Question

A rope making 1 1/4 turns around a stationary horizontal drum is used to support a weight W Fig. If the coefficient of friction is 0.3 what range of weight can be supported by exerting a 600 N force at the other end of the rope?

Answer 1

Angle of contact = 1.25 × 2π = 2.5π 

(1) Let the impending motion of the weight be downward.

(2) Let the impending motion of weight be upwards. Then 

T₁ = W; T₂ = 600 N

T₂ = T₁ e^µθ 

600 = W e^0.75π 

W = 56.87 N 

Thus, a 600 N force can support a range of loads between 56.87 N to 6330.43 N weight on the other side of drum.