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Relative Motion : Kinetic and potential energy

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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.

**See attachment for diagrams and proper citation of energy law

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Solution Summary

A good conceptual question of relative motion in which the the loss in potential energy does not appears to be equal to gain in kinetic energy.

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