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 = P_{1}cosθ
∑V = 0; R = W - P_{1}sinθ
Also F = µR
µ(W - P sin θ ) = P_{1}cosθ
or P_{1} = µ W / (cosθ + µsinθ ) ...(i)
With reference to the free body diagram when push is applied
∑H = 0; F = P_{2}cosθ
∑V = 0; R = W + P_{2}sinθ
Also F = µR
µ(W + P_{2}sinθ ) = P_{2}cosθ
P_{2} = µW/(cosθ - µsinθ ) ...(ii)
From equation (i) and (ii),
P_{1}/ P_{2} = (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
By solving
µ = 0.192 .......Ans
Putting value of µ in the equation (i) we get value of W
W = 120.25N .......Ans