Question

PROBLEM 2 - (20 points) Partial credit will not be given unless the solution procedure is clearly detailed. 2A. Consider the system in figure where a weight Wis suspended by an inextensible cable connected to a pulley. The pulley is free to rotate without friction around the pinned joint B. A lever is hinged at A and can be actuated by a force of magnitude F so that the breaking pad can come into contact with the pulley. The coefficient of static friction between the breaking pad and the pulley is Mo. • Draw a complete free body diagram of both the bar and the pulley on the schematic provided below on the right. • Determine the minimum magnitude of the applied force F that will prevent the pulley from rotating under the effect of the weight W. Assume W = 10 N, a = 0.5 m, b = 1 m, c = 0.1 m, Mo = 0.3. Hint: note that the point of contact between the breaking pad and the pulley is at a distance c from the point A. Assume the friction force between the pad and the pulley to be solely in the vertical direction (i.e. the curvature of the pad does not have any effect). FBD (5pts) LAU HE

Answer 1

given is

W = 10 N

a = 0.5m

b = 1m

c = 0.1m

$\mu _{o}$ = 0.3

now FBD of lever and pulley is shown below

since the drum is not rotating that means the moment generated due to load W is balanced by moment generated due to friction force

$\mu _{o}$ * N*r = W*r

0.3*N*r = 10*r

N = 33.33(N)

now consider FBD of the lever

taking moment about A

N*b + fs*c - F*(a+b) = 0

33.33*1 + 10*0.1 = F( 0.5 + 1)

F = 22.88 N

thus the minimum force which will prevent the pulley from rotating under the weight W is 22.88 N