Determine force on a body to pull or push, Mechanical Engineering

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.

605_Determine force on a body to pull or push.png

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 ) = Pcosθ

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.

Posted Date: 10/17/2012 6:39:40 AM | Location : United States

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