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A block of mass M is pulled along a hori...

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.

Text Solution

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Forces on the block are
its weight Mg
ii the normal force N
the applied force F and
the kinetic friction `muN`.

The forces are shown in filgure. As the block moves with a uniform velocity, the forces and up to zero.
Taking horizontal and vertical components.
`F costheta=mu(Mg-Fsintheta)`
`F=(muMg)/(costheta+musintheta)`
the work done by this force during a displacement d is
`W=Fd costheta=(muMgdcostheta)/(costheta+musintheta)`
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