Power and measuring it

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C.G.S System erg/sec

M.K.S System joule/sec (or) kg m2 s-3 (or) watt

In the British system, work is expressed in foot-pounds, and the unit of power is the foot-pound per second. A larger unit called the horsepower (hp) is also used:

1 hp = 550 ft.lb/s = 33,000 ft.lb/min

That is, a 1-hp motor running at full load does 33,000 ft-lb of work every minute. A conversion factor is

1 hp = 746 W = 0.746 kW

That is, 1 horsepower equals about ¾ of a kilowatt.

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Slide 10

Units of power

The watt is a familiar unit of electrical power; a 100-W light bulb converts 100 J of electrical energy into light and heat each second.

The units of power can be used to define new units of work and energy. The kilowatt-hour (kWh) is the usual commercial unit of electrical energy. One kilowatt-hour is the total work done in 1 hour (3600 s) when the power is 1 kilowatt (103 J/s), so

1 kWh = (103 J/s) (3600 s) = = 3.6 MJ

The kilowatt-hour is a unit of work or energy, not power.

Our electricity bills carry the energy consumption in units of

kWh.

The dimension formula for power is given by

ML2T-3

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Slide 11

Alternative formulae for power

Thus the power associated with force F is given by

P = F .v

where v is the velocity of the object on which the force acts. Thus

P = F . v = Fvcos

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Special cases

Power = work/time = Energy/time =P.E/time = K.E/time

= (mgh)/t = (1/2mv2)/t

If a gun fires ‘n’ bullets each of mass ‘m’ with a velocity ‘v’ in ‘t’ seconds, the power of the gun is given by

P = n(1/2mv2)/t

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Quiz

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Power of motor

The power of a motor required to lift ‘m’kg of water from a well of depth ‘h’ in time ‘t’ is given by

P = (mgh)/t (1m3 = 1000kg)

If the efficiency of the motor is ‘x%’ then

P = (100/x)(mgh)/t

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Slide 15

POWER OF MOTOR

If a motor lifts the water from a depth ‘h’ and delivers

them with a velocity ‘v’ in time ‘t’ then the power of the

motor is given by

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Slide 16

POWER OF MOTOR