d : Q i = 6000 kcal thi Q = Q i i | [ | | ^ )
Q « 2,98.6000 « 18000 kcal.
Nhu vay sudi dm ddng luc lgi ban toilu (gdp gto ba ldn).
Hinh 3G
166
MUC LUC
Ldd ndi ddu
PH^N MOT : DE BAI
ChuangI Chuang II
-Chuang III ..Chuang IV ChuangV Chuang VI Chuang VII 'Chuang VIII
Ddng hge ehdt dilm Ddng luc hgc chdt dilm Tito hge vat rdn Cac dinh luat bao toan Co hge ehdt luu Chd't khf Chdt rdn va chdt long. Su chuyin tbl Co sd cfia nhidt ddng luc hgc
Mdt sdbdi tap tdng hgfp ve ca vd nhiet
PHXN H A I : Hir6NG D A N GIAI VA DAP SO
ChuangI Chuang II Chuang III Chuang IV ChuangV Chuang VI Chuang VII Chuang VIII
Ddng hge chdt dilm Ddng lue hge ehdt dilm Tinh hge vdt rdn Cae dinh luat bao toan Co hge cha't luu Chdt khf Chat rto va cha't long. Sir chuyin tbl Co sd cua nhidt ddng luc hge
Mdt sdbdi tap tdng hgp ve ca vd nhiet
Trang
3
5
5 18 31 40 59 65 71 82 88
90
90 106 122 129 146 150 154 159 162
167
Chiu trdch nhiem xudt bdn : Chu tich HDQT kiem Tdng Giim d6c NGO TRAN AI Pho T6ng Giam d6c kiem T6ng bien tap N G U Y I I N QUt THAO
Bien tap ldn ddu : NGUYfeN TIEN BINH - VU THANH MAI
Bien tap tdi bdn: D 6 THI BICH L I £ N
Bien tap Id thudt: CAO LAN PHlTONG - DINH XUAN DUNG
Trinh bdy bia : TA THANH TtJNG
Sica bdn in : D 6 THI BICH LifiN
Che bdn : CONG TY CP THI^T K£ VA PHAT HANH SACH GIAO DUC
BAI TAP VAT Ll 10 NANG CAO
Ma sd: NB006T0
In 10.000 ban, (Qe44BT) khd 17 x 24 cm In tai Cong ty.co phan in Son La
Sd in: 10SL. sd xuat ban 01-2010/CXB/639-1485/GD. In xong va nop luu chi lu thang 5 nam 2010;
168
•Xl-B
HUAN CHl/CJNG HO CHI MINH
Q U A L I T Y C R O W N
VaONG MIEN KIM CUONG C H A T LI/0NG QUOC TE
SACH BAI TAP LCfP 10
1. BAI TAP OAI SO 10
2. BAI TAP HiNH HOC 10
3. BAITAPVATLI IO
4. BAI TAP HOA HOC 10
5. BAI TAP NGff VAN 10 (tap mot, tap hai)
6. BAITAPTINHOCIO
7. BAITAPTI^NGANHIO
8. BAI TAP TI^NG PHAP 10
9. BAI TAP TI^NG NGA 10
SACH BAI TAP LOP 10 - NANG CAO
. BAI TAP OAI S6 10 . BAI TAP HOA HOC 10
. BAI TAP HINH HOC 10 • BAI TAP NGUrVAN 10 (tap mot, tap hai)
. BAI TAP VAT LI 10 . BAI TAP TI^NG ANH 10
Ban dpc co the mua sach tai : • Cac Cong ty Sach - Thiet bi tnroTig hoc a cac dia phuofng. • Cong ty CP Diu tu va Phat triSn Giao due Ha Noi, 187B Giang Vo, TR Ha Noi. • Cong ty CP.Dau tu va Phat trien Giao due Phuomg Nam, 231 Nguyin Van Cu, Quan 5, TR HCM. • Cong ty CP Dau tu va Phat tri8n Giao due Da Nlng, 15 NguySn Chi Thanh, TP. Da Nlng. hoac cac cua hang sach cua Nha xuat ban Giao due Viet Nam :
- Tai TR Ha Noi :
Tai TR Da Nang :
- Tai TR H6 Chi Minh
- Tai TR Can Tho
8 934980"0 06399
187 Giang Vo ; 232 Tay Son ; 23 Trang Tign ; 25 Han Thuyen ; 32E Kim Ma ; 14/3 Nguyin Khanh Toan.
78 Pasteur ; 247 Hai Phong.
104 Mai Thi Luu ; 2A Dinh Tien Hoang, Quan 1 ;
240 Trkn Binh Trong ; 231 Nguyen Van Cu, Quan 5 ;
5 Binh Thai, Quan 11.
5/5 Duong 30/4.
Website: www.nxbgd.com.vn
Gid: 7.600 d