multiple representation problem solving-4 (rocket sled ...physedu/web_hw/131_f01/hw2_sol.pdf ·...
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Multiple Representation Problem Solving-4 (Rocket Sled)
A rocket sled used to test automobile restraining devices (seat belts, airaISbions, and so forth) acceleratcs from rest at 8.0 m./s 2 for a distanceof 16 m. In what time interval should the rocket now be stopped so thatthe mamimdc of the avcrage accclemtion is 32 m/s2?
Save space below
PICTORIAL R.EPRESENTAnON
CD(~
6:;1
a~~~a =. --32. rnls "2.
-32.m;s "2.a.=
4-
l~: "0-:.0 ..4
I )c'o ':. O rri
Mi(\tl~ S\~n
jndlC.c;l~ d\red1(t
CG1strUd. a pictoria1lepaeDtatiooof the Iituati~ descn"bed in thepn)blem. ~ude:
.a~uis,
.a Iketd1 that aWl the sled at theinitial aIMi rmal situatioos for ead1 partof the .-oblem,
.Iymbols that ~ie-.t the knownvalues of kinematic quantities at th~
ti-.aIMi.Iymbo1s repr~~Dting the unknownsthat you wish to determine.
'- ~ -"I' v~
x~llo~ ...,~cXy- 7
-.tf ~ ?
b=,?
PHYSICAL REPRESENTATION -fu~
~~
( aca~~ ~ )~orna:
CaJstnJd a ae.-r.re DK)tim1 diagramfm' tbe a1ed duriD& eacb ~ of tbepoblem. U- tbe dUec:tim1S of the
) 8rIOWS iD tbe mOOm1 di8Ir8mI to
dIeCk tbe 8iIDS of tbe qU8Dtities iD
~ pidmia1...J2i~-*..tatimL
~--.,.
1 ~ILI ttt
-
~~@,
I l~vY\ = 0 + 0 + i( "6' ~~2Jt '2.
t;:.2.s
MAm REPRESENTAnONandSOLUTION
a.ooee a ~~~c equltim. that Iel8Iesthe v8riabla involved in the rJnt part ofthe problem. Solve the equation to de-~ mIne needed qIantity that cm1then be used in the ~ ~ of the
poblem.
v
u. the results ofthe previous calcu1a-tim18Dd other information in the pid-mia1..~~OO to determine theUDkDown.
\I.f-'JL~---"
~ -tl(R~\f'j
~2.b+- -2.5
-I(o0/s
~~~~
--1-s2
t-+ ::; 2.5-5
~~IR
EVALUAnON.. .Ik»es tbe siID oftbe 8DSwa' agree
with tbe aituati= s}K)WD iD tbe pidor-
ia1 i~-.t.t:.--il? "{ <2.. 5
.Is tbe 1IDit of the 8DSwa' comd.? y L~
.Is tbe magDitude 18~ble? '\.1 /)S 1T ~ -Q..'('o.e
C AI.PS Kit, Box 4013, Univenity Pt., J
Las Cruces, NM 88003
de.. c-e.1 c2..roJ) 0\1\ -Ir lit L.l s ~ hay- -t +; ~ +0 ~ ~ [).I -23 {¥JJ!~~Q) A FIPSE PIoject'f
to Dote commonerrors.
I x=~:~2 '._.
~4.~
x-= )( c. 0\-- '\( 0"'<:1 + ~a.-*2.
Changing Kinematic Representations-2
(a) An object moves along a horizontal surface.The applia.tion or three kinematic equations tothat motion is shown below .ConstrUct a motiondiagram replaCDliDg the motion and then inventscxne real p~ that might be rcp~ted bythe equations and by the motion diasmm.
9.0 m -O -0 + t<2.0 mts2)t:
(b) An object moves on an incline. The applicationof one kinematic equation to that motion is shownbelow. ConstrUd a motion diagram representingthe motion and then invent some ~ process thatmight be reprcscnted by the equation and by themotion diagram.
-2 (-8.0 m/s1 (x -0)v I -(2.0 m/s2) tl
36 m -9.0 m -VI (t2 -tl)
Solve the equation for the unknown.
\L-'2-4 =:. -12..~~ -=- -1~.()f1.I/l?- ')<
~-+!2- -3
:+i""<;-4x - c I rb M
--:.
Solve the equations for the unknowns.
q\'Y\ :. i (2. O ~~-t12
~ 1..- l.\ -
-61 = 3s .
/ -Vl =. (2 '"I5~ 3.5 ) -
=~
3~ --= lCo~s)(4 I
--~~ "S5lDmW a motion diI8I8aI(s) that is -withthe tiIaDaIic ~tities and with the motiCXldescn"bed by the equatiom. The object is movinghorizon1aUy. y CRl need one motion diI8I8aI foreadI part of the motion-for eadI ~ with adiffercnt accelelation.
-~~ -
-3s "\--"
q :27
Dmw a motion diagram that is amsistcnt with thekinematic quantitim and with the motiondeocribed by the equations. The objectmov~ aJoog an incline.
J;0
/O.::.2M/SZ /...'.--:.,0
I <::"=-- - .q~-~1~~S
--=1>1
-QyVI '=: <0 ~ -" .",. .~ 0.. :::- ° 7s'2
--~-~ 'r--- 3/; -9. ==- 21
Constmd a pictorial ~resentation or someprocess that is oonsistent with the motiondiagIam and the equations above ( there are
many ~ibilities).
c uuct a pictorial reprcsentation of some processthat is consistent with the motion diagram andthe equation above (there are manypossibilities).
A bo-ll (1'(-" to~ c~(' \6\\5 lAp
}h
?l-A""' \1 edCAy-A mQ+~ b~ .\.$
\'n \' ~l)..l
s~~s
3s
-thCt+ i+iStaws
~l t\5r6 u. '\'Y\.Q-
~~ .\-looy-
I -28 (Kinematia) A FIPSE Project