Conceptual Momentum/Energy Problem

[JB83]

Determine for each of the following statements whether it is always true or can be false.

Two objects of different masses but moving at the same velocity have different momentum.
-this should be true because p=mv and if there are different v then the p should be different.
Kinetic energy is conserved in an elastic collision.
-true
Momentum of a system may be conserved even when mechanical energy is not.
-false
In an elastic collision the momentum is conserved.
-true
In a perfectly inelastic collision, all the kinetic energy of the objects involved in the collision is lost.
-true

These are the answers I believe to be true. Does anyone have any idea why at least one of them is wrong?

 

[Doc Al]

Two of your answers are wrong. Here are some things to consider. (Imagine the collisions to take place on a frictionless surface):
(1) Say two identical chunks of clay, moving towards each other at the same speed, smack into each other and stick together. What kind of collision is this? What's conserved? What's not conserved? (This might give you a hint about one of your answers.)
(2) Say a chunk of clay, moving at some speed, smacks into another piece of clay that is at rest. They stick together. What kind of collision is this? What's conserved? What's not conserved? After the collision, does the clay still have kinetic energy? (This might give you another hint.)

 

[iliah]

Think of an inelastic collision and you will know why number three is wrong.

In the last one: think of the equation to find kinetic energy. If the velocity of both objects after the collision is not zero, then what would the kinetic energy be? Is it all lost?

[and I apparently posted at the same time as the the above poster. Heh...]