Question

A 5-kg ball collides inelastically head-on with a 10-kg ball, which is initially stationary. Which of the following statements is true? (There could be more than one correct choice.)
a. The magnitude of the change of the momentum of the 5-kg ball is equal to the magnitude of the change of momentum of the 10-kg ball.
b. Both balls lose all their momentum since the collision is inelastic.
c. The magnitude of the change of velocity the 5-kg ball experiences is greater than that of the 10-kg ball.
d. The magnitude of the change of velocity the 5-kg ball experiences is equal to that of the 10-kg ball.
e. The magnitude of the change of velocity the 5-kg ball experiences is less than that of the 10-kg ball.

Answer 1

a. The magnitude of the change of the momentum of the 5-kg ball is equal to the magnitude of the change of momentum of the 10-kg ball.

c. The magnitude of the change of velocity the 5-kg ball experiences is greater than that of the 10-kg ball.

Explanation:

For an inelastic collision:

• The total momentum of the system is conserved
• The total kinetic energy of the system is not conserved

Using these facts, let's now analyze each statement given.

a. The magnitude of the change of the momentum of the 5-kg ball is equal to the magnitude of the change of momentum of the 10-kg ball.  --> TRUE. Since the total momentum is conserved, we can write:

$p_1 = p_1'+p_2'$

where

$p_1$ is the initial momentum of the 5-kg ball

$p_1'$ is the final momentum of the 5-kg ball

$p_2'$ is the final momentum of the 10-kg ball

The equation can be rewritten as

$p_1-p_1'=p_2'$

which is equivalent to

$-\Delta p_1 = \Delta p_2$

which means that the magnitude of the change of momentum of the two balls is the same.

b. Both balls lose all their momentum since the collision is inelastic.  --> FALSE, the 10-kg ball gains momentum, so it does not lose it.

c. The magnitude of the change of velocity the 5-kg ball experiences is greater than that of the 10-kg ball.  --> TRUE. We already said that the magnitude of the change in momentum of the two balls is the same. However, it can be written as

$\Delta p = m\Delta v$

where m is the mass of the ball and $\Delta v$ its change in velocity. Therefore, the 5-kg ball (which has smaller mass) will have a larger $\Delta v$, so a larger change in velocity.

d. The magnitude of the change of velocity the 5-kg ball experiences is equal to that of the 10-kg ball.  --> FALSE, as we discussed in c).

e. The magnitude of the change of velocity the 5-kg ball experiences is less than that of the 10-kg ball. --> FALSE, as we discussed in c).

Learn more about change in momentum:

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