Question

What is meant by the power of a machine? Name and define its SI unit. How is kilowatt different from kilowatt-hour? From a 20 m high fall, nearly 25 metric tonnes of waterfall per second. Calculate the equivalent power if all this energy is utilized.

Answer 1

1. The power of a machine is defined as may be defined as the rate of doing work or the rate of energy supplied.
2. $Power=\frac{Energysupplied\left(E\right)}{time\left(t\right)}$---------(I)
3. SI unit of power is the watt.
4. Power is said to be one watt if work is being done at the rate of 1 joule per second.
5. A kilowatt is a bigger unit of power that is equal to 1000 watts whereas kilowatt-hours is the commercial unit of energy consumption.
6. 1kWh is equal to 1 unit.

Step 01:Water falling from height (h)= 20 m
Amount of water falling in one second (m)= 25 metric tonnes= 25000 kg
Let E is the energy possessed by the water. Energy E must be equal to the potential energy of the water.
$$\begin{gathered} E=mgh \\ herem=massofwater \\ g=accelerationduetogravity \\ h=heightofthewaterfall \end{gathered}$$

Substituting the value of m, g, and h we get-
$$\begin{gathered} E=25000\times 10\times 20J \\ E=5000000J \\ or5\times {10}^{6}J \end{gathered}$$
Let P is the equivalent power of water which can be calculated using equation (I)
$$\begin{gathered} P=\frac{(5\times {10}^{6}J)}{1s} \\ P=5\times {10}^{6}W \\ SInce{10}^{6}W=MW \\ \Rightarrow P=5MW \end{gathered}$$

Hence the equivalent power =5MW