Question

A body resting on a rough horizontal plane required a pull of 24N inclined at 30º to the plane just to move it. It was also found that a push of 30N at 30º to the plane was just enough to cause motion to impend. Make calculations for the weight of body and the coefficient of friction.

Answer 1

∑H = 0; F = P₁ cosθ

∑V = 0; R = W – P₁ sinθ

Also F = µR

µ(W – P sinθ) = P₁ cosθ

or P₁ = µ W / (cosθ + µsinθ) ...(i)

With reference to the free body diagram (Fig)when push is applied)

∑H = 0; F = P₂cosθ

∑V = 0; R = W + P₂sinθ

Also F = µR

µ(W + P₂sin θ) = P2cosθ

P₂ = µW/(cosθ – µsinθ)......(ii)

 From expression (i) and (ii),

P₁/ P₂ = (cos θ – µsin θ )/ (cos θ + µsin θ)

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

On solving

µ = 0.192

Putting the value of µ in equation (i) we get the value of W

 = 120.25N