Question

A block of mass $m$ slides from the top of an inclined plane of angle of inclination $\theta$ and length $l$. The coefficient of friction between the plane and the block is $\mu$. Then it is observed over a distance $d$ along the horizontal surface having the same coefficient of friction $\mu$, before it comes to a stop. Find the value of $d$.

• A. $l[5\sin \theta -\mu \cos \theta ]/\mu$
• B. $l[\sin \theta -2\mu \cos \theta ]/\mu$
• C. $l[2\sin \theta -3\mu \cos \theta ]/\mu$
• D. $l[\sin \theta -\mu \cos \theta ]/\mu$

Answer 1

Answer: (D)

$l[\sin \theta -\mu \cos \theta ]/\mu$

Acceleration of block on rough inclined plane =$Netforce/mass$

=$(mgsin\theta -\mu mgcos\theta )/m$

=$gsin\theta -\mu gcos\theta$

Apply third equation of motion

$v^2=u^2+2as$

$v^2=0+2(gsin\theta -\mu gcos\theta )l$

$v^2=2(gsin\theta -\mu gcos\theta )l$

Suppose after travelling distance d it come to rest on horizontal plane

retardation due to friction=$-\mu g$

Apply third eqauion of motion

$v^2=u^2+2as$

$0=2\left(gsin\theta \right)-\mu gcos\theta )l-2\mu gd$

$d=\frac{l(gsin\theta -\mu gcos\theta )}{\mu }$