A body of mass m is released from the top of a rough inclined plane of length l and height h If f is the force of friction prove that the body will reach the bottom with a velocity `upsilon = sqrt((2)/(m) (m g h - f l))` .

Explanation

On reaching the battom loss in `P.E` = mgh
Gain in `K.E = (1)/(2) m upsilon^(2)` and
work done against friction `f xx l`
According to the law of conservation of energy
`(1)/(2) m upsilon^(2) + f xx l = mgh`
`upsilon =sqrt((2)/(m) (mgh- fxxl))`
which was to be proved.