A2L Item 074
- Description: Find the final velocity of perfectly inelastic collision of two cars.
- Goal: Problem solving using momentum conservation.
- Source: UMPERG-ctqpe90
- Keywords: Conservation, Mechanics, Momentum
The question for students:
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 for teachers:
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.