What’s the difference between kinetic energy and momentum?

Question

I understand that they have two similar but different formula’s that both scale differently with velocity. I also understand that momentum has a direction ie. Vectored, and kinetic energy is directionless. What I can’t wrap my head around is how they are seperate properties with differing values and how it interacts with forces on an object.

For example, when an object collides with a wall, momentum drops to zero, the change in momentum requires the wall to exert force on the object and it involves some work done, and therefore energy. At the same time, the kinetic energy of the object is also released as heat(?)

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Answer 1

> For example, when an object collides with a wall, momentum drops to zero, the change in momentum requires the wall to exert force on the object and it involves some work done, and therefore energy. At the same time, the kinetic energy of the object is also released as heat(?)

Collision with a wall is a bad example; the wall is usually so much heavier than the object that it doesn’t seem to move at all. So it’s better to look at two objects of roughly similar mass colliding.

When one object meets the other, it will transfer momentum to it until both have the same velocity. You now have both objects moving, but at a lower speed than the original speed of the first object. As kinetic energy scales with the square of speed, the sum of kinetic energy will be lower than the original kinetic energy; the difference has been transformed into deformation.

If one of the objects is made of putty or soft clay, that’s the end of it. The deformation energy is transformed into heat; the two objects now stick together and move as one. That’s called an inelastic collision. In an elastic collision, the deformation energy is transformed back into kinetic energy, dished out to the two objects in reverse proportionality to their mass, such that the total momentum stays the same; the two objects now fly away from each other. Most real-world collisions are somewhere in between, with part of the deformation energy being transformed into heat or sound.