Evaluate Force to slide the body over the surface:
A body having weight 100N rests on 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 make the body to slide over the surface?
Sol.: In limiting equilibrium, the forces are balanced.
∑H = 0;
F = P cosθ
∑V = 0;
R = W - Psinθ
Also F = µR
P.cos θ = µ(W- P.sinθ )
P.cosθ = µ.W- µ.P.sinθ
µ.P.sinθ + P.cosθ = µ.W
P(µ.sinθ + cos θ ) = µ.W
P = µ.W/(Cosθ + µ.sinθ )
= 0.3× 100 / (Cos30° + 0.3sin30°)
= 29.53N .......Ans