Newton's Third Law in Inelastic Collisions

[Sammy101]

Lets say that I have a cart on a track with silly putty on the end. This first cart is moving with an initial "x" velocity. There is another cart about a foot ahead of it with sillyputty on its bumper also. (Both carts have the same mass) This cart has an initial velocity of zero. Of course when the two cars collide, they will stick and move together. I am just trying to understand this through Newton's third law. When the first moving cart hits the second cart, the first cart is applying a force to accelerate the nonmoving car, and the nonmoving cart is applying an equal and opposite reaction force on the moving car, slowing the moving cart down. Why does the reaction force the initially nonmoving cart is applying on the initially moving cart not completely slow down the initially moving cart?

I know that in this case in an elastic collision, the first cart would completely stop and the second cart would take all of the momentum of the first cart. So what is it about the inelasticity of the collision that overrides the fact that the first cart is not able to transfer all of its momentum to the second cart?

 

[bp_psy]

Momentum must be conserved.If the trucks are stuck together they will move with a smaller velocity but the momentum is conserved.

 

[Sammy101]

I think I understand that part well its why in an elastic collisison in this situation, the first car would come to a stop while in an inelastic collision like my example they continue to move forward with a reduced velocity.

why is the opposite reaction force the nonmoving car applies to the moving car when they collide not able to slow the moving car to a stop? I know the collision is inelastic but what about an inelastic collision does not allow the first moving car to come to rest?

 

[technician]

In an ELASTIC collision Kinetic energy is conserved as well as momentum (which is always conserved) With carts of identical mass this means that the first one stops and the second one goes off with the original velocity.

 

[JHamm]

I know the collision is inelastic but what about an inelastic collision does not allow the first moving car to come to rest?

It is inelastic because the two are now stuck to one another, if the first one stopped then the second one must also stop and we've just lost a whole lot of momentum into the aether, the first one continues to move precisely because the two bodies have now joined to form one.

 

[Filip Larsen]

As you probably know, Newtons third law applies equally well no matter what the coefficient of restitution is for the collision. However, if you plot the force between the two carts as a function of time during collision for scenarios with different coefficients of restitution you will find that different scenarios will have different "plots". Since the total exchange of momentum is equal to the the integral of the force over time, more elastic collisions will in general have a force plot with more "room" below the curve.

The reason why "reaction forces are not able to transfer all momentum in inelastic collisions" should be found in the geometry and micro-interaction between the carts. For instance, elastic collision requires that the interaction takes place with little or no loss to frictional forces, so if the interaction has friction the collision will not be completely elastic.

 

[ehild]

I know that in this case in an elastic collision, the first cart would completely stop and the second cart would take all of the momentum of the first cart. So what is it about the inelasticity of the collision that overrides the fact that the first cart is not able to transfer all of its momentum to the second cart?

You are on the right track...
You can imagine elastic collision in the way that there is a spring attached to one cart and the other cart gets in touch with the spring. First the spring is compressed by the second cart, and the compressed spring pushes the first cart forward, the second cart bacwards. At a certain moment, both carts move with the same velocity, so they do not compress the spring further. The spring starts to release, pushing the first cart forward and the second cart backward, till it completely releases, converting its elastic energy to the KE of the carts.
In case of inelastic collision, the spring is replaced by some "putty" that exerts force when compressed by the carts, but it can not regain its original size after the carts move together, as it did not store elastic energy.

ehild