Question

If reaction is $R$ and coefficient of friction ${\mu }_r$ , what is the work done against friction in moving a body by distance $d$ ?

• A. $\frac{{\mu }_{r}Rd}{4}$
• B. $2{\mu }_r,Rd$
• C. ${\mu }_{r}Rd$
• D. $\frac{{\mu }_{r}Rd}{2}$

Answer 1

Answer: (C)

(c) Magnitude of frictional force acting on the block is given as
$f={\mu }_r\times$ Reaction force $={\mu }_{r}R$
Work done against friction force, $=f\cdot s=fs\cos \theta$
where, $s$ is the displacement and $\theta$ is the angle between the frictional force and displacement.
Here, $\theta =180^{\circ },s=d$
$\Rightarrow W={\mu }_{R}Rd\cos 180^{\circ }=-{\mu }_{R}Rd$
$\left[\because \cos 180^{\circ }=-1\right]$
where, negative sign implies that the displacement is in the opposite direction to that of the frictional force.