Question

A body of mass $m$ rests on horizontal surface, the coefficient of friction between the body and the surface is $\mu$. if the mass is pulled by a force $P$ as shown in the figure, the limiting friction between body and surface will be:

• A. $\mu mg$
• B. $\mu \left[ mg+\left( \frac{P}{2} \right) \right]$
• C. $\mu \left[ mg-\left( \frac{P}{2} \right) \right]$
• D. $\mu \left[ mg-\left( \frac{\sqrt{3}P}{2} \right) \right]$

Answer 1

Answer: (C)

$\mu \left[ mg-\left( \frac{P}{2} \right) \right]$

Answer 2

Sketch the free body diagrams. Resoles the force $P$ is horizontal and vertical components.
The free body diagram of the various forces acting on body is shown. $R$ is the reaction of the surface on mass, $f_{s}$ is frictional force.

Taking the horizontal and vertical components, we have
$R=mg-P\,\sin \,30^{\circ }=mg-\frac{P}{2}$
Limiting frictional force is
$F=\mu R=\mu \left[ mg-\frac{P}{2} \right]$