Question

A small body of mass m is located on a horizontal plane at the point O. The body acquires a horizontal velocity $v_0$ due to friction. Find, the mean power developed by the friction force during the motion of the body, if the frictional coefficient $\mu =0.27,m=1.0kgand{v}_0=1.5m/s.$

• A. $2.0W$
• B. $2.5W$
• C. $3.0W$
• D. $3.5W$

Answer 1

The correct option is A $2.0W$

The body gains velocity due to friction. The acceleration due to friction.

$a=\frac{forceoffriction}{mass}=\frac{\mu mg}{m}=\mu g$

Further, $v_0=at$

Therefore, $t=\frac{v_0}{a}=\frac{v_0}{\mu g}$

From work energy theorem,
work done by force of friction=change in kinetic energy

or $W=\frac{1}{2}m{v}_0^2$

Mean power $=\frac{W}{t}$

From Eqs. (i) and (ii)

$P_{mean}=\frac{1}{2}\mu mg{v}_0$

Substituting the values, we have

$P_{mean}=\frac{1}{2}\times 0.27\times 1.0\times 9.8\times 1.5$ $=2.0W$