Problem 1
A small particle of mass m starts from rest on a smooth approach track and then enters the inside of a vertical circular loop of radius R at its lowest point. The approach joins the loop smoothly, and the initial height H is measured above the loop bottom. Take g=9.8 m/s² and neglect all friction. (a) Find speed at position angle θ from the upward vertical, taking the bottom as zero potential. (b) Write the normal force and contact condition at the top. (c) Find minimum H to maintain contact throughout, then find the bottom normal force in this limiting case. Use SI units throughout and treat the track and constraints as ideal as specified. State sign conventions, retain units, and check the contact condition at every point of the loop.
problems.proof.stepOf
problems.proof.analysis
Substitute the established relation and isolate the requested quantity. Keep the physical solution consistent with the initial conditions and assumptions.