Question

An electric motor exerts a force of $40N$ on a cable and pulls it by a distance of $30m$ in one minute. The power supplied by the motor (in watts) is

Answer 1

Power

1. Power is the work done by a body in unit time.
2. Power is defined by the form, $P=\frac{W}{t}$, where, w is the work done in time t.
3. Power is defined by another form, $P=F.V$ where, F is the force exerted on the body and v is the velocity of the body.

Step 1: Given data

1. The tension due to the electric motor is $F=40N.$
2. The distance traveled by the cable is, $S=30m.$
3. Total time of travel by the cable is, $t=60seconds.$

Step 2: Calculating velocity

As we know that, $Velocity/speed=\frac{Dis\tan ce}{time}$

$Velocity\left(V\right)=\frac{30}{60}$

$$\begin{gathered} Velocity\left(V\right)\hspace{0.17em}=\frac{1}{2}m{s}^{-1} \\ V=0.5m{s}^{-1} \end{gathered}$$

Step 3: Power of the electric motor

As we know, power, $P=F.V$

So,

$$\begin{gathered} P=F.V \\ P=40\times 0.5 \\ P=20watt. \end{gathered}$$

Therefore, the power of the electric motor is $20watt.$