Energy in Different Frames

Kinetic energy = half mass times velocity squared, where velocity (and I guess mass) are measured in a reference frame. Two equal masses are moving towards each other at non-relativistic velocity v from the point of view of a stationary observer. The total kinetic energy from the observer's pov is therefore 1/2 mv2 + 1/2 mv2 = mv2. However the kinetic energy of one mass from the pov of the other is 2mv2. How much energy is liberated when they crash into one another?
- Andrew (age 40)
UK

We need some more info on what happens in the collision. Let's say they stick together, and they're in a vacuum so all the energy stays in the masses themselves in some form.

Then in the center-of-mass frame all the kinetic energy is turned into thermal energy in the masses. That's mv², as you say. What about in the frame of one of the masses? It's got to be the same, since for non-relativistic velocities the thermal energies are the same in the two frames. How can that be? The final velocity in that frame is v/2, the final mass is 2m. So the net change in the large-scale kinetic energy is the same as in the other frame, although the initial and final values are not the same in the two frames.

Mike W.

(published on 03/23/2017)