Question

A block of mass $5\text{kg}$ 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 $20\text{N}$ is required in horizontal direction to move the box in a direction parallel to the motion of compartment, while a force of $10\text{N}$ is required in horizontal direction to move the box in opposite direction. If coefficient of friction between the surface of the block and the surface is $\frac{x}{10}$, then find out value of $x$.
(Take $g=10{\text{ms}}^{-2}$)

Answer 1

$x=3$
As seen by an inside observer, the forces acting on the block are pseudo force, frictional force and the applied force.
When the applied force is in the direction of pseudo force (in this case less force will be required to move the block)
$10+$ pseudo force $=\mu mg$ ... (1)
When the applied force is opposite to the pseudo force,
$20-$ pseudo force $=\mu mg$ .. (2)
Adding (1) and (2)
$30=2\mu mg=2\mu 50$
$\mu =0.3$