Question

2. A small particle of mass m is pulled to the top of a frictionless half-cylinder (of radius by a light cord that passes over the top of the cylinder as shown. The force F is such that the particle moves at a constant speed v. R) (a) What is the normal foce on the particle when it is in the position shown? (3pts) (a) What is the normal force on the particl (b) Show that F = mg cost. [2pts] (c) By directly integrating w F dr, find the work done in moving the particle at constant speed from the bottom to the top of the half-cylinder. [4pts] (d) What is the net work done on the particle? 2pts]

Please answer all the parts, show all work and explain the components. I will give you a thumbs up.

Answer 1

A) since the mass moves in circular motion,

Mgsin theta - N= Mv²/R

N = Mg sin theta -Mv²/R

b)For moving at constatnt speed, tangential force has to be zero

F - Mg cos theta = 0

F = Mg cos theta

C) W = integral F.dr

dr = R d theta

W = integral Mg cos theta R d theta from 0 to pi/2

W = MgR sin pi/2 = mgr

D) net work done is zero because work done is equal to change in kinetic energy and kinetic energy remains same because of constant velocity