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11.3 Inelastic Collisions in One Dimension 349

(a)
Boxcar 1 is Boxcar 2 is
moving “projectile.” stationary “target.”
v 1

1 2
x

(b)

v CM
1 2
x

In a totally inelastic
collision, target and
projectile lock together.

FIGURE 11.7 (a) Initially, boxcar 1 is moving toward the right, and boxcar 2 is stationary,
as in Fig. 11.5. (b) After the collision, the boxcars remain locked together. Their common
velocity must be the velocity of the center of mass.

1 2 1 2 1 2
2 m v m v (m m )v CM
1
2 CM
2
1 CM
2
2
2
5
1
(20 000 kg 65 000 kg) (1.2 m s) 0.61 10 J
2
Thus, the loss of kinetic energy is
5 5 5
2.5 10 J 0.61 10 J 1.9 10 J (11.21)
This energy is absorbed by friction in the bumpers during the coupling of the
boxcars.

Figure 11.8a shows a ballistic pendulum, a device once com-
EXAMPLE 6
monly used to measure the speeds of bullets. The pendulum
consists of a large block of wood of mass m suspended from thin wires. Initially,
2
the pendulum is at rest.The bullet, of mass m , strikes the block horizontally and
1
remains stuck in it. The impact of the bullet puts the block in motion, causing it
to swing upward to a height h (see Fig. 11.8b), where it momentarily stops. In a test
of a Springfield rifle firing a bullet of 9.7 g, a ballistic pendulum of 4.0 kg swings
up to a height of 19 cm. What was the speed of the bullet before impact?

SOLUTION: The collision of the bullet with the wood is totally inelastic. Hence,
immediately after the collision, bullet and block move horizontally with the veloc-
ity of the center of mass:
m v
1 1
v (11.22)
CM
m m
1 2