A pair of railway boxcars are moving toward each other on a rail with negligible friction. One boxcar is twice the mass of the other. On collision, the boxcars couple to each other. In order for the coupled pair to have zero velocity (relative to a bystander next to the track) after the collision, what is the ratio of velocities of the more massive to the less massive boxcar before the collision?
A)1/2
B)1/3
C)-1/3
D)-1/2

Question

Quizplus · Accepted Answer

For the total momentum of the system to be zero (which is necessary for the coupled boxcars to have zero velocity), the momentum of the two boxcars before the collision must cancel each other out. Since momentum is the product of mass and velocity, and one boxcar has twice the mass of the other, its velocity must be half but in the opposite direction (negative sign) for the momenta to cancel out. Hence, the ratio of the velocities is -1/2.

A Pair of Railway Boxcars Are Moving Toward Each Other