By application of a force F , a body of mass m is raised to the top of a hill .F is tangential along the whole path. If the height of the hill is h, the length of the base of the hill is l , and the coefficient of friction is `mu` , then find the work done.

Explanation

Total path from the bottom to the top of the hill can be considered as an assembly of a large number of inclined planes of varying angles of inclination. Consider an incline of length `Deltas`. Its vertical height is `Deltah` and the angle of inclination is `alpha` [Fig.1.31].

Total work done in lifting the body along this inclined surface= work done against gravity +work done against friction.
`Delta W= mg Delta h+mu mg cos alpha *Deltas`
`=mg Delta h+mu mg cos alpha(Deltal)/(cos alpha) =mg (Deltah+mu Deltal)`
`therefore` Total work done to lift the body up to the top of the hill,
`W=sum Delta W=mg(sum Deltah +mu sum Deltal) =mg (h+mul)`