Cal Poly State University, SLO
D. Niebuhr
Physics Department
Winter 2008
Phys 141
Homework Solutions
Chapter 9
Assigned Problems:
Ch. 9:
2, 9, 10, 13, 19, 21, 24, 26, 28, 38, 42, 49, 57
9.2.
Model:
Model the bicycle and its rider as a particle. Also model the car as a particle.
Solve:
From the definition of momentum,
car
bicycle
p
p
=
car
car car
bicycle bicycle
bicycle
car
bicycle
m
m v
m
v
v
v
m
⇒
=
⇒
=
(
29
1500 kg
5.0 m/s
75.0 m/s
100 kg
=
=
Assess:
This is a very high speed (
≈
168 mph). This problem shows the importance of mass in comparing two
momenta.
9.9.
Model:
Use the particle model for the falling object and the impulsemomentum theorem.
Visualize:
Note that the object is acted on by the gravitational force, whose magnitude is
mg
.
Solve:
Using the impulsemomentum theorem,
f
i
f
i
( )
t
y
y
y
y
t
p
p
J
F t dt

=
=
∫
f
i
y
y
mv
mv
mg t
⇒

= 
∆
i
f
y
y
v
v
t
g

⇒ ∆ =
(
29
2
5.5 m/s
10.4 m/s
0.50 s
9.8 m/s

 
=
=
Assess:
Since
y
F
mg
= 
is independent of time, we have taken it out of the impulse integral.
9.10.
Model:
Model the tennis ball as a particle, and its interaction with the wall as a collision.
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D. Niebuhr
Physics Department
Winter 2008
Phys 141
Visualize:
The force increases to
F
max
during the first two ms, stays at
F
max
for two ms, and then decreases to zero during the
last two ms. The graph shows that
F
x
is positive, so the force acts to the right.
Solve:
Using the impulsemomentum theorem
f
i
x
x
x
p
p
J
=
+
,
(
29
(
29
(
29
(
29
(
29
6 ms
0
0.06 kg 32 m/s
0.06 kg
32 m/s
x
F t dt
=

+
∫
The impulse is
(
29
(
29
(
29
(
29
(
29
(
29
(
29
(
29
(
29
6 ms
max
max
max
max
0
max
1
1
area under force curve
0.002 s
0.002 s
0.002 s
0.004 s
2
2
0.06 kg 32 m/s
0.06 kg 32 m/s
960 N
0.004 s
x
F t dx
F
F
F
F
F
=
=
+
+
=
+
⇒
=
=
∫
9.13.
Model:
Choose car
+
gravel to be the system.
Visualize:
Solve:
There are no
external
forces on the car
+
gravel system, so the horizontal momentum is conserved. This
means
p
f
x
=
p
i
x
. Hence,
(
29
(
29
(
29
(
29
(
29
f
10,000 kg
4,000 kg
10,000 kg 2.0 m/s
4,000 kg 0.0 m/s
x
v
+
=
+
f
1.43 m/s
x
v
⇒
=
9.19.
Model:
The two cars are not an isolated system because of external frictional forces. But during the
collision friction is not going to be significant. Within the impulse approximation, the momentum of the
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 Winter '06
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 Momentum, Work, m/s, Cal Poly State University, D. Niebuhr, SLO Physics Department Phys

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