How Is Momentum Conserved in an Inelastic Collision When Both Vehicles Stop?

[pivoxa15]

Homework Statement

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?

Homework Equations

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.

 

[cristo]

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.

 

[pivoxa15]

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

 

[cristo]

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.

 

[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.

 

[Doc Al]

Homework Statement

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?

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.

 

[pivoxa15]

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

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.

 

[Doc Al]

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.

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.)

 

[pivoxa15]

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.)

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 transferred to the earth.