Randall D. Knight — Work and Kinetic Energy: Problem 57

a. FIGURE P9.57 shows a rope holding a mass \(m\) in place at angle \(\theta\) on the side of a frictionless circular slope of radius \(R\). What is the tension in the rope? b. How much work does tension do to pull the mass from the bottom of the hill (\(\theta = 0\)) to the top at constant speed? To answer this question, write an expression for the work done when the mass moves through a very small distance \(ds\) while it has angle \(\theta\), replace \(ds\) with an equivalent expression involving \(R\) and \(d\theta\), then integrate.