Power

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Imagine two students positioned at track A and track B of 100 m length shifting 10 bricks from one end of the track to the other end. What is the amount of work done by each one of them? The amount of work done is same but the time taken to perform the work varies. In order to find out the fastest among the two we calculate the work done in unit time. That means work done and work done in unit time are two different quantities.

Work done in unit time or rate of doing work is defined as power.

Power is denoted by the letter 'P'.

As energy is the capacity to do work, power can also be defined as energy consumed in unit time.

SI unit of power

SI unit of work is joule and time is second. Therefore, SI unit of power is joule/second.

1 joule/second = 1 watt

If one joule of work is done in one second by any agent then its power is said to be one watt.

Kilowatt and megawatt are higher units of power.

Another unit of power is horse power

1 horse power = 746 watts

Numericals

01. A man of mass 60 kg runs up a flight of 60 steps in 40 seconds. If each step is 20 cm high, calculate his power.

Solution:

Since the man runs up a flight of steps, the work done will be equal to the potential energy.

Height = height of one step x number of steps

Acceleration due to gravity (g) = 9.8 m/s²

Time = 40 s

02. Calculate the power of the engine required to lift 10⁵ kg of coal per hour from a mine 100 m deep.Given g = 10 m/s².

Solution:

The work done in lifting coal is nothing but gravitational potential energy.

Mass of coal = 10⁵ kg

Time = 1 hour

= 60 x 60 s = 3600 s

Power of the engine = 27777.78 W

03. A man buys an electric motor of 2 h.p. What is its power in watts?

Solution:

1 h.p. = 746 W

Power of the electric motor = 2 h.p.

Power of the electric motor = 2 x 746

= 1492 W