Question

Determine the minimum value of weight W required to cause motion of a block, which rests on a horizontal plane. The block weighs 300N and the coefficient of friction between the block and plane is 0.6. Angle of warp over the pulley is 90º and the coefficient of friction between the pulley and rope is 0.3.

Answer 1

Since the weight W impend vertical motion in the down ward direction, the tension in the two sides of the pulley will be as shown in fig. Given date: 

T₁ = W, µ = 0.3, θ = 90° = π/2 rad

Using the relation of Ratio of belt tension, T₁/T₂ = e^µ.θ

W/T₂ = e^(0.3).(p/2) = 1.6

W = 1.6 × T₂ .......(i)

Considering the equilibrium of block:

∑V = 0

R = 300N

∑H = 0 ......(ii) 

T₂ = µR = 0.3 × 300 = 180N ......(iii)

Equating equation (i) and (iii), we get

W = 1.6 × 180

W = 288N