Determine force on a body to pull or push:

Q: A wooden block having weight of 50N rests on the horizontal plane. Determine force required which is acted at an angle of 15° to just (a) Pull it, and (b) Push it. Take the coefficient friction = 0.4 between the mating surfaces. Also comment on the result.

Sol.: Let P₁ be the force needed to just pull the block. In limiting equilibrium, forces are balanced. That gives

∑H = 0; F = P₁cosθ

∑V = 0; R = W - P₁sinθ

Also F = µR

µ(W - P₁ sinθ) = P₁cosθ

or P₁ = µW / (cosθ  + µsinθ)

= 0.4 × 50 /( cos 15° + 0.4 sinl5°)

= 18.70N                                                                                  .......Ans

(b) Let P₂  be the force which is required to just push the block. With reference to free body diagram

Let us write equations of equilibrium,

∑H = 0; F = P₂cosθ

∑V = 0; R = W + P₂Sinθ

Also F = µR

µ (W + P₂sin θ ) = P₂ cosθ

or P₂ = µW / (cosθ - µsinθ)

= 0.4 × 50 /( cos 15° - 0.4 sinl5°)

= 23.17N                                                                  .......Ans

Comments. It is easier to pull the given block than push it.