A small mass m is pulled to the top of a frictionless halfcylinder (of radius R) by a cord that passes over the top of the cylinder. (a) If the mass moves at a constant speed, show that [tex]F=mg cos(\theta)[/tex]. The angle is between the horizontal and the radius drawn to the mass.
(b) By directly integrating
find the work done in moving the mass at constant speed from the bottom to the top of the half-cylinder. Here ds represents an incremental displacement of the small mass.
The Attempt at a Solution
The a-part was easy when I drew a diagram. The b-part is the one I'm struggling with. With the Work-Energy theorem I get that the work done by F is mgR. But what integral should I compute and why? Have no idea whatsoever..