Phys 205
Chapter 7 Solutions (Part 1)
7.20
Two objects of mass
m
and 3
m
undergo a completely inelastic collision in one dimension. If the two objects
are at rest after the collision, what was the ratio of their speeds before the collision?
This is a completely inelastic collision problem.
Given:
Masses:
m,
3
m
Final velocity:
v
f
= 0
We want to ﬁnd the ratio of their initial speeds. We can use conservation of momentum. For a completely
inelastic collision, we have:
m
1
v
1
i
+
m
2
v
2
i
= (
m
1
+
m
2
)
v
f
→
mv
1
i
+ 3
mv
2
i
= 0
→
v
1
i
=

3
mv
2
i
v
1
i
v
2
i
=

3
The smaller mass will be traveling in the opposite direction as the larger mass with three times the speed.
7.21
Two particles of mass
m
1
= 1
.
5 kg and
m
2
= 3
.
5 kg undergo a onedimensional headon collision as shown
in the Figure. Their initial velocities along
x
are
v
1
i
= 12 m
/
s and
v
2
i
=

7
.
5 m
/
s. The two particles stick
together after the collision ( a completely inelastic collision), (a) Find the velocity after the collision. (b) How
much kinetic energy is lost in the collision?
Fig. P721, p. 236
This is a completely inelastic collision problem.
Given:
Masses:
m
1
= 1
.
5 kg
,
m
2
= 3
.
5 kg
Initial velocities:
v
1
i
= 12 m
/
s
,
v
2
i
=

7
.
5 m
/
s
(a) We want to ﬁnd their velocity after the collision. We can use conservation of momentum. For a completely
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 Spring '11
 MARKO
 Kinetic Energy, Mass, Momentum, Velocity, kg, m/s

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