Serway & Jewett — Energy of a System: Problem 15.

A small particle of mass \(m\) is pulled to the top of a frictionless 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 \(F = mg \cos \theta\). 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 \(W = \int \vec{F} \cdot d\vec{r}\), find the work done in moving the particle at constant speed from the bottom to the top of the half-cylinder.