Elastic Collision: Who Experiences Larger Accel?

[justagirl]

A cart of mass M and a second cart of mass 2M collide head on elastically and bounce apart. Which cart experiences a larger magnitude of acceleration during the collision?

 

[cepheid]

I think the strategy for this question may be as simple as: think Newton's second law

 

[Jamesss]

apply conservation of momentum.
m1v1 = m2v2, assuming they are traveling at the same velocities.

you derive then for the acceleration. (algebraically speaking)
James

 

[cepheid]

?

I'm not sure what you're getting at here...there is no reason to assume that they are traveling at the same velocity, and even if they were, why should the momentum of the first cart equal that of the second? Conservation of momentum states that the TOTAL momentum of the system should be the same before and after the collision. So, using primed quantities to represent values after the collision:

m1v1 + m2v2 = m1'v1' + m2'v2'

In any case, I don't see how that helps her answer the problem. Using Newton's third law, the two carts exert equal and opposite contact forces on each other. By Newton's second law, the same force accelerates two different masses by different amounts, and it imparts a cart twice as heavy with half the acceleration, right?

 

[Jamesss]

Touche!~ I now remember a tennis ball and basketball demonstration. Yes it is the action/reaction forces at play here. Forget what I said before.

Duh!