Why is gravitational potential energy path independent? Gravitational potential energy depends upon difference in height of initial and final position of a body and it's independent of the path followed by the body by moving from initial and final position. Why is it so?
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Potential energy is energy that is stored. Stored in the way that some force tries to release it. Like in a spring. You can compress it and put a rubber band around it, and now you have stored elastic potential energy because the spring wants to release itself.
Note that it only wants to release itself in the axial direction.
Imagine gravity like such a spring. It wants to "release itself", but only in the up/down direction. You store energy by lifting stuff, because gravity pulls downwards. You don't store energy by moving it sideways, since no force wants to release anything in the sideways direction.
So, when you walk up the stairs, it is the upwards motion that is hard, because gravity fights it. The sideways motion is not any harder than at a plain ground and no energy is stored due to you walking sideways. Therefore it doesn't matter which path you took to reach a higher altitude. Only the height itself matters.
Steeven
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