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Calculate the weight of body and the coefficient of friction:
Q: Bodies resting on rough horizontal plane required pull of 24N inclined at 30º to the plane just to move it. It was found that a push of 30N at 30º to plane was just sufficient to cause motion to impend. Calculate the weight of body and the coefficient of friction.
Sol.: ∑H = 0; F = P1cosθ
∑V = 0; R = W - P1sinθ
Also F = µR
µ(W - P sin θ ) = P1cosθ
or P1 = µ W / (cosθ + µsinθ ) ...(i)
With reference to the free body diagram when push is applied
∑H = 0; F = P2cosθ
∑V = 0; R = W + P2sinθ
Also F = µR
µ(W + P2sinθ ) = P2cosθ
P2 = µW/(cosθ - µsinθ ) ...(ii)
From equation (i) and (ii),
P1/ P2 = (cosθ - µsinθ)/ (cosθ + µsinθ)
24/30 = (cos 30°- µ sin 30°)/ (cos 30°+ µsin 30°)
= (0.866 - 0.5µ)/(0.866 + 0.5µ)
0.6928 + 0.4µ = 0.866-0.5u
µ = 0.192 .......Ans
Putting value of µ in the equation (i) we get value of W
W = 120.25N .......Ans
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