Conservation of Energy in Springs

We can use WET in any inertial frame of reference..., When no ext force is applied, and there is no change of height... Change in KE = -(Change in PE(spr)) However..., KE change depends upon the frame of reference and the Extension of a sprinbg does not depend upon frame's choice..! HOW IS THIS POSSIBLE??
- Divjot (age 16)
Chandigarh. India

That's a wonderful question.

First, I should explain to other readers that we're not discussing special relativistic frames but just low-speed Galilean frames, where you can ignore the disagreements about lengths, etc.

So you're right that the change in spring potential energy is the same in each frame. Yet the change of kiinetic energy of that mass is  different, by an amount m(v•v₀), where v is the velocity in the original rest frame and v0 is the initial velocity according to the other frame. What can make up that difference?

The whole physical set-up makes no sense unless there's another mass, say M, attached to the other side of the spring. It's momentum, Mv₂, must change by exactly the opposite amount as the momentum change of the other mass, mv. So its energy changes by an amount Mv₂•v₀​= -m(v•v₀). So the net change of kinetic energy, counting the masses on both end of the spring, comes out the same in either frame.

Mike W.

(published on 09/25/2014)