Question

A body of mass m was slowly hauled up the hill as shown in fig. 9.18 by a force F which at each point was directed along a tangent to the trajectory. Find the work performed by this force, if the height of the hill is h, the length of its base is l and the coefficient of friction is $\mu$.

Answer 1

We know that friction force is $f=\mu N=\mu mg\cos \theta$ where $\theta$ is inclination at that particular instant

Hence, work done against friction in moving distance $dL$ along the incline is $d{W}_f=\mu mg\cos \theta dL=\mu mgdx$ $(dx=dL\cos \theta )$

Hence, total work done against friction $W_f=\mu mgl$ where $l=$ total horizontal distance

Work done against gravity is $W_g=mgh$

Hence total work done is $W=W_f+W_g$

$⟹W=(\mu l+h)mg$