Question

A $30\text{kg}$ block rests on a rough horizontal surface. A horizontal force of $200\text{N}$ is applied on the body. The block acquires a speed of $4\text{m/sec}$, starting from rest, in $2\text{sec}$. What is the value of coefficient of friction?

• A. $\frac{10}{\sqrt{3}}$
• B. $\frac{\sqrt{3}}{10}$
• C. $0.47$
• D. $0.185$

Answer 1

The correct option is C $0.47$


So equation for the motion is,
$F-f_k=ma$
where $f_k=\mu R=\mu mg=\mu \times 30\times 9.8=294\mu$
Since initial velocity of the body is zero & its velocity increases from zero to $4\text{m/sec}$ in $2$ seconds, so acceleration of the body is given by,
$v=u+at$
$\Rightarrow 4=0+a\times 2$ or $a=2{\text{m/sec}}^2$
So, $F-f_k=30\times 2$
$\Rightarrow 200-\mu \times 294=60$
$\Rightarrow \mu =\frac{140}{294}=0.476$