Question

An inclined plane is moving up with constant velocity `v`. A block kept on incline is at rest. Calculate the work done by gravity, friction force, and normal reaciton on block in time interval of t.

Answer 1

As the block is at rest w.r.t. inclined plane, hence, the friciton between blocks and plane will be of static nature and will act in the direciton up the plane

Free-body diagram of block:
a. For work done by gravity
`W_(gravity)=vecF*vecs`
`=mg*vtcos180^@`
`=mgvt(-1)`
`=-mgvt`

b. Work done by normal reaction
`W_(normal)=N*vt*costheta`
`=(mgcostheta)vtcostheta`
`=mgvtcos^2theta`

c. Work done by friction force
`W_(f riction)=F*vt cos(90-theta)`
`=(mgsintheta)*vtsintheta`
`=mgvtsin^2theta`