Question

A block of mass $M$ is held against a rough vertical wall by pressing it with a finger. If the coefficient of friction between the block and the wall is $\mu$ and the acceleration due to gravity is $g$, calculate the minimum force required to be applied by the finger to hold the block against the wall.

Answer 1

$\text{Step1: Draw the diagram as per the given information}.$



$\text{Step2: Find the minimum force required to hold the block}.$

Given:

Mass of the block $=M$

Co-efficient of friction between the block and the wall $=\mu$

Let $F$ be applied on the block to hold the block against the wall.

Normal reaction $=N$ and

Force of friction acting upward be $f$ as the surface is rough

In equilibrium, all forces should be balanced separately.

Therefore,

$f=Mg$ .....$\left(i\right)$

and $f=N$ .....$\left(ii\right)$

As we know,

Force of friction $\left(f\right)=\mu N$

By putting the value of $f$ in equation $\left(i\right)$ we get

$\mu N=Mg$

Therefore, $N=\frac{Mg}{\mu }$

By putting the value of $N$ from equation $\left(ii\right)$ we get

$F=N$

Therefore,

$F=\frac{Mg}{\mu }$

$\text{Final answer}:F=\frac{Mg}{\mu }$