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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
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.
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