Sample Exam 3
1.
A spring stores 50 J when it is compressed by 10 cm.
What is the spring constant k?
U
=
1
2
kx
2
k
=
2
U
x
2
=
2
⋅
50
J
(0.1
m
)
2
=
10, 000
N
/
m
2.
A conservative force has
the form F = b x
3
i
.
What potential energy is associated with this
force?
U
=
−
F
⋅
d
r
∫
=
−
F
⋅
(
dx
ˆ
i
+
dy
ˆ
j
+
dz
ˆ
k
)
∫
=
−
bx
3
ˆ
i
⋅
(
dx
ˆ
i
+
dy
ˆ
j
+
dz
ˆ
k
)
∫
=
−
bx
3
dx
∫
=
−
b
4
x
4
3.
Is it possible to write a potential energy for the frictional force?
Why or why not?
No.
Frictional forces are not conservative.
4.
A ball is dropped from of a height of 10 m.
What is its kinetic energy just before it hits the
ground?
What is its velocity?
v
i
=
0
Δ
K
=
K
f
−
K
i
=
W
K
f
−
0
=
mgh
K
f
=
mgh
Δ
K
=
1
2
mv
f
2
−
1
2
mv
i
2
=
W
1
2
mv
f
2
−
0
=
mgh
v
f
=
2
gh
=
2
⋅
9.8
m
/
s
2
⋅
10
m
=
14.0
m
/
s
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5.
A potential has the form V = b x
2
.
What force can be associated with this potential?
F
=
−
dV
dx
=
−
2
bx
6.
Identical masses are placed at
(2,0), (2, 0) and (0,3.464).
Compute the position of the center
of mass.
Suddenly the masses exert repulsive forces on each other and fly off at high speed.
What is the position of the center of mass after this event?
r
cm
=
m
⋅
(
−
2
i
+
0
j
)
+
m
⋅
(2
i
+
0
j
)
+
m
⋅
(0
i
+
2
j
)
m
+
m
+
m
=
0
i
+
2
3
j
The position remains unchanged since the forces are internal.
7.
A 5000 kg automobile has a momentum of
p
=
10,000
kgm
/
s
ˆ
i
What velocity does it have?
p
=
m
v
v
=
p
m
=
10,000
kgm
/
s
ˆ
i
5,000
kg
=
2
m
/
s
ˆ
i
8.
A 2000 kg car is heading westward with a velocity of 20 m/s.
It collides with a 4000kg car
heading eastward at 10 m/s.
Compute the momentum after the collision and the change in the
kinetic energy.
p
i
=
2000
kg
⋅
(
−
20
m
/
s
ˆ
i
)
+
4000
kg
⋅
(10
m
/
s
ˆ
i
)
=
0
p
f
=
p
i
=
0
E
i
=
1
2
⋅
2000
kg
⋅
(20
m
/
s
)
2
+
1
2
⋅
4000
kg
⋅
(10
m
/
s
)
2
=
6.0
×
10
5
J
E
f
=
0
J
Δ
E
=
0
J
−
6.0
×
10
5
J
=
−
6.0
×
10
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 Spring '10
 jojo
 Energy, Force, Kinetic Energy, Mass, Potential Energy

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