For example, if Jack and Jill, who both weigh 20kg each, are moving in the same direction at 1m/s, they should both have 10J of kinetic energy each, and they are both moving at 0m/s relative to each other and so there is a difference of 0J of kinetic energy between Jack and Jill. If Jack accelerates to 2m/s, while Jill stays at 1m/s, Jack now has 40J of kinetic energy, while Jill still has 10J, so Jack has 30J more kinetic energy than Jill. However, relative to Jill, Jack is moving at 1m/s, and so should only have 10J more energy than her. What am I missing?
In: Physics
Energy is also reference frame dependent. In Jill’s reference frame, Jack does indeed have 10 J of kinetic energy. In a rest frame, he has 30 J more than Jill does. There’s no contradiction here – Jack would hit Jill much less hard than he’d hit a stationary object.
Traditionally, though, when we speak of kinetic energy we usually speak of it in a specific frame of reference that we think of as being “at rest” unless otherwise specified.
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