WORK, ENERGY AND POWER  
WORK  
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Is the product between force applied and the distance in the same direction  
Mathematically:  
Work done = Force x distance  
→ 푾. 풅  
=
푭 풙 풅  
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The SI unit of work is Joule (J)  
Joule is a force of 1N that moves an object through a distance of 1m in the  
same direction of the force  
Equivalent Units of Work are:  
•
1Nm = 1Joule = Kgm2S-2 = 0.001 KJ  
Examples of work done in daily life  
o
o
o
o
When a person pushes a wall (No work is done since d = 0 m)  
When a farmer carrying a hole (No work done since d = 0 m)  
Lifting a pen (Work is done since d > 0 m)  
Lifting a cup (Work is done since d > 0 m)  
Example  
1. A sack of maize which weights 800N is lifted to height of 2 m. What work done  
against gravity  
Solution:  
Wight, w = 800 N  
Distance, d = 2 m  
Work done, W.d =?  
From:  
W.d = F x d  
W.d = 800 x 2 = 1600 J  
Individual Task – 1  
1. How much work is done to lift a 7 kg object a distance of 2 m and then hold it at  
that height for 10 s (ANS: work done to lift = 140 J, Work done to hold = 0 J)  
2. A force of 80N pulls a box along a smooth and level ground a distance of 5m.  
Calculate the work done by force. (ANS: work done = 400J)  
3. How much work is done by a force of 10 N in moving an object through a  
distance of 4 m in the direction of the force. (ANS: Work done = 40 J)  
4. Calculate the work done in lifting 200 kg of water through a vertical height of 6 m  
(ANS: Work done = 1200 J)  
Energy  
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Energy is the ability of doing work.  
The SI unit of energy is Joule (J).  
Forms of Energy  
Energy can exists in various forms such as:  
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Chemical energy  
Heat energy  
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Electromagnetic energy  
Sound energy  
Electrical energy  
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Nuclear energy  
Mechanical energy  
Chemical Energy  
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Is the energy stored in the food and other fuels. Human get energy from the  
food that they eat  
OR  
Is the energy that results from chemical reactions between atoms or molecules  
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Example of chemical energy is an electrochemical cell or battery  
Thermal (Heat Energy)  
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Is the energy that reflects the temperature difference between two system  
Example, A cup of hot coffee has thermal energy.  
Electromagnetic Energy (Radiant energy)  
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Is the energy from light or electromagnetic waves  
Examples are Infrared radiation, Light energy, Ultraviolet radiation, radio  
waves, x-rays, Solar energy etc  
Sound Energy (Sonic Energy)  
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Is the energy that transfers in the form of waves.  
Examples, your voice, Microphone converts sound energy to electrical energy.  
Loud speaker convert electrical energy to sound energy  
Electrical Energy  
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It is due to the kinetic energy of the moving electric charge in a current  
Nuclear Energy  
Is the energy resulting from changes in the atomic nuclei or atomic reactions  
Nuclear energy is the energy from the weak and strong nuclear force.  
Examples are Nuclear fission, Nuclear fusion and Radioactive decay  
OR  
Mechanical energy  
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Is the energy that results from movement or location of an object  
Mechanical energy exists as kinetic and potential energy  
Examples, A book sitting on the table (PE), A Moving car (KE) etc  
Types of Energy (Mechanical energy)  
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Kinetic energy  
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Potential energy  
Kinetic Energy  
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Is the energy possessed by a body due to its motion.  
Examples of kinetic energy are wind energy, Moving water ,Ocean Waves  
,Ocean Tides ,Moving Machines, Falling bodies  
Mathematically:  
Kinetic energy is given by  
Example  
1. An object has a mass of 5kg. What is its kinetic energy if its speed is  
(a) 5m/s  
(b) 10m/s  
Data given  
Mass, m = 5kg  
Speed, va = 5m/s  
Speed, vb = 10m/s  
Solution  
(a)  
ퟏ
× ퟓ × ퟓퟐ = ퟔퟐ. ퟓ 푱  
Kinetic energy, 푲. 푬 =  
ퟐ
(b)  
ퟏ
Kinetic energy, 푲. 푬 =  
× ퟓ × ퟏퟎퟐ = ퟐퟓퟎ 푱  
ퟐ
Individual Task – 2  
1. What is the kinetic energy of a 12g bullet travelling at 320m/s? (K.E = 6144J)  
2. Anna has a mass of 80kg. If she runs at a speed of 10m/s. calculate her kinetic  
energy (ANS: K.E = 4000J)  
POTENTIAL ENERGY  
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Is the energy possessed by a body due to its state or position.  
The potential energy is given by  
;
Potential Energy = mass x height x acc. due to gravity  
The PE can be observed into the following areas;  
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A boy sitting on a bench  
A book placed onto a table  
A brick put on the ground etc.  
● A pen put on the table  
● A ruler put on the table  
● A man sleeping on a bed  
● A man standing on a bus stop  
Example  
1. A stone of 2kg falls from a height of 25 m above the ground. Calculate potential  
energy possessed by the stone  
Solution:  
Mass, m = 2kg  
Height, h = 25 m  
Gravitational force, g = 10N/kg  
∴ Potential energy, P.e = 풎품풉 = ퟐ × ퟏퟎ × ퟏퟎ = ퟐퟎퟎ푱  
Individual Task – 3  
Use:  
Acceleration due to gravity, g = 10 m/s2  
1. A ball of mass 0.5 kg is kicked vertically upwards and rises to a height of 5 m.  
Find the potential energy acquired by the ball. (ANS: P.E = 25 J)  
2. A body of mass 0.5 kg is projected vertically upwards such that it attains a  
height of 40 m. What is the potential energy at its highest point?  
3. A 2kg object is at rest on a table 1.2 m above the floor. The ceiling in the room  
is 2.8m above the floor  
What is the potential energy of the object relative to?  
a) Top of the table (ANS: P.E = 0 J)  
b) The floor  
(ANS: P.E = 24 J)  
c) The ceiling  
(
ANS: P.ELOST = 32 J)  
Transformation of Energy  
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Energy can be changed from one form to another by the device known as transducer  
Transducer  
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I
s a device used to convert energy from one form to another form  
For Example,  
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Battery convert chemical energy to electrical energy  
Generator convert mechanical energy to electrical energy  
A motor convert electrical energy to mechanical energy  
A microphone converts sound energy to electrical energy  
Solar panel convert solar energy to electrical energy  
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Heater convert electrical energy to heat energy  
A fan convert electrical energy into mechanical energy  
The green plants convert light energy into chemical energy by the process of  
photosynthesis  
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Thermal power stations convert heat energy to electrical energy  
A torch converts chemical energy to light and heat energy  
A bulb converts electrical energy to light and heat energy  
Heat engines convert heat energy to mechanical energy  
A blender convert electrical energy into mechanical energy  
A natural gas stove converts chemical energy from burning into thermal energy  
The law of conversation of energy  
States that:  
“Energy can neither be created nor destroyed but can be  
transferred from one form to another”  
Consider the diagram below  
At point A and C  
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The body is momentarily stationary (zero kinetic energy) and has maximum potential  
energy as it starts swinging to position B (At maximum height, P.Emax = mgh)  
Since: energy cannot be destroyed  
(
ET = K.E + P.E= 0 + mgh = mgh)  
At point B  
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The bob has maximum kinetic energy which takes it to position C  
.
1
That is K.Emax  
=
mv2  
2
NB: At any point the total energy (mechanical energy) is equal to the sum of kinetic  
energy and potential energyi.e  
ET = P.E + K.E  
Example  
1. A stone of mass 2 kg is released from a height of 2m above the ground. Find  
a) Total energy  
b) Potential energy at heat of 0.5m  
c) Kinetic energy at height of 0.5m  
d) Velocity acquired at 0.5m  
Diagram:  
(a) Total energy, E =?  
Maximum height, h = 2 m  
Mass of object, m = 2 kg  
Gravitation force, g = 10 N/kg  
Minimum velocity, v = 0 m/s  
From: E = P.E + K.E  
E = mgh + ퟎ = 2 x 10 x2 = 40 J  
(b) Potential energy, P.E =?  
Height, h = 0.5m  
From: P.E = mgh  
P.E = mgh = = 2 x 10 x 0.5 = 10 J  
(c) Kinetic energy, K.E= ?  
From: E = P.E + K.E---------- make K.E, the subject  
K.E = E – P.E = 40 – 10 = 30 J  
(d) Velocity acquired at 0.5m  
Velocity acquired at 0.5m, v =?  
2
From: K.E = mv --------------------- make v the subject  
1
2
= √ퟐ풙ퟑퟎ = ퟓ. ퟒퟖ 풎/풔  
ퟐ푲.푬  
√
∴ 풗 =  
풎
ퟐ
N.B  
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When the ball rebounds, it rebounds to the height less than the original height. This  
is due to:-  
(a) Some energy is used to overcome air resistance as the ball falls  
(b) The collision between the ball and the ground is not perfectly elastic  
(c) As the ball hits the ground, some energy is converted into other forms of  
energy causing its energy to be reduced  
Individual task – 4  
1. A ball of mass 0.2kg is dropped from a height of 20m. On impact with the  
ground it loses 30J of energy. Calculate the height which it reaches on the  
rebound (ANS: h = 5 m)  
2. A its highest point A 1.2 m a pendulum of mass 0.8kg is reached what.  
(a) Velocity swings at lowest point (ANS: v = 4.85 m/s)  
(b) Velocity at 0.9m  
(ANS: v = 2.4 m/s)  
(c) Height at 2m/s  
(
ANS: h = 0.98 m)  
Power  
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Power is the rate of doing work  
OR  
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Power is the rate at which energy is consumed.  
Its SI unit is Watt (W)  
Mathematically:  
푬
(
)
풘풐풓풌 풅풐풏풆 푾.풅  
풘.풅  
→ 푷 =  
( )  
푷풐풘풆풓 푷 =  
→ 푷 =  
( )  
풕풊풎풆 풕  
풕
풕
Equivalent units  
Whereby  
:
h.p = horse power used by engineering,  
kW = kilowatt,  
MW = megawatt  
Example  
1. A pump raises 100kg of water through a height of 30m in 10s. What is the  
power developed by the pump  
Solution  
Given: Mass, m = 100kg  
Height, h = 30m  
Time taken, t = 10s  
Gravitation force, g = 10N/kg  
Power, p =?  
(
)
풘풐풓풌 풅풐풏풆 푾.풅  
( )  
푷풐풘풆풓 푷 =  
From:  
( )  
풕풊풎풆 풕  
풎품풉  
ퟏퟎퟎ 풙 ퟏퟎ 풙ퟑퟎ  
ퟏퟎ  
∴ 푷 =  
=
= ퟑퟎퟎퟎ 푾  
풕