**Goal:** Reasoning and recognizing the implications of momentum conservation.

**Source:** UMPERG

For ANY collision between two objects there is a time when both of the

objects are traveling with the velocity of the center of mass.

(Assume no external forces act on either object.)

- True
- False
- Depends upon the details of the collision

## Commentary:

## Answer

(2) This statement is false despite the fact that it is true for just

about all of the instances of collision that students see. In a

perfectly inelastic collision it is certainly true that both bodies have

the velocity of the center of mass after the collision. In a general one

dimensional collision with only spring forces it is also true. For the

statement to be true about a specific collision, there must be a time

when the relative velocity of the two objects is zero. The statement is

clearly false in general for two-dimensional collisons. As an example of

a one-dimensional collision for which the statement is false, consider a

bullet that passes through a block of wood initially at rest. The bullet

slows down and the block speeds up but they never have the same

velocity.