Question

A block of mass $5$kg is placed on a rough horizontal surface of a moving compartment. It is seen by an observer sitting inside the compartment, that a force of $10$N is required in horizontal direction to move the box in a direction parallel to the motion of compartment while a force of $20$N is required in horizontal direction to move the box in opposite direction. Find the coefficient of friction between the surface of the block and the surface.

Answer 1

Here,

$F_1+ma=f$ ......................(1)

Again in oppoite direction;

$F_2=f+ma$ ......................(2)

From eq. (1) and (2);

$F_1+F_2=2f$

$2f=20+10$

$f=15N$

Also, $f=\mu N=\mu \left(mg\right)=\mu (5\times 10)=\mu \left(50\right)$

$\Rightarrow \mu \left(50\right)=15$

$\Rightarrow \mu =\frac{15}{50}=0.3$