A box is raised to the same height either by lifting it vertically or by pushing it up an ideal inclined plane. Which quantity is the same in both cases?
Potential energy gained by the box
The gravitational potential energy gained by a body is PE = mgh, which depends only on its mass and the vertical height through which it is raised, not on the path taken.
Since the box reaches the same height in both cases, the potential energy gained is the same.
On an inclined plane the box moves a longer distance along the slope, but the effort needed is smaller, so the mechanical advantage is greater than when lifting vertically. Distance, effort and mechanical advantage therefore differ between the two methods.
Hence, the answer is Potential energy gained by the box.
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