# Energy in Different Frames

Q:
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
A:

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)

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