**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 *= µ*R*

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 *= µ*R*

µ(*W *+ *P*_{2}sinθ ) = *P*_{2}cosθ

*P*_{2} = µ*W*/(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**