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 m gamma y^2 where gamma is a constant and y is the mass's height above the horizontal ground, Find the work done by gravity on a mass m moving from r_1 to r_2, and use your answer to show that gravity on Planet X, although most unusual, is still conservative. Find the corresponding potential energy, Still on the same planet, 1 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? If I release the bead from rest at a height h, how fast will it be going when it reaches the ground?
