A lightweight cart of mass moves without friction along a rigid track that forms a…
PHYSICS · Multi-part · CBSE · Physics · Laws of Motion · Laws of Motion
Problem
A lightweight cart of mass m moves without friction along a rigid track that forms a full vertical circle of radius r. At the instant the cart is upside-down at the top of the loop, it is moving with some speed vtop.
(a) Draw and label all forces acting on the cart at the top of the loop.
(b) Write a qualitative argument, based only on the directions and magnitudes of the forces you identified in part (a), that establishes the specific condition under which the cart would just lose contact with the track at the top.
(c) Explain, without performing detailed calculations, how the requirement you stated in part (b) leads to a unique minimum value of vtop that depends on the loop’s radius. In your explanation, describe the physical role of both gravitational and contact forces.