A
1
B
2
C
3
D
4
E
5
F
(acceleration due to gravity)
A
1
2
3
AB
m1
B
2
7
D
4
2ℓ
O
AB
d
m2
AB
θ
1
1
g
G
O A B
O
A
6
2
m1
m2
1
ℓ cos θ + d sin θ
ℓ
ℓ
ℓ cos θ − d sin θ
ℓ cos θ + d sin θ
ℓ cos θ − d sin θ
ℓ cos θ + d tan θ
ℓ
ℓ
ℓ cos θ − d tan θ
ℓ cos θ + d tan θ
ℓ cos θ − d tan θ
1
B
h
L
A
2
v
A
B
v
2
√
g
L
h
√
L
√
g
2L
h
2g
h
2
√
2L
2g
h
C
A
B
3
mB
A
v
mA
A B
B
A
3
−
2mA mB
v
mA + mB
−
mA (mA − mB )
v
mA + mB
mA (mA − mB )
v
mA + mB
2mA mB
v
mA + mB
3
D
m
v
kv k
4
4
mg
k
(mg)2
k
mg
k2
4
(mg)2
k2
E
m
A
M
B
A
B
F
A
pA B
pB
5
pA
pB
5
m
M
√
m
M
√
1
5
M
m
M
m
F
1.0m
1.0kg
P
9.8m/s
4.0m/s
2
6
P
N
6
6.2
9.8
16
6
26
N
A
A −20◦ C
1
B
2
C
3
100g
1
50
2.1J/(g·K)
3
3.3×10 J/g
10J
4.2J/(g·K)
3
2.3×10 J/g
1
50
7
7
B
S
n
T0
k
p0
T0 + ∆T
∆x
CV
2
8
nCV ∆T
nCV ∆T + p0 S∆x
nCV ∆T + 1 k(∆x)2
2
nCV ∆T − 1 k(∆x)2
2
nCV ∆T + p0 S∆x + 1 k(∆x)2
2
nCV ∆T + p0 S∆x − 1 k(∆x)2
2
8
C
p-V
A
3
1
B
C
A
A
B
C
C
A
A
9
1
20
1
12
1
10
9
1
6
A
A x
1
B
2
C
3
2m/s
t=0s
x [m]
y [m]
T [s]
t = 0.1T
1
y
t
x
10
y = −0.02 sin 2π(0.5t − x)
y = 0.02 sin 2π(0.5t + x)
y = −0.02 sin 2π(2t − x)
y = 0.02 sin 2π(2t + x)
10
B
2
S1
S1
S2
A
S2
5.0m
12m
B
S1
P0
P0
S2
P0
P1 P2
2.5m
P2
340m/s
2
Hz
11 Hz
170
340
680
11
1360
C
f
a (< f )
b
3
a
b
12
b
12
A
A
1
B
A
2
C
3
D
4
E
5
F
6
B
1
13
13
B
4
2
R1 R2 2
A B C D
S1 S2
V
S1
A
Q
A
2
S1
Q
S2
′
Q′
Q
14
1
2
2
3
1
14
3
2
2
C
6.0V
3
AB
2
10Ω
I
A
3
A
B
15 A
−1.2
−0.80
−0.40
0.40
0.80
1.2
15
0.0
D
1
xzy
2a 0
xy
O
a
A 0
x
I1
O
I1
0
H
2
I2
3
O
I1 I2
A
z
4
3
O
x y z
16
(0, H , H )
(H , 0, H )
(H , H , 0)
( 2H , 0 , 0 )
( 0 , 2H , 0 )
( 0 , 0 , 2H )
16
E
2
AB
P Q
CD P Q
ABCD
P Q
I1
I2
5
17
P Q
P Q
P Q
P Q
17
F
1
A
t
B
IA
A
B
t
2
IB
1
B
6
IB
t
18
18
A
1
−e
A
r
v
m
m
v2
e2
= k0 2
r
r
k0
nh
mvr = −
2π
v1 n = 2
1
e
v
n
h
r
n=1
v2
v1
v2
19
1
4
√
2
1
2
√1
2
2
4
19
1