Question

A block od mass m is slowly pulled along a curved surface from position 1 and 2. If the coefficient of kinetic friction between the block and surface is $\mu ,$ find the work done by the applied force.

Answer 1

We know that friction force is $f=\mu N=\mu mg\cos \theta$

Hence work done by friction in moving distance $dl$ along incline is $f.dl=\mu mgdl.cos\theta =\mu mgdx$

Hence total work done against friction is $\mu mgx$

And work done against gravity is $mgy$

Hence total work done by the applied force is $W=\mu mgx+mgy$

$⟹W=mg(\mu x+y)$