A small block of mass is released from rest at the top of a smooth quarter-circular…
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A small block of mass m is released from rest at the top of a smooth quarter-circular track of radius R. The block starts at point A, a vertical distance R above the lowest point B of the track, and slides to B where the track becomes horizontal. Friction is negligible throughout the motion.
(a) Calculate the speed vB of the block when it reaches point B.
(b) While passing through point B the block is momentarily moving in a horizontal circle of radius R. Determine the magnitude of the normal force exerted on the block by the track at B.
(c) The horizontal section of the track rises smoothly to a point C that is a height h above B before leveling again. Determine the speed of the block at C in terms of h, g, and any other relevant variables.
(d) Qualitatively describe how the kinetic and potential energies of the block change during the entire trip from A to C, and comment on the value of the total mechanical energy of the system at all points of the motion.