A man of mass `m` speeds up while running from rest to a speed v in a straight track along an inclined plane, after raising through a height `h`.
`W_(gravity)="work done by gravity on the man"`
`W_(friction)="work done by friction on the man"`
`W_(man)="work done by man"`
If in the previous problem, we replace the man by a block of mass m and release it from top of the inclined plane, and let it gain a speed v, then

Options

A. (a) `W_(f riction)=-mgh+1/2mv^2`
B. (b) `W_(gravity)=-mgh`
C. (c) `W_(f riction)=0`
D. (d) `W_(f riction)=-mumgx`, where x is the horizontal distance covered and `mu` is the coefficient of friction between the block and the ground.

Answer

A, B, D

Explanation

`W_f+W_(mg)=DeltaKE`
`impliesW_f+mgh=1/2mv^2`
`impliesW_f=-mgh+1/2mv^2`
Also `W_f=-mumgcos theta l =-mumgx`