Question

A body of mass $1kg$ rests on a horizontal floor with which it has a coefficient of static friction $\frac{1}{\sqrt{3}}$. It is desired to make the body move by applying the minimum possible force $FN$. The value of F will be __________. (Round off to the Nearest Integer) [$g=10m{s}^{-2}$]

Answer 1

Step 1. Given data

Mass of the body, $m=1kg$

Coefficient of friction, $\mu =\frac{1}{\sqrt{3}}$

Step 2. Finding the minimum force,

By applying the formula,

Minimum force$=\frac{\mu mg}{\sqrt{1+{\mu }^2}}$

$=\frac{1\times 1\times 10}{\sqrt{3}\sqrt{1+{\left({\displaystyle \frac{1}{\sqrt{3}}}\right)}^2}}$ [$g=10m{s}^{-2}$]

Minimum force$=5N$

Comparing this by minimum force is equal to $FN$, we get

Therefore, $F=5N$