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Discover Physics
GCE ‘O’ Level Science
Unit 6: Energy, Work and Power
6.1 Energy
In this section, you’ll be able to:
• identify different forms of energy – kinetic energy,
elastic potential energy, gravitational potential energy,
chemical potential energy and thermal energy
• state the Principle of Conservation of Energy
• solve problems using the Principle of Conversation of
Energy
6.1 Energy
What is Energy?
• Energy is the capacity to do work.
• The SI unit of energy is the joule (J).
6.1 Energy
Different forms of energy and energy conversions
There are many forms of energy. Examples include:
• Kinetic energy
• Potential energy
• Sound energy
• Electrical energy
• Thermal energy
• Light energy
6.1 Energy
Kinetic Energy
• Moving objects have
kinetic energy.
• Kinetic energy can be
used to do work.
In windy places, wind is used to
turn turbines that convert kinetic
energy to electrical energy.
6.1 Energy
Potential Energy
• Energy that is stored is known as potential energy.
• Potential energy can be converted to kinetic energy
and vice versa.
• Potential energy exists in many forms.
6.1 Energy
Chemical Potential Energy
• Food contains chemical potential energy which is
converted from solar energy via photosynthesis.
• These can be converted to kinetic energy.
How energy is transferred from the sun to humans and animals.
6.1 Energy
Chemical Potential Energy
• Chemical potential energy is also stored in fossil fuels
like coal and oil.
• A battery also stores chemical potential energy that
can be converted to electricity.
6.1 Energy
Elastic Potential Energy
• A spring or rubber band possesses elastic potential
energy when it is compressed or stretched.
• This energy is converted to kinetic energy when the
spring or rubber band is released.
An archer makes use of the elastic potential
energy stored in the bow to propel the arrows.
A fully flexed bow stores about 300 J of energy.
6.1 Energy
Gravitational Potential Energy
• An object has gravitational potential energy when it is
raised to a certain height above the ground.
• When released, it falls and gravitational potential
energy is converted to kinetic energy.
When a ball is being dropped from a height, it
falls and the gravitational potential energy it
has is converted to kinetic energy.
6.1 Energy
Principle of Conservation of Energy
Energy can neither be created nor destroyed in any
process. It can be converted from one form to another or
transferred from one body to another, but the total
amount remains constant.
20 J energy
in one form
20 J energy in
another form
When energy is converted from one form to another, the total amount
remains constant.
6.1 Energy
Conversion of Energy
Diver on a diving board
Stored chemical energy in the body of a diver allows him to
exert a push to bend the diving board. This causes the bent
diving board to store elastic potential energy which is then
converted to kinetic energy that helps push the diver upwards.
Elastic potential energy is converted to
kinetic energy, helping to push the boy
upwards.
6.1 Energy
Conversion of Energy
Hammering a nail
A raised hammer possesses gravitational potential energy.
When it falls, this energy is converted to kinetic energy
which is used to do work in driving the nail into the wood
block. Sound and thermal energy are also produced and
released by the block, nail and hammer.
When the hammer falls, gravitational potential
energy is converted to kinetic energy.
6.1 Energy
Conversion of Energy
Burning of Fuels
By burning fuels, the stored chemical energy in these fuels
is converted to thermal and light energy.
Burning charcoal in a barbecue pit emits a lot of thermal energy to cook food.
6.1 Energy
Conversion of Energy
In real life, energy is easily dissipated into the surroundings.
This makes it difficult for us to compare the amount of
energy before and after conversion in order to study the
Principle of Conservation of Energy effectively.
6.1 Energy
Principle of Conservation of Energy and the
ideal pendulum
6.1 Energy
Principle of Conservation of Energy and the
ideal pendulum
6.1 Energy
Principle of Conservation of Energy and the
non-ideal pendulum
In the real world, frictional forces convert some of the
total energy of a swinging pendulum to thermal energy.
This thermal energy is dissipated to the surroundings and
cannot be converted back into kinetic or gravitational
potential energy of the pendulum.
6.1 Energy
Principle of Conservation of Energy and the
non-ideal pendulum
The pendulum eventually comes to a stop.
Height gained is lower than the original because some of the energy
has been converted to thermal energy.
6.1 Energy
Efficiency
From the Principle of Conservation of Energy, the total
energy output by a machine must be equal to its energy
input.
In real life, energy output is always less than energy input
as energy is dissipated, due to friction, or as a form of
sound and thermal energy.
This energy lost is considered wasted energy output.
6.1 Energy
Efficiency
Energy input = useful energy output + wasted energy
Efficiency =
useful energy output
energy input
 100%
6.1 Energy
Key Ideas
1. Energy is the capacity to do work.
2. Energy can be converted from one form to another.
3. The Principle of Conservation of Energy states that
energy can neither be created nor destroyed in any
process. It can be converted from one form to another
or transferred from one body to another but the total
amount remains constant.
6.2 Work
Learning Outcomes
In this section, you will be able to:
• Understand the concept of work and apply the relationship
W = F  s to solve problems
1
• Apply the relationships E k =
m v 2 and Ep = m g h
2
to solve problems
6.2 Work
Work Done
Definition: Work done by a constant force on an object is given
by the product of the force and the distance moved by the object
in the direction of the force.
W =
Fs
where W = the work done (in J),
F = the constant force (in N)
s = the distance moved in the direction of the force (in m)
6.2 Work
The SI unit of work is the joule (J).
Definition: One joule (J) is defined as the work done by a force
of one newton (N) which moves an object through a distance of
one metre (m) in the direction of the force.
one joule = one newton
1J= 1Nm
 one metre
6.2 Work
Example of work being done: Lady pushing a pram
6.2 Work
No work is being done when:
1. The direction of the applied force and the direction in which
the object moves are perpendicular to each other.
A man carrying a load while walking.
No work is done on the load in the
upward direction as the load is only
moving horizontally.
6.2 Work
No work being is being done when:
2. The force is applied on the object (such as the wall or the
pile of books) but the object does not move.
Boy pushing against a
solid wall.
A girl holding a heavy pile of books in a
stationary position does no work.
6.2 Work
How is energy related to work and force?
We need energy to move an object, run and climb
stairs.
To move a stationary object, we need to apply
force to them.
For a moving object, we also need to apply force to
increase its speed.
Hence, work is done when we move a stationary
object or make a moving object move faster.
6.2 Work
6.2 Work
Mechanical Energy
There are two types of mechanical energy:
1. Kinetic energy
2. Gravitational potential energy
A roller coaster uses a motor-andchain system to pull the riders up the
first hill before letting gravity take
over the rest of the ride.
6.2 Work
Kinetic energy and work done
A moving body has kinetic energy. When a force moves
an object, it does work and the object gains kinetic
energy.
Kinetic energy is defined as:
E =
k
1
mv2
2
where E = kinetic energy (in J),
k
m = mass of the body (in kg) and
v = speed of the body (in m s –1)
6.2 Work
Gravitational potential energy and work done
Potential energy is stored energy
• Gravitational potential energy (G.P.E) is the energy a body
has due to its position
• To find G.P.E. of an object near surface of Earth, we need to
consider its mass and its height above the ground.
An object of mass m raised to a height h above ground level
possesses G.P.E. of mgh.
6.2 Work
Gravitational potential energy and work done
Gravitational potential energy is defined as:
Ep = mgh
where
E p = gravitational potential energy (in J),
m = mass of the body (in kg)
g = gravitational field strength (in N kg –1 )
h = height (in m)
6.2 Work
WORKED EXAMPLE 6.4
6.2 Energy, Work and Power
Figure 6.23
6.2 Work
Key Ideas
1. Force, work and energy are interrelated.
2. Work done W by a constant force F is given by the
product of the force F and the distance moved in the
direction of the force, i.e. W = F  s.
3. The SI unit of work is the joule (J), which is the same
as the SI unit of energy.
6.2 Work
Key Ideas
4. No work is done when
a. The direction of the applied force and the
direction in which the object moves are
perpendicular to each other
b. The force is applied on the object but the object
does not move.
5. Moving objects have kinetic energy. The kinetic
energy of an object of mass m in kilograms and
speed v in m s–1 is given in joules by the expression:
E = 1 mv 2
k
2
6.2 Work
Key Ideas
6. An object of mass m kg at height h has gravitational
potential energy given by Ep = mgh where g is the
gravitational field strength (10 N kg–1).
7. Potential energy can be converted to kinetic energy and
vice versa. The total energy in a system is fixed. If all the
gravitational energy is converted to kinetic energy or all
the kinetic energy is converted to gravitational potential
energy, the equation mgh = 1 mv 2 is true.
2
6.2 Work
Test Yourself 6.2
2. A block of mass 4 kg slides from
rest through a distance of 30 m
down a frictionless slope, as
shown in the diagram. What is
the kinetic energy of the block
at the bottom of the slope?
G.P.E
5m
Answer:
At the top, the block has G.P.E
G.P.E
= mgh
= 4  10  5 = 200 J
At the bottom, the G.P.E is converted into K.E.
Hence, the K.E of the block at the bottom is 200 J.
K.E
6.2 Work
Test Yourself 6.2
3. If the speed of a springboard diver decreases by half on
entering the water, by how much will his kinetic energy
decrease?
Answer:
Let the initial speed of the diver just before he hit the water be vi ,
and the final speed after he entered the water be vf . Since speed
is decreased by half, i.e. vf = 1 vi
2
Initial K.E =
1
mv i2
2
2
v 
Final K.E = 1 m  i 
2 2
1

= 1  mvi2 
4 2

Hence, the final K.E is now one quarter of the initial K.E.
6.2 Work
Test Yourself 6.2
4. A package of 5 kg is lifted vertically through a distance of
10 m at a constant speed. Taking acceleration due to
gravity to be 10 m s–2, what is the gravitational potential
energy gained by the package?
Answer:
Gravitational P.E
5 kg
= mgh
= 5  10  10
= 500 J
Hence, the package gained 500 J of
gravitational potential energy.
G.P.E
10 m
6.3 Power
Learning Outcomes
In this section, you will be able to:
• Recall and apply the relationship power = work done
time taken
to solve problems.
6.3 Power
What is power?
Power is defined as the rate of work done or rate of
energy conversion.
P=W=E
t
t
where P = power
W = work done (in J)
E = energy converted (in J) and
t = time taken (in s)
6.3 Power
The SI unit of power is the watt (W). One watt (W)
is defined as the rate of work done or energy
conversion of one joule per second.
one joule
one watt =
one second
1 W = 1 J s-1
6.3 Power
WORKED EXAMPLE 6.6
A windmill is used to raise water from a well. The depth of the
well is 5 m. The windmill raises 200 kg of water everyday.
What is the useful power extracted from the wind? (g = 10 N
kg-1)
Solution
Work done in raising 200 kg of water up a height of 5 m = mgh
= 200  10  5 = 10 000 J
There are 24  60  60 seconds in one day.
Therefore power = 10 000 / (24  60  60) = 0.12 W
6.3 Power
WORKED EXAMPLE 6.7
A man pushes a heavy box across the floor at a constant speed
of 0.5 m s-1 by exerting a horizontal force of 120 N on it.
(a) Explain why the resultant force on the box is zero.
(b) How much work is done by the man in five seconds?
(c) At what rate is the man doing work?
Solution
(a) The resultant force on the box is zero because the box is
moving at a constant speed. A resultant force will cause the
box to accelerate and the speed would not be constant.
(b) In five seconds, the box would have moved a distance of
0.5  5 = 2.5 m
Work done = force  distance moved in the direction of the force
= 120 N  2.5 m = 300 J
(c) Rate of doing work = work done/time taken = 300/5 = 60 W
WORKED EXAMPLE 6.8
A 60 W fluorescent lamp transfers half the electrical energy
supplied into light energy. How much light energy does it emit
in 10 s?
Solution
Energy used by lamp in 10 s = 60  10 = 600 J
Half of this energy is converted to light energy.
Therefore, amount of light energy = 600 / 2 = 300 J
6.3 Power
Key Ideas
1. Power is the rate of work done or energy converted.
2. The SI unit of power is the watt (W). One watt is the
rate of work done at 1 joule per second.
6.3 Power
Test Yourself 6.3
1. (c) In the following situations, calculate the power involved.
(i) A force of 50 N moves through a distance of 10 m
in 5 s.
Answer: P = W = F  s = 50  10 = 100 W
t
t
5
(ii) An object of mass 1 kg is lifted up vertically through
5 m in 10 s.
mgh
Answer: P = E =
t
t
= 1  10  5 = 5 W
10
6.3 Power
Test Yourself 6.3
2. An electric motor in a washing machine has a power
output of 1.0 kW. Find the work done in half an hour.
Answer:
Given Power P = 1.0 kW = 1000 W and
1
hour = 0.5  60  60 = 1800 s
time t =
2
W
P=
t
W=P t
= 1000  1800
6
= 1.8  10 J
Hence, the work done W = 1.8  106 J