Question

A block of mass $m$ is located on a horizontal plane. The block acquires a horizontal velocity $v_0$ due to friction. Find the mean power developed by the friction force during the motion of the body. The frictional cofficient is $\mu =0.3,m=2\text{kg}$ and $v_0=5\text{m/s}$ (Take $g=10{\text{m/s}}^2$)

• A. $30\text{watt}$
• B. $45\text{watt}$
• C. $60\text{watt}$
• D. $15\text{watt}$

Answer 1

The correct option is D $15\text{watt}$

The body gains velocity due to friction.
Acceleration due to friction.
$a=\frac{\text{friction force}}{\text{mass}}=\frac{\mu \text{mg}}{\text{m}}=\mu g{v}_0=at$
$\Rightarrow t=\frac{v_0}{a}=\frac{v_0}{\mu g}$ ....(i)

From work energy theorem,
Work done by the friction force = change in K.E.
i.e $W=\frac{1}{2}m{v}_0^2$ .....(ii)
Mean power $=\frac{W}{t}$

From (i) and (ii) equation,
Mean power $=\frac{\frac{1}{2}m{v}_0^2}{\frac{v_0}{\mu g}}=\frac{m{v}_0\mu g}{2}$
$=\frac{1}{2}\times 2\times 5\times 0.3\times 10=15\text{watts}$