Question

Calculate the power of a motor which is capable of raising $1000kg$ of water in $5$ minutes from a well $60m$ deep. $g=9.8m/{{s}^{2}}$

Answer 1

We have to find the power of the motor. Let’s visualise the question like this:
Power is nothing but the work done per unit time; we know the time (since it’s been given to us), if we can find work done then we can easily find the power. Now work done is nothing but the change in energy of the object. This is how we’ll proceed.

Complete step-by-step solution:
We have been given that,
Mass of water to be raised $(m)=1000kg$
Height to which it has to be raised $(h)=60m$
Acceleration due to gravity $(g)=9.8m/{{s}^{2}}$
Now, work done = change in the gravitational potential energy of the water

& \Rightarrow W=mgh \\\ & \Rightarrow W=1000kg\times 9.8m/{{s}^{2}}\times 60m \\\ & \Rightarrow W=588000J \\\ \end{aligned}$$ As discussed above, power is nothing but the work done in a unit time In the given time, that is, $$5$$ minutes or $$300$$ seconds, the work done is $$588000J$$ . So Power of the given motor, $$\begin{aligned} & P=\dfrac{mgh}{t} \\\ & \Rightarrow P=\dfrac{588000J}{300s} \\\ & \therefore P=1960J/s=1960W \\\ \end{aligned}$$ **Additional Information:** The SI unit of power is watt or joule/sec but the power of engines/motors is usually expressed in horsepower (HP), where $$1HP$$ is approximately equal to $$746watts$$ . Power is defined as the rate at which energy is transferred or converted. The mechanical energy of the motor’s shaft is being converted into the gravitational potential energy of the water. **Note:-** Power can also be defined as the energy spent in unit time, so instead of finding energy and equating it to the work done, we can directly divide the gravitational potential energy change taking place by the time given to obtain the same result.