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
Kinetic energy is dependent on frame. In Newtonian physics, Newton assumed (and even argued for) a absolute universal coordinate system, then velocity are all relative to this absolute system. But in Einstein’s relativity, or even just Galileo’s relativity, there are no absolute velocity, so there are no absolute kinetic energy. But Einstein’s theory deal with this by only require total energy to be absolute but its make up can change, in different reference frame kinetic energy can turn into mass and vice versa.
You’re not missing anything. Kinetic energy is frame-dependent, which means that it is totally fine for different reference frames to disagree about how much kinetic energy an object has.
In Jill’s frame of reference Jack does only have 10J more energy; from a stationary observer, he has 30J more energy.
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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