I see how they got 1/2mv^2 for kinetic energy but can i get mgh for potiental Le

Question

I see how they got 1/2mv^2 for kinetic energy

but can i get mgh for potiental

Let us first write the resultant force on the box in the frame in which the incline is at rest. Fr = mg sin theta cos theta x - mg sin^2 theta y. This resultant force is the same in all inertial frames. Hence, acceleration is same in both the frames. ar = g sin theta cos theta x - gsin^2 theta y Consider first the situation as seen in the frame in which the incline is at rest. Initial velocity u0 = 0 Considering the point of release as the origin, initial position x0 = 0; y0 = 0. Solving Newton's laws we get Work done is just

Explanation / Answer

Subtract final energy( K.E found above) from initial energy(i.e when the body is at rest) to get potential energy of the body.

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