Question

A board of mass $3m$ is placed on a rough inclined plane and a man of mass $m$ walks down the board. If the coefficient of friction between the board and inclined plane is $\mu =0.5$, the minimum acceleration of man, so that the board does not slide is:

• A. $6m/s^2$
• B. $8m/s^2$
• C. $4m/s^2$
• D. $3m/s^2$

Answer 1

The correct option is B $8m/s^2$

Given: mass of man $=m$, mass of board $=3m$,$\mu =0.5$ between board and plane.
Let $f$ be force applied by man on board.
Friction force between board and plane
$\mu (mg+3mg)\cos {37}^{\circ }=0.5\left(4mg\right)\cos {37}^{\circ }$
$=2mg\cos {37}^{\circ }$
Force equation along the plane on man
$mg\sin {37}^{\circ }+f=ma\dots \left(i\right)$
Force equation along the plane for board which is in equilibrium
$mg\sin {37}^{\circ }-f-2mg\cos {37}^{\circ }\dots \left(ii\right)$
Add equation $\left(i\right)$ and $\left(ii\right)$
$\frac{3}{5}mg+\frac{9}{5}mg-\frac{8mg}{5}=ma$
$\frac{4g}{5}=a$
$a=8m/s^2$