Chapter 9: Linear Momentum and CollisionsSolutions to Problems
4.
Picture the Problem
: The two carts approach each other on a frictionless track at different speeds.
Strategy:
Add the momenta of the two carts and set it equal to zero.
Solve the resulting expression for
2
v
.
Then use
equation 76 to find the total kinetic energy of the twocart system.
Let cart 1 travel in the positive direction.
Solution:
1. (a)
Set
0
=
∑
p
arrowrightnosp
and solve for
2
:
v
(
)(
)
1
1
2
2
1
1
2
2
0
0.35 kg
1.2 m/s
0.69 m/s
0.61 kg
m
m
mv
v
m
=
+
=
= 
=
=
∑
p
v
v
arrowrightnosp arrowrightnosp arrowrightnosp
2.
(b)
No, kinetic energy is always greater than or equal to zero.
3. (c)
Use equation 76 to sum the kinetic
energies of the two carts:
(
)(
)
(
)(
)
2
2
1
1
1
1
2
2
2
2
2
2
1
1
2
2
0.35 kg
1.2 m/s
0.61 kg
0.69 m/s
0.40 J
K mv
mv
=
+
=
+
=
∑
Insight:
If cart 1 is traveling in the positive
ˆ
x
direction, then its momentum is
(
)
ˆ
0.42 kg
m/s
⋅
x
and the momentum of
cart 2 is
(
)
ˆ
0.42 kg
m/s

⋅
x
.
8.
Picture the Problem
: The force of the kick acting over a period of time imparts an impulse to the soccer ball.
Strategy:
Multiply the force by the time of impact to find the impulse according to equation 95.
Solution:
Apply equation 95 directly:
(
)
(
)
3
av
1450 N
5.80
10
s
8.41 kg
m/s
I F t

= Δ =
×
=
⋅
Insight:
The 1450N force is equivalent to 326 lb!
The same impulse could be delivered to the ball with 8.41 N
(1.89 lb) of force acting over a period of one second.
17.
Picture the Problem
: The two skaters push apart and move in opposite directions without friction.
Strategy:
By applying the conservation of momentum we conclude that the total momentum of the two skaters after the
push is zero, just as it was before the push.
Set the total momentum of the system to zero and solve for
2
m
. Let the
velocity
1
v
arrowrightnosp
point in the negative direction,
2
v
arrowrightnosp
in the positive direction.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 CROFT
 Physics, Friction, Kinetic Energy, Mass, Momentum, m/s

Click to edit the document details