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Relativity and the Law of Conservation of Energy

You (A) are in a sledge sliding down an inclined plane. (Friction is neglected). An observer (B) at the foot of the plane looks at your initial position at the top of the slide and sees your energy as potential energy (mgh). You (A) slide down to the bottom of the plane and have a velocity of V0. So, the observer sees mgh = mV02/2 which is the law of conservation of energy.

I am freezing so I (B) decide to get in the car and move in the same direction of the sliding sledge (A) with constant speed V0 while am still watching you (A). So relative to me (B) I see: mgh + mV02/2 = 0 + 0

According to Galileo, if all laws of physics are the same in all frames of reference, why is mgh + mV02/2 = 0 + 0 in fig 2. Save the law of conservation of energy.

I just want an interpretation of what happened, preferably no equation, lets assume I don't know anything in physics.

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Solution Preview

The velocity of a body B relative to a body A is found by considering the observer body A to be stationary. Hence if A happens to be moving at a velocity v due west, then an equal and opposite velocity has to be applied to it to bring it to rest.
To maintain the system unchanged, the same (v, due east) has to be applied to the body B. The body B now has two velocities. One is its own original velocity. The other is a velocity equal and opposite to that of the ...

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363 words.