Work, Power, Energy

- Made by Bijita Ma’am

 What is Work?
• Work is any physical or mental activity which one does
to perform daily tasks.
• However, in scientific parlance, Work is defined as a
force acting upon an object to cause a displacement.
• There are several good examples of work that can be
observed in everyday life - a horse pulling a plow
through the field, a father pushing a grocery cart down
the aisle of a grocery store, a freshman lifting a
backpack full of books upon her shoulder, a weightlifter
lifting a barbell above his head, an Olympian launching
the shot-put, etc. In each case described here there is a
force exerted upon an object to cause that object to be
displaced.
 Mathematical Equation
• The amount of work depends on two factors:
The magnitude and direction of force applied to an object.
The distance/displacement through which the object moves.
• It is expressed as the product of force and displacement in the direction of
force.
W=F . s
Here, W= work done on an object
F = Force on the object
s = Displacement of the object (some refer displacement by d)
• Thus, the expression of work is W = F.s cosθ
Thus, the amount of work done is the product of force, displacement and
the cosine of the angle between the force and displacement.
• If the displacement is in the direction of the force, i.e. θ = 0°, then the
work done is W = F × s .
This work is maximum and positive.
• If the displacement is normal to the direction of the force, i.e. θ = 90°,
then the work done is W = 0. Thus, no work is done.
• If the displacement is zero, then the work done is zero. This is the case
when a body is moving in circular motion.
• If the displacement is in the direction opposite to that of the force, i.e. θ =
180°, then the work is W = - F × s. This work is minimum and negative.
• So no work is done if:
The displacement is zero
The force is zero
The force and displacement are mutually perpendicular to each other.
 Units of Work
• The SI unit of work is newton metre (N m) or joule
(J).
One joule of work is said to be done when a force of
one newton displaces the body through a distance of
one metre in its direction.
• The CGS unit of work is erg.
• Work has only magnitude and no direction. Hence,
work is a scalar quantity. (The dot product of two
vectors is a scalar.)
 Power
• We can define power as the rate of doing work, and it is the amount of
energy consumed per unit of time.
• Power is the rate at which work is done. It is the work/time ratio.
Mathematically, it is computed using the following equation.
Power = Work / time
P=W/t
• Power is a scalar quantity and is basically the amount of energy consumed
per unit of time which has no direction.
• The SI unit of power is watt which is represented by the symbol (W).
• One joule per second is also equal to one watt.
• 1 watt = 1 J/s = 1 kg-m2/s3

Units Abbreviation Equivalent Watt Unit

Horsepower HP 746 watts

Kilowatts kW 1×103W
Megawatts MW 1×106W
Gigawatts GW 1×109W
decibel-milliwatts dBm 30 dBm = 1 W
British Thermal
BTU/hr 3.412142 BTU/hr = 1 w
Unit/Hour

0.24 calories per second

Calories per Second cal/sec
cal/sec = 1 W
 Energy
Types of Energy:
Some other types of energy are
given below:
➢ We can define energy as the • Mechanical energy
capacity to do work. • Mechanical wave energy
➢ The amount of energy possessed • Chemical energy
by a body is the amount of work • Electric energy
it can do when that energy • Magnetic energy
released.
• Radiant energy
➢ Energy can neither be created nor • Nuclear energy
destroyed, and it can only be
• Ionization energy
transformed from one form to
another. • Elastic energy
• Gravitational energy
• Thermal energy
• Heat Energy
 Units of Energy
• Energy is a scalar quantity.
• The SI unit of energy is the same as the unit of work, i.e. joule (J), and its
CGS unit is erg.
• Another unit of energy is watt hour or kilowatt hour. The commercial unit of
electric energy is kilowatt hour (kW h), commonly known as unit.
1 kW h = 3.6×10 J = 3.6 MJ
• Heat energy is usually measured in calorie.
One calorie is the energy required in raising the temperature of 1 g of water
through 1°C.
• 1 J = 0·24 calorie
1 calorie = 4·18 J
1 kilocalorie = 1000 calorie = 4180 J
1 eV is the energy gained by an electron when it is accelerated through a
potential difference of 1 volt.
1 eV = 1·6 × 10−19 J
✓ The energy possessed by a body due to its state of rest or of motion is called
mechanical energy.

Kinetic Energy:
• It is the energy possessed by a body due to its motion. Kinetic energy of an
object increases with its speed.
• Kinetic energy of body moving with a certain velocity = work done on it to
make it acquire that velocity
• Potential Energy
The energy possessed by a body due to its position or shape is called its potential energy.
For Example: Water stored in a dam has large amount of potential energy due to its
height above the ground, A stretched rubber band possesses potential energy due to its
distorted shape.
• Types of Potential Energy: On the basis of position and change in shape of object,
potential energy is of two type:
1. Gravitational Potential Energy: It is the energy possessed by a body due to it position
above the ground. Eg.: Pen on a table, Water in a lake etc.
2. Elastic Potential Energy: It is the energy possessed by a body due to its change in
shape. Eg.: Stretching a spring or a rubber band.
 Law of Conservation of Energy
• In a closed system, i.e., a system that is isolated from its surroundings,
the total energy of the system is conserved.
• Energy can neither be created nor destroyed, but it can be transformed
from one form to another.
The total energy before and after the transformation remains the same.

Law of conservation of mass and energy:

It states that although mass may convert to energy, and vice versa,
neither may disappear without compensation in the other quantity.
 Conversion of Energy
Scenario Energy conversions involved

Rubbing both hands together for

Kinetic Energy to Thermal Energy
warmth

Gravitational Potential Energy to

A falling object speeding up
Kinetic Energy

In the battery: Chemical to Electrical

Energy
Using battery-powered torchlight
In the bulb: Electrical to Radiant
Energy

In Geothermal Power Plant Heat Energy to Electrical Energy

In Thermocouple Heat Energy to Electrical Energy

Gravitational potential energy to

In Hydroelectric Dams
Electric Energy
 Scenario Energy conversions involved
Kinetic energy / Mechanical Energy to
In Electric Generator
Electric Energy
Wind Energy to Mechanical Energy or
In Windmills
Electric Energy
In OTEC (Ocean Thermal Energy Heat Energy to Electric Energy or
Conversion) Mechanical Energy
Using Microphone Sound Energy to Electric Energy
Photosynthesis in Plants Solar Energy to Chemical Energy
Electric Energy to Heat Energy and Light
In Electric lamp
Energy
Burning of wood Chemical energy to Heat and Light Energy
In Fuel cells Chemical Energy to Electric Energy
In steam engine The heat energy to Mechanical Energy
In Electric heater Electric Energy to Heat
 Types of Energy Resources
• Non-renewable Resources: Fossil fuels like oil, natural gas and coal are known as non-
renewable resources, because once used, they cannot be renewed by natural process
or means.
• Renewable Resources: Natural resources like wind, water, solar, and geothermal are
called renewable resources as they come from sources that regenerate them back after
consumption and are continuously available in nature.
 Some Numerical Examples
• Q:
A roller is pushed with a force of 100 N along its handle, which is at an
angle of 60 degrees with the horizontal. Find the work done in moving it
through 20 m.

• Ans:
W = F s cos θ
= 100 x 20 x cos 60
= 100 x 20 x (1/2)
= 1000 J
• Q:
Calculate the power of an electric motor that can lift 800 kg of water to
store in a tank at a height of 1500cm in 20s. (g=10m/s2).

• Ans:
Weight of the water =800×10=8000 N
Height =1500 cm = 15 m
t=20 sec

Power= work done/ time

=mgh / t
= 8000×1520
=6000Watt
=6KW
• Q:
An electric heater of 1000 W is used for two hours in a day? What is the
cost of using it for a month of 28 days, if one unit costs 3.00 rupees?

• Ans:
Power= 1000 W = 1 KW
Time per day=2 hour
Total time= 2 X 28 = 56 hour
Energy= power X time
= 1 X 56
=56 KWH

Now 1 KWH costs Rs 3

Then 56 KWH will cost = 3 X 56 = Rs 168
• Q:
Calculate the kinetic energy of a car of mass 500kg moving with a velocity
of 36km/h. Find the kinetic energy if the velocity of car doubles?

• Ans:
m=500 Kg, v=36 km/hr=10 m/s
K= (1/2) mv2
Hence
K= 25000 J=25KJ

When the velocity of the car is doubled

m=500 kg, v=20 m/s
Hence
K=100000J = 100KJ
• Q:
An object with 100 N weights is raised to a height of 15m. Find the
potential energy possessed by the object at that height. Also find the new
potential energy:
a.If the same object is raised half of its original height.
b. If the same object is raised to three times of its original height?
Given g=10m/s2
• Ans:
Potential Energy is given by, PE=mgH
Given mg=100N and H=15 m
PE=100×15=1500J

If the same object is raised half of its original height i.e H= 7.5 m
PE=100×7.5=750J
If the same object is raised to three times of its original height i.e H=45 m
PE=100×45=4500J
Thank You