**Goal:** Problem solving using momentum conservation.

**Source:** UMPERG-ctqpe90

On an icy road, an automobile traveling east with speed 50 mph collides

head-on with a sports car of half the mass traveling west with speed 60

mph. If the vehicles remain locked together, the final speed is:

- 10 mph, West
- 20 mph, West
- 30 mph, West
- 10 mph, East
- 20 mph, East
- 30 mph, East
- The vehicles remain stationary.
- None of the above
- Cannot be determined

## Commentary:

## Answer

(8) None of the above. This is a straightforward totally inelastic

collision situation.

## Background

Students are frequently bothered by the idea of a totally or perfectly

inelastic collision. They are inclined to think of inelasticity as

imperfection, so the idea of perfect imperfection is distressing.

Consequently the scale shifts and they label collisions when objects

stick together as inelastic, the general collision as elastic, and

collisions conserving kinetic energy as perfectly elastic.

## Questions to Reveal Student Reasoning

How fast would the car have to be traveling for the combined vehicles to

remain at rest after the collision?

If the collision was elastic, in which direction would the sports car

travel after the collision?

## Suggestions

By relating the general collision problem to that of two masses

colliding with a spring between them, it is possible to get students to

realize that all two body collisions pass through the state with both

objects traveling with the CM velocity. This helps unify the concepts

of elastic, inelastic and perfectly inelastic collisions.