1) Which of the following forces is conservative?
(a) F = k (x, 2y, 3z) where k is constant.
(b) F = k (y, x, 0).
(c) F = k (-y, x, 0).
For those which are conservative, find the corresponding potential energy U, and verify by direct differentiation that F = -ΔU.
2) The figure shows a child's toy, which has the shape of a cylinder mounted on top of a hemisphere. The radius of the hemisphere is R and the CM of the whole toy is at height h above the floor.
(a) Write down the gravitational potential energy when the toy is tipped to an angle θ from the vertical.
(b) For what values of R and h is the equilibrium θ = 0 stable?
