A block of mass M is pulled along a horizontal surface by applying a force at angle `theta` with the horizontal. The friction coefficient between the block and the surfasce is `mu`. If the block travels at a uniform velocity, find the work donen by this applied force during a displacement d of the blcok.

Explanation

The forces acting on the block are shown in Figure. As the block moves with uniform velocity the resultant force on it is zero.
`therefore F cos theta = mu`N ….(i)
F sin `theta` + N = Mg …..(ii)
Eliminating N from equations (i) and (ii),
F cos `theta = mu `(Mg - F sin `theta`)
F = `(mu Mg)/( cos theta + mu sin theta)`
Work done by this force during a displacement d
W = F . d cos `theta = (mu" Mg" cos theta ) /(cos theta + mu sin theta )`