A solid metal cylinder of mass m rolls down parallel metal rails spaced a distance L apart with a constant acceleration of magnitude a0 [part (a) of figure]. The rails are inclined at an angle θ to the horizontal. Now the rails are connected electrically at the top and immersed in a magnetic field of magnitude B that is perpendicular to the plane of the rails [part (b) of figure].
(a) As it rolls down the rails, in what direction does current flow in the cylinder?
(b) What direction is the magnetic force on the cylinder?
(c) Instead of rolling at constant acceleration, the cylinder now approaches a terminal speed vt. What is vt in terms of L, m, R, g, θ, and B? R is the total electrical resistance of the circuit consisting of the cylinder, rails, and wire; assume R is constant (i.e., the resistances of the rails themselves are negligible).
