Question

A block of mass $m$ is pulled along a horizontal surface by applying a force at an angle $\theta$ with the horizontal. If the block travels with a uniform velocity and has a displacement $d$ and the coefficeint of friction is $\mu$, then determine the work done by the applied force.

Answer 1

Let the applied force be F. Force F is making an angle of x with the horizontal so the component of force in the horizontal direction is Fcosx. This force takes the block in forward direction. The frictional force acting on the block acts in the opposite direction of the applied force.

The frictional force is given as

f=uR

The reaction force R=mg-Fsinx

therefore f=u(mg-Fsinx). For the horizontal motion, Fcosx is greater than or equal to F.

Fcosx > u (mg-Fsinx)

F>umg/cosx+usinx

Therefore the workdone is

W=F.d.=Fdcosx=umgdcosx/cosx+usinx