Question

A body of weight 100N rests on a rough horizontal surface (µ = 0.3) and is acted upon by a force applied at an angle of 300 to the horizontal. What force is required to just cause the body to slide over the surface? 

Answer 1

In the limiting equilibrium, the forces are balanced. That is

∑H = 0;

F = P cosθ

∑V = 0; 

R = W – P sinθ

Also F = µR

P.cosθ = µ(W– P.sinθ)

P.cosθ = µ.W– µ.P.sinθ

µ.P.sinθ + P.cosθ = µ.W

P(µ.sinθ + cosθ) = µ.W

P = µ.W/(Cosθ + µ.sinθ)

= 0.3× 100 / (Cos 30° + 0.3 sin 30°)

= 29.53N.