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364 CHAPTER 11 Collisions

Checkup 11.2 an elastic collision, the total kinetic energy is unchanged; since
the net momentum is zero, the particles must again have
1. As in the cases just discussed, and as in Eq. (11.13), where the opposite velocities. If we ignore the possibility that the parti-
projectile’s final velocity is proportional to m m , the veloc-
1 2 cles might have passed through each other, then this means
ity of the projectile will be positive when it is more massive that their velocities were reversed by the collision.
than the target (m m ), and it will be negative when it is
1 2 3. The velocity of the joined particles after a totally inelastic
less massive than the target (m
m ).
1 2 collision is the velocity of the center of mass, v CM m v
1 1
2. No. As we saw in the cases just discussed, the speed of recoil of (m m ); this is equal to one-half of the velocity of the
2
1
a massive target is very small; in the limit of a very light target, incident projectile when the masses of the target and projectile
the speed approaches twice the speed of the projectile. For any are equal, or m m .
1
2
values of m and m , the final speed of the target (v ), given by
1 2 2 4. No, assuming the wires are long enough to permit the upward
Eq. (11.14), cannot exceed twice the projectile speed (v ).
1 motion of the pendulum to the maximum height h.
3. No; for instance, in the collision of the Super Ball and the 1
5. (B) v. Momentum is conserved, so equating the initial and
3
wall, the ball is instantaneously at rest before it bounces back. 3
final momenta, we have mv (m 2)v ( m)v', which implies
2
The kinetic energy is transformed into elastic energy momen- 1
v' v.
3
tarily, and then converted back into kinetic energy.
4. (E) 0; v . As discussed above, when the masses of the target
1 Checkup 11.4
and projectile are identical, the speed of the projectile is zero
after the collision [since we have m m 0 in Eq. (11.13)].
1 2 1. Because the cars have equal mass and speed, the total momen-
For identical masses, the target speed is equal to the initial
tum before and after this totally inelastic collision is directed
speed of the projectile, v [since we have m m in
1 1 2 due southwest.
Eq. (11.14)].
2. (B) Southeast. This explosion is like a three-particle totally
inelastic collision in reverse. Since the total momentum before
Checkup 11.3 the “collision” (explosion) is zero, so must it be afterward: the
third particle must have momentum components which cancel
1. No; for example, if the target is initially at rest, it gains kinetic
the northward and westward momentum contributions of the
energy.
other two particles; thus, the third particle travels in the
2. Two particles of equal mass and opposite velocities have zero southeast quadrant of directions.
net momentum. Thus, in a totally inelastic collision, the com-
posite particle has zero momentum, and thus zero velocity. In