Energy discrepencies depending on frame of reference

[aalnaif]

The other day, I was arguing that a car traveling 70mph rear-ending a car traveling 55mph is the same as a car traveling 15mph rear-ending a stationary car. My argument was that, from the frame of reference of the car that was traveling 55mph, the energy of the other car is k(15²), where k = mass/2. But then I thought, from the speedy car's frame of reference, the energy that must be dissipated to slow down to 55mph is k(70²-55²), which is not equal to k(15²).

How come the energy that must be dissipated in the speedy car's frame of reference is different from the energy of the speedy car from the slower car's frame of reference?

 

[kcdodd]

Energy is frame dependent.

Also, if you are talking about the reference frame of the car, conservation of energy goes out the window because they are not inertial reference frames during the crash. I think the question is ill-posed on that ground. You can ask what it looks like in a moving reference frame not attached to either involved vehicle, but it will be different depending on which one you specify.

 

[tiny-tim]

Welcome to PF!

Hi aalnaif! Welcome to PF!

… But then I thought, from the speedy car's frame of reference, the energy that must be dissipated to slow down to 55mph…

But it won't slow down to 55mph … why should it?

If you take into account the actual final speeds of the two cars, you'll find that the energy lost is the same in both frames.