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Chapter - 1
Course for IITJEE - 2012
PHYSICSPHYSICSIntroduction to VectorsIntroduction to Vectors
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Y 5 a _
b _
6
–X +X
c _
4
–Y
d _
7
a _
a _
a _
a _
-a _
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a _
2a _
– 3a _
j
i
O
Y
–X X
–Y –2i
3i
1.5j
– 4j
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a _
5b _
4
a + b _
_
| a + b| = | a | + | b | = 9 units _
_
_
_
3
a _
8
b _
a + b _
_
5
| a + b| = | a | – | b | if | a | > | b | _
_
_ _
_
_
| a + b| = | | – | |b a if | b | > | a | _
_ _
_
_
_
a +
b_
_
a _
b _
a + b_
_
b _
a _
O
Q _
P _
q
Q
q R
a
PO
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c
a
b
a b
c
3 R
5
60 a
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Y
X
i
a_
j
O
Y
X
j
i
P Aax
a _
ay
B
q
O
a = s in qy a
a cos q= ax
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2
c _
1b_
2
3
a _
1
1
Y
OX
5
60° 60°
5 sin 60°
5 cos 60°
645°
6 sin 45°
6 cos 45° 45°
30°
10
10 sin 30°
10 cos 30°30°
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10
30°
60°
8
10 sin 30°
8 cos 60° 10 cos 30°
8 sin 60°
Ry
Rx
Rq
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2 120°
2
2 cos 30°
2 sin 30° 2
Ö3R
q
1
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a 30°
b
10
a cos 30°
a sin 30°
10
b
q
a
60°
5
5
5 sin 60°
a cos q 5
5 cos 60°
a sin q
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F
120°
120° 120°F
F
X
Resolving F cos 60°
F cos 60°
F sin 60°
F
F sin 60°
F2
135°
90°F1
10Ö2 N
F2
F1
45° 1 0 Ö 2 c s 4 5 o °
1 0 Ö s i 4 5
2 n °
Y
X
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A
W1 20 N
B
50 NW2
T (tension in string B)B
W = 50N (wt. of block)2
TA
TB W1
W1
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B
60°
O
W
A
100 N
60°
T0
100 N
ÞT = 100 N0
T cos 60°2
T sin 60°2
T0
T1
B
A
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N1
B
15 N (wt. of B)
N1
A
20 N (wt. of A)N2
s t r i n g
q
P l a n eq
q
normal
N
m g s i n q
T
mg cos qq
mg
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A
B
30°
C
NA
T 1
W s i n
q A
q
WA
W cos qA
W i n
q s
B
W
c o s q
B
WB
q
T 2
T 1
N B
T2
WC
F1
30° A B F = 15 N2
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NB
F = 15 N2RB
20 N (wt. of B)
NA
AR
30 N
30°
F1
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f
0.1 N
mNs
N
25 N
100 N
W sin 30°
N
W30°
W cos 30°
mNs
30°
F
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F sin 30°
mNs F cos 30°
W
N
30°
n 3 W s i 0 °
N1 T
m N 1 k
W cos 30°
W
N2
mNk 2
W
T
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T
W
37°
R
mR
B A
37°
W
R 1
RmR1
mR
T1
T2
B
C
A
O
T2 T1
C B
10Ö3 10 N
T = 10Ö32 T = 10 N1
T1
q
q
T2
O
T (tension in0
string OA)
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T1
T0
T2
Y X
q
T3T1
T2
W2 W1
53° 37°
T2
T3
W2
53°
53°
T2
T1
W1
37°
37°
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T1
O
T3
T2
60°
T2
T1
60°
T3
30°
T
W
T = 10
30°
T1
T2
T2
W
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q
w
w
q
T T
W
W
T
T = W
2 0 0 N
w
37°
A 45°
W
N
100
f T1
T cos45°0
T2
N
T sin45°0T0
T1
T2
W
45°
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F = 50 N40
R
50N
40N
mR
45°
F
70g
N
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a + b_
_
a
_
b _
a + b_
_
b _
a _
O
Q
q R
a
PO
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