A block of mass m is placed on an inclined plane which is moving with constant velocity v in horizontal direction as shown in figure. Then find out work done by the friction in time t if the block is at rest with respect to the incline plane.

Explanation

F.B.D. of block with respect to ground


Block is at rest with respect to wedge
`rArr " f " = " mg sin "theta `
In time t the displacement of block with respect to ground d = vt
Work done by friction for man A
`W_(f)` = (component of friction force along displacement) `xx`displacement
`W_(f)` = mg `sin theta.`vt cos`(180^(@) - theta))`
`W_(f) = - "mg vt cos"theta sin theta`

`W_(f)` for man B = 0 (displacement is zero with respect to man B)