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Q.
If reaction is $R$ and coefficient of friction $ \mu_r $ , what is the work done against friction in moving a body by distance $ d $ ?
AMUAMU 2017
Solution:
(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, $=f \cdot s=f s \cos \theta$
where, $s$ is the displacement and $\theta$ is the angle between the frictional force and displacement.
Here, $\theta=180^{\circ}, s=d$
$\Rightarrow W=\mu_{R} R d \cos 180^{\circ}=-\mu_{R} R d$
$\left[\because \cos 180^{\circ}=-1\right]$
where, negative sign implies that the displacement is in the opposite direction to that of the frictional force.
