Question

A particle is moving with kinectic energy E,straight up an inclined plane with angle $\alpha$, the coefficient of friction being $\mu$.The work done against friction before the particle comes down to rest is

• A. $\frac{E\mu cos\alpha }{sin\alpha +\mu cos\alpha }$
• B. $\frac{Ecos\alpha }{sin\alpha +\mu cos\alpha }$
• C. $\frac{E}{sin\alpha +\mu cos\alpha }$
• D. $\frac{E}{g(sin\alpha +\mu cos\alpha )}$

Answer 1

The correct option is A $\frac{E\mu cos\alpha }{sin\alpha +\mu cos\alpha }$

when body starts moving up on inclined rough plane, kinetic energy will be converted to potential energy and some part will be lost to friction.

so $E=energy$ $lost+potential$ $energy$

$energy$ $lost=frictional$ $force\times distance$ $traveled$, $force=\mu mgCos\alpha$ and $distance=l$

and $potential$ $energy$$=mg\times distance\times Sin\alpha$

so

$E=l\times \mu mgCos\alpha +mg\times l\times Sin\alpha$

$l=\frac{E}{(sin\alpha +\mu cos\alpha )mg}$

as we know $force=\mu mgCos\alpha$

work done against friction will be $force\times distance=\frac{E\mu cos\alpha }{sin\alpha +\mu cos\alpha }$

so answer is optiom A.