POWER

A certain amount of work done appears to be tiring if done quickly and in a very short time. Same amount of work is done slowly in a larger interval of time gives no feeling of tiredness.

This fact has given rise to a new concept i.e. the rate at which work is done ant it defines power.

DEFINITION:

Power is defined as the rate of doing work or rate of doing work i.e. work done per unit time (second) by a man or machine, is called power of the man or the machine. it is represented by the symbol P. Power is a scalar quantity.

EXPRESSION FOR POWER:

Let a force F displaces a body by distance S in its own direction in time t, to give it a velocity, 

v=S/t

Then, by definition -

Hence 

 P = F × v

i.e. Power = Force × Velocity

Unit

S.I. unit of power is watt (W).

One watt is the power of a man or a machine capable of doing work at the rate of one joule per second

i.e. or W = J s-1

Since watt is a smaller unit, higher units used are

1 Kilowatt (kW) = 10o watt

1 Megawatt (MW) = 106 watt

1 Gigawatt (GW) = 109 W

commercial unit of power is horse power

1 horse power (1 H.P) = 746 watt (W)

DISTINCTION WITH ENERGY:

Energy measures total work done.

Power measures work done per unit time (second).

e.g. An old man works slowly for eight hours and manufactures 24 items in a day. His younger son works quickly for two hours and manufactures 16 items in a day.

The old man has more energy but less power.

The young mas has less energy but more power.

Energy of an object tells us the total amount of work it can performed. But power is rate at which work is done and not the total work done.

The unit of power called watt is named after a Scottish inventer, Engineerand designer James Watt

Question 13. A boy of mass 50 kg runs up a staircase of 45 steps in 9 s. If the height of each step is 15 cm. Find his power. (g = 10 m/s2)

Solution:
 Mass of man, m = 50 kg.

Height covered, h = 45 × 15 = 675 cm = 6.75 m

Power P =

P = 375 watt.