We all are familiar with the word power. In our daily life power
is usually related to taking decision and implementation. In science the word
“power” is related to the devices motor, pump, and engine etc. i.e. any device
that can work. Sometimes
we want to solve any task quickly. Suppose we want to fill a water tank on the
roof of a multi-storied building taking water from its reservoir at the ground
floor or from a pond. It takes a lot of time if we want to fill the tank
carrying water with a bucket. It takes less time to fill the tank with the help
of a motor or a pump. Sometimes a work is done quickly or slowly. Power is the
measure of a source by which how fast or how slow a source can work is
measured. Suppose two friends- John and Vicki live on the fifth floor of a
building. The mass of the two friends is the same. Coming to the lift at the
ground floor they found the lift not working. They had to use the stairs to go
up the building. John took 40 seconds and Oni took 80 seconds to reach the 5th
floor. We say John has more power than Oni. Though both of them has done same
amount of work to reach the same height John has more power because he has done
the work faster. Power is the rate of doing work or transformation
of energy. Power of a person or a source is measured by the amount of work
done per unit time.
Power = Work / Time
If a person or a device can do W amount of work or transform
energy at time t then the power P will be,
P = W / t
Power has no direction. So it is a scalar quantity.
Dimension of power
The dimension of power is the dimension of Work / Time
Power = Work / Time
= Force x Displacement / Time
= Mass x Acceleration x Displacement / Time
= Mass x Displacement x Displacement / Time x Time2
= Mass x Displacement2 / Time3
∴ [P] = ML2
/ T3
= [ML2T-3]
Unit of power
We can get the unit of power by dividing the unit of work with
that of time. Since the unit of work is
joule (J) and the unit of time is second (s), the unit of power will be Joule/second
(J/s). It is called Watt. Watt is denoted by W.
If one joule work is done in one second or the rate of transformation
of energy is called one watt.
1W = 1J / 1S
= 1 Js-1
Since watt is very smaller, its thousand times larger unit
kilo-watt is used.
1 kilo-watt = 1000 watt
You have probably heard the word “Horse Power”. This unit of power
was used earlier. Still today this unit is sometimes used to mean the power of
a motor or a car.
1 Horse Power = 746 watt
Have you heard the word “kilowatt-hour”? What does it mean?
Actually it is the unit of work or energy. We
usually pay the bill of electricity of houses, factories etc. measured in this
unit. One kilowatt-hour means the energy that a machine with a power of one kilowatt
uses in one hour. 60 watt mark on a bulb means that it transforms 60 Joules electrical
energy to light and heat energy in one second.
200 megawatt power of an electrical power station means that it
supplies 200000000 joules energy in one second. We are using this energy in
houses, factories and offices.
Mathematical Example: A person of mass 70 kg can stair up 30
steps of 25 cm height each in 15 s. What is his power? (g = 9.8 ms-2)
Here,
Mass of the person, m = 70 kg
Force = Weight of the person
= mg
= 70 kg x 9.8 ms-2
= 686 N
Displacement, S = 35 x 25 cm
= 750 cm
= 7.5 m
Time, t=15s
Power, P =?
We know,
P= Work / Time
=Fs / t
= 686 N x 7.5 m / 15 s
= 343 W
Ans: 343 W
Do it: Count the number of steps of the stairs to
reach the roof of your school or house or any other building. Measure the
height of the roof in meter. Measure your mass with the help of a weight
measuring machine in kilogram. Multiply your mass with 9.8 and then you will
find your weight in newton. Then run to the top of the roof. Measure the total
number of time of reaching the roof with the help of a stop watch.
Your work done will be, your weight × total height
Your power will be, your total work done ÷ total time i.e.
Perform these activities with your friends and compare your power
with them. Who is the most powerful student in your class?
Efficiency
We fulfill our daily needs with the help of transformation
of energy. For example we run an engine by transforming chemical
energy stored in petrol into kinetic
energy. According to the principle of conservation of energy,
we should obtain the amount of energy which is given to the engine. But it is
seen that the energy gained is always less than the energy given to. This is
because some energy is lost due to the work done against
the frictional force of the engine. The amount of energy obtained from the
engine is called effective energy. In this case the equation of energy is,
Given energy = Effective energy + the energy lost in other ways
The efficiency of an engine means that how much of the given
energy is obtained as effective energy. So, the efficiency means the ratio of
effective energy and the total given energy. Usually the efficiency is
expressed in percentage.
∴ Efficiency,
η = Effective energy / Total input energy × 100%
Energy
transformation takes place in different steps in a normal electricity
production center. This transformation continues from coal, oil, natural gas or
Uranium up to the production of electricity. It is seen that up to 70% of this
energy is lost as heat energy.
At last only the 30% of input energy is transformed into useable
electrical energy. So, we can say the efficiency of the electricity production center
is 30%.
Mathematical Example: An electric motor is used to lift a
body of weight 10N at a height 5m. It uses electrical energy of 65J.
a) What is the energy lost by the motor?
b) Find the efficiency of the motor.
Ans:
a) Here, energy used = work done
= Force x displacement
= Weight x height
= 10N x 5m
= 50J
∴ The energy
lost = Energy supplied – energy used
= 65J – 50J
= 15J
b) Efficiency, η =
Effective energy / Total input energy x 100%
= 50J / 65J x 100%
= 76.92%
End
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