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