Conservation of momentum

1. Feb 16, 2007

pivoxa15

1. The problem statement, all variables and given/known data
In an inelastic collision, momentum is conserved but kinetic energy is not conserved. How can this be true in the situation where a car runs into the back of a stationary truck, since after the collision neither are moving and so cannot have momentum?

2. Relevant equations

3. The attempt at a solution
If neither the car nor the truck is moving than the momentum must have transferred to the earth and the earth is actually moving. Although it’s mass is so large that the velocity is basically undetectable.

2. Feb 16, 2007

cristo

Staff Emeritus
I disagree with the setting up of the situation. If a car hits a stationary truck, and the collision is perfectly inelastic, then the car and truck will move after the collision, even if the velocity is very small.

3. Feb 16, 2007

pivoxa15

The question didn't have the word 'perfect' before inelastic.

4. Feb 16, 2007

cristo

Staff Emeritus
Ok, well if the collision is not perfectly inelastic, then the car and the truck will not "stick together" and so the car will be moving after the collision.

5. Feb 17, 2007

pivoxa15

True but after a slightly longer period of time than in the case you described which was immediately after when things are still moving i.e. the car moving backwards, everything will have stopped. At that time, we would have to say that all the initial momentum have been converted to the earth.

6. Feb 17, 2007

Staff: Mentor

The momentum of car + truck would only be conserved if no external forces act on them. But the earth exerts a force on them. If you include the earth in your system, then momentum will be conserved.

If car and truck collided inelastically on a frictionless surface, you would see the combined car + truck continue moving after the collision.

7. Feb 17, 2007

pivoxa15

It's not necessarily the case if the collision is very light. The car could move a little bit and truck continue to be stationary.

8. Feb 18, 2007

Staff: Mentor

If the collision takes place on a frictionless surface, the truck will move no matter how lightly it was struck. (Note that in my example I specified an inelastic collision, one in which they stick together.)

9. Feb 18, 2007

pivoxa15

Perfectly inelastic is when they stick together. Inelastic by itself could mean that or not. The problem didn't have perfectly inelastic.

Your point about friction is good. Friction would have to be present if they both stop after the collision. Meaning energy and momentum has been transfered to the earth.