Momentum and Energy and Galilean Relativity

[Red Rubbie]

Homework Statement

Suppose you have two bodies (assume a unit mass) approaching one another at the same speed, i.e., the velocities, v, have the same magnitude but are in opposite directions. Presumably the center of mass is half way between them, and it is not moving. It appears that the momentum of the system is 0. When they collide they both stop, i.e., their individual momentum becomes 0, their total momentum is 0, and the collision results in something happening - they both coalesce into a (hotter) stationery mass, they explode, etc.

Now consider the same situation from a frame of reference located on one of the bodies. Relative to this frame of reference, the momentum of the system seems to be 2v, the velocity of the moving body relative to the stationery body forming the frame of reference. When the 'moving' body hits the 'stationery' body, then the center of mass ( hot coalesced bodies, a mess of particles, whatever) will move in the direction of the moving body with a velocity, v.

What's wrong with this?

Consider the same situation with energy replacing momentum.

Homework Equations

The Attempt at a Solution

Abject failure.

 

[ehild]

Now consider the same situation from a frame of reference located on one of the bodies. Relative to this frame of reference, the momentum of the system seems to be 2v, the velocity of the moving body relative to the stationery body forming the frame of reference. When the 'moving' body hits the 'stationery' body, then the center of mass ( hot coalesced bodies, a mess of particles, whatever) will move in the direction of the moving body with a velocity, v.

What's wrong with this?

Nothing. The frame of reference moves with velocity -v with respect to the stationary frame of reference: that is, the bodies are in rest in it.

ehild