Conservation of Momentum/KE

[Speedking96]

Homework Statement

Two pieces of clay collide and stick together. During the
collision, which of these statements are true?
(a) Only the momentum of the clay is conserved,
(b) only the mechanical energy of the clay is conserved,
(c) both the momentum and the mechanical energy of the clay are conserved,
(d) the kinetic energy of the clay is conserved.

2.The attempt at a solution

I would say the momentum of the clay is conserved. This is because when the piece that is traveling faster strikes the slower piece, the faster piece slows down whereas the slower piece speeds up.

Applying the same logic to the mechanical energy tells me that it is also conserved.

 

[rpthomps]

This is an example of an inelastic collision. By definition, kinetic energy is not conserved only momentum.

 

[gneill]

Homework Statement

Two pieces of clay collide and stick together. During the
collision, which of these statements are true?
(a) Only the momentum of the clay is conserved,
(b) only the mechanical energy of the clay is conserved,
(c) both the momentum and the mechanical energy of the clay are conserved,
(d) the kinetic energy of the clay is conserved.

2.The attempt at a solution

I would say the momentum of the clay is conserved. This is because when the piece that is traveling faster strikes the slower piece, the faster piece slows down whereas the slower piece speeds up.

While your conclusion is correct (total momentum is conserved), your argument is just hand-waving. You haven't specified how much the slower piece speeds up, or how much the faster piece slows down or why either of those things occur, nor have you stated what is the relationship between those amounts that would result in a conservation of momentum. So, full points for the result but zero points for the argument :)

Conservation of momentum happens to be one of the conservation laws that you can always count on. So you are correct to conclude that momentum is a conserved quantity in the collision (or ANY collision).

Applying the same logic to the mechanical energy tells me that it is also conserved.

And this is where your hand-wavey logic fails you. Kinetic energy is not always conserved because the energy of motion can be transformed into other forms such as heat or sound or light. When two blobs of clay hit each other some of the energy of motion will go into heating the clay and some will go into producing sound during the impact. Energy may also go into stressing the material in some way, or setting up oscillations of the material (vibrations).

So in general, kinetic energy is NOT conserved in collisions unless the collisions are perfectly elastic, where all the energy that goes into deforming the colliding objects is returned to them as kinetic energy --- they "spring back" without loss to heat or other forms of energy.