2.10
ENERGY, WORK AND POWER
2.10.3 Energy conversions
Lesson Objectives
At the end of the lesson; learners should be able to:





give examples of energy in different forms, its conversion and conservation and apply the principle
of energy conservation to simple examples (e.g. the kinetic energy changing to potential energy in
a pendulum and the sum of the two is constant if air resistance is negligible)
describe energy transfer in terms of work done and make calculations involving F × d
describe kinetic energy as energy of motion and potential energy as energy of position
(e.g. gravitational potential energy and strain potential energy)
recall and use the formulae for kinetic energy and gravitational potential energy
Ep = mgh
and Ek = ½ mv2
Give examples of energy in different forms, its conversion and conservation
and apply the principle of energy conversion to simple examples
Give examples of energy in different forms
• Chemical potential energy- stored energy in chemicals and released
during chemical reactions. E.g., in food, battery, fuels and etc.
• Kinetic energy- energy of motion. E.g. in moving ball (objects), an
• arrow from bow and etc.
• Potential energy- energy of position.
-Gravitational potential energy- stored energy of a body due to its position
above the earth’s surface (ground). E.g. stored water in dams or containers.
-Strain (elastic) potential energy- stored energy objects that stretches,
compressed or deformed. E.g., stretched bow, catapult, rubber bang and
etc.
• Mechanical energy – the sum of kinetic energy and potential energy of
a body.
• Hydro-electric energy- energy from falling water.
• Light energy- energy from light emission objects. E.g., stars, sun and
etc.
• Tidal energy- energy caused by tides at the sea/oceans.
• Heat energy- energy due to heat. E.g. from fire.
• Sound energy- energy caused by vibration of objects. E.g. string of
guitar.
• Electric energy- energy from electricity (current)
State the Law or Principle of conservation of energy
• Energy cannot be created or destroyed, but it can be changed from one
form to another
Describe conversion of energy in simple examples by which energy is
converted from one form to another (energy flow diagram)
i)
Pendulum
 Kinetic energy TO
potential energy
NB: When pendulum bob is at its highest, it has its maximum potential energy. As it
falls, its potential energy decreases, and its kinetic energy increases. Its total energy
(mechanical energy) stays constant provided the air resistance (resistive forces) are
negligible.
ii)
Radio using cells
 Chemical energy  electrical energy sound
energy
iii)
Electric kettle
 Electrical energy  heat energy
iv)
Light bulb
 Electrical energy  light energy + heat
energy
Describe energy transfer in terms of work done and make calculations
involving F × d
• When work is done, energy is transferred from one form to another.
Thus, transferred energy is equal to the amount of work done.
• The unit for both energy and work is Joules (J) or Newton meter (N/m),
Therefore: 1 Nm = 1J
• Work is a scalar quantity, the product of two vectors: force and
displacement.
• Work can be calculated using the formula: W = F x d
W= work done (in
joules) F = force
applied (in
Newton)
d= distance over which the force is applied (in metres)
Example
1. A man lifts a weight of 500 N upward over a distance of 2 m. how
much work does the man do?
Describe kinetic energy as energy of motion and potential energy as energy of position (e.g.
gravitational potential energy and strain potential energy)
POTENTIAL ENERGY (P.e.)


This a stored energy a body has because of its position above the earth surface
Any object has stored energy if it is held in a position from which it can fall under the
influence of gravity
Potential energy is also called gravitational potential energy
This energy is possessed by all bodies which are raised above the earth surface.
Potential energy of a given body is directly proportional to the height a body is raised
above the ground.
The high the height a given body is raised above the earth surface the more potential
energy it has.




Formula for potential energy:
P.e. = mgh



Where;
m is mass of a body
g is gravitational field strength
h is height at which a given body is raised
Illustrations
1. A body of mass 80kg was hanged 10m above the ground. Calculate its potential energy.

2.
P.e. = mgh

= (80kg)(10N/kg)(10m)

= 8000J
A 900g fruit hanging from a fruit tree has a potential energy of 700J. How high is the
fruit above the ground?

P.e. = mgh

h



P.e.
mg
700 J
(0.9kg)(10 N / kg)
 77.78m
3. A pendulum was made to swing and its bob passed a point where potential energy and
kinetic energy are equal. The speed with which the bob passed the point is 5m/s. How
high is the point?
 P.e.  K.e.
1
 mgh  mv2 (m is appearing on both side, it can get cauncelled out)
2
2
v
 gh  (after m is cauncelled out we get this formula)
2
v2
 gh  (after m is cauncelled out we get this formula)
2
2
v
(5m / s) 2
25m2 / s 2
 h


 1.25m
2 g (2 x10m / s 2 ) 20m / s 2
4. A 200kg stone broke off the mountain tip and roll down. At a certain point 80m
from the ground potential and kinetic energy were equal. Find the speed of the
stone as it passes that point.




K.e.  P.e.
1
mv 2  mgh
2
v2
 gh
2
v 2  2 gh v  2 gh  (2 x10m / s 2 x80m)  40m/ s
5. Calculate the work done by a crane for lifting a 200kg body to the height of
25m.

Work done  potential energy gained (this is because work is the amount of energy tra nsfered

W P.e.

W  mgh

 (200kg)(10 N / kg)( 25m)

 50,000 J

W = Fd
2000N]

W = 2000N x 25m = 50 000J
[F = mg = 200kg x 10N/kg =
6. A lift in a shop can carry 8 people through the height of 20m in 5s. If the lift
plus the passengers has the mass of 800kg, calculate the power of the crane.

Power 
work done
( work done in this case is equal to potential energy)
time taken

Power 
P.e.
[ P.e.  mgh  (800kg)(10 N / kg)( 20m)  160,000 J ]
t
160000 J
= 32000 W
5s
KINETIC ENERGY (K.e.)

Power 


This the energy possessed by every moving body
Anything that moves has kinetic energy
Formula for kinetic:
K.e. =
1 2
mv
2


Where;
m is mass of a body in kg
v is velocity of a moving body in m/s
Illustrations
1. A football of mass 400g is kicked and moves at a speed of 20m/s. Determine the
ball’s kinetic energy.

1
mv 2
2
1
 (0.4kg)( 20m / s ) 2
2
 80 J
K .e. 
2. If the kinetic energy of a rolling body with speed of 30m/s is 125J. Find its mass.

1
mv 2
2
2 K .e.  mv 2
2 K .e.
m
v2
2 x1250 J
 2.78kg
m
(30m / s) 2
K .e. 
3. A 1200kg moving car has 540,000J. Determine the car’s speed.

K .e. 
1
mv
2
2 x540000 J
2 K .e.

 30m/ s
m
1200kg
4. A force of 6000N was applied on a stationary body and caused it to move with the
acceleration of 30m/s2 for 5s. Find the car’s kinetic energy.
mv 2  2 K .e.
v
1
mv 2
2
first find mass and speed of the body :

K .e. 
speed

a
v u
 v  u  at  v  at  u  v  (30m / s 2 x5s )  0  150m / s
t
mass
 F  ma
F 6000 N
 m 
 200kg
a 30m / s 2
Now we have all we need to calculate kinetic energy
1
 K .e.  (200kg)(150m / s ) 2  2,250,000 J
2
5. Masses of a bicycle and cyclist are 7kg and 75kg respectively. If the cyclist is cycling
at a speed of 6m/s, determine the kinetic energy involved.

1
mv 2
2
1
 (7kg  75kg)(6m / s ) 2
2
 1,476 J
K .e. 
6. A 15kg stone is thrown vertically upward and reach the height of 40m. Calculate the
speed of the stone as it strikes the ground.

K.e.  P.e.
1 2
mv  mgh
2
v 2  2 gh
v  2 gh
 2x10m / s 2 x40m
 28.28m/ s