Determine minimum value of weigh to cause motion:

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

Sol: As the weight W impend vertical motion in down ward direction, the tension in two sides of the pulley will be as shown in figure given below

Given date:

T₁  = W, µ = 0.3, θ = 90° = p/₂ rad

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

                                                                                                                                                      ...(i)

Considering equilibrium of block:

ΣV = 0

R = 300N                                                                                                                             ...(ii)

ΣH = 0

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

By equating the equation (i) and (iii), we get

W  = 1.6 × 180

W = 288N                                                                      .......ANS