Gravity

Question:

Near to the point where I am standing on the surface of Planet X, the gravitational force on a mass m is vertically down but has magnitude myy2 where y is a constant and y is the mass's height above the horizontal ground. (a) Find the work done by gravity on a mass m moving from r1 to r2, and use your answer to show that gravity on Planet X, although most unusual, is still conservative. Find the corresponding potential energy. (b) Still on the same planet, I thread a bead on a curved, frictionless, rigid wire, which extends from ground level to a height h above the ground. Show clearly in a picture the forces on the bead when it is somewhere on the wire. (Just name the forces so it's clear what they are; don't worry about their magnitude.) Which of the forces are conservative and which are not? (c) If I release the bead from rest at a height h, how fast will it be going when it reaches the ground?

Solution: