Chapter 7, Problem 7.25P

A small particle of mass m is pulled to the top of a friction less half-cylinder (of radius R) by a light cord that passes over the top of the cylinder as illustrated in Figure P7.15. (a) Assuming the particle moves at a constant speed, show that F = mg cos θ. Note: If the particle moves at constant speed, the component of its acceleration tangent to the cylinder must be zero at all times. (b) By directly integrating $W={\displaystyle \int \stackrel{\to }{F}\cdot d\stackrel{\to }{r}}$, find the work done in moving the particle at constant speed from the bottom to the top of the hall-cylinder.

Figure P7.15