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 P_{1} be the force needed to just pull the block. In limiting equilibrium, forces are balanced. That gives
∑H = 0; F = P_{1}cosθ
∑V = 0; R = W - P_{1}sinθ
Also F = µR
µ(W - P_{1} sinθ) = P_{1}cosθ
or P_{1} = µW / (cosθ + µsinθ)
= 0.4 × 50 /( cos 15° + 0.4 sinl5°)
= 18.70N .......Ans
(b) Let P_{2} 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 = P_{2}cosθ
∑V = 0; R = W + P_{2}Sinθ
Also F = µR
µ (W + P_{2}sin θ ) = P_{2 }cosθ
or P_{2} = 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.