Elastic Collision: Momentum & KE - What's the Difference?

[ananthu]

In an inelastic collision, it is said that the total KE is not conserved but the total momentum is. When both the momentum and KE are the products of mass and some power of velocity, how total value of one remains constant and the other not. This is very confusing.

 

[cepheid]

Be careful:

- momentum is a vector, because it depends on velocity, which is a vector. For momentum, the direction in which things are moving must be taken into account.

- kinetic energy is a scalar, because it depends on speed. In other words, for kinetic energy, we only care about the magnitude of the velocity, and not on its direction.

Example: two equal-mass objects travel towards each other at the same speed, collide, and stick together. After the collision, the merged object is stationary.

In this situation, momentum is conserved: the total momentum was zero before the collision because the momentum vector of the first object had the same magnitude and the exact opposite direction from the momentum vector of the second object. Therefore, the vector sum of the two momenta was zero. After the colllision, the total momentum was also zero, because nothing was moving.

In contrast, before the collision, there was a non-zero amount of kinetic energy in the system, since both objects had some non-zero speed. The energies of the two objects added together to result in the total kinetic energy. After the collision, there was no kinetic energy in the system, since both objects had zero speed. That kinetic energy was simply lost.*

*of course, energy in general is never lost, just converted from one form to another. The kinetic energy in question would have been converted into heat and sound energy, as well as being used to do the work needed to deform the objects upon collision.

 

[ananthu]

Thank you. Your reply is enlightening.