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 P7.25. (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 = ∫ F . d r, find the work done in moving the particle at constant speed from the bottom to the top of the half-cylinder .