WORK, ENERGY AND POWER
Work is a product of force and distance moved in a given direction. The quantity of work done is always equal
to the quantity of energy put in.
Work = Force x Distance moved in the direction of application of force.
The Unit of force is Newton (N); the unit of distance is Meter (m). Therefore the unit of work is = N x m or Nm.
Nm is known as joule (J). Therefore, Joule is the unit of work done.
Example 1: What work is done when a mass of 20kg is raised through a hill 50m high? (Take g=10ms-2)
Solution:
Work done = force x distance
Force = mass x acceleration due to gravity (g)
Force = 20kg x10m/s2 = 200N
Work done= 200N x 50m
Ans.= 10 000 Joules
CONCEPT OF POWER
Power is defined as the rate of doing work.
Power = work done
Time taken
The S.I unit of power is Watt (W)
EXAMPLE: 2
What is the power of a child that has done work of 50 Joules in 10 seconds?
SOLUTION:
Power = work done = 50
Time is taken 10
Ans. =5 watts
EXAMPLE: 3
A little girl with a mass of 25kg climbs a platform that is 2m in height in her 20s. Calculate the power used by
the girl [g = 10ms-2].
SOLUTION:
WORK DONE = Force x Distance
Force = mass x acceleration due to gravity
Force = 25kg x 10ms-2
= 250N
Work done = 250 x 2 = 500Nm
Power = work done
Time taken
= 500Nm
The 20s
Ans. = 25Watts
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TYPES OF ENERGY
Energy is the ability or capacity to do work. There are different types of energy, mechanical energy, electrical
energy, heat energy, sound energy, light energy and chemical energy (from food, coal, oil and gas). Kinetic and
potential energy are two forms of mechanical energy. The S.I. unit of energy is joule other units of energy
including meter, kilowatt and kilowatt hour.
The kinetic energy (KE) of an object is the energy that it possesses due to its motion.
K.E = 1mv2
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M = mass of the object
V = velocity of object
Example: Calculation of Kinetic Energy
An 11 kg brick falls off a 44 mm high roof. It reaches the ground with a velocity of 8.858.85 m⋅s−1m·s−1. What is
the kinetic energy of the brick when it starts to fall and when it reaches the ground?
Step 1: Analyze the question to determine what information is provided
 The mass of the brick =1 kg
 The velocity of the brick at the bottom v=8.85 m⋅s−1v=8.85 m·s−1
Step 2: Calculate the kinetic energy at the top
Since the brick is not moving at the top, its kinetic energy is zero.
Step 3: Substitute and calculate the kinetic energy
KE=1mv2= 1 (1)(8.85)2 = 39.2 J
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POTENTIAL ENERGY
POTENTIAL ENERGY (P.E): Is the energy possessed by an object by its position of rest (its height). Potential
energy is stored energy. The potential energy of a body depends on its position and mass.
P.E = mgh
m = mass of the object
g = acceleration due to gravity
h = height of the object from the ground.
EXAMPLE 4: If an object weighing 6kg is placed on a platform 5m high. Calculate its potential energy. (Assume g = 10ms-2)
SOLUTION:
m= 6kg h = 5m g= 10ms-2
P.E = 6 X 5 X 10
Ans. =300J
CALCULATION OF THE AMOUNT OF ELECTRICAL ENERGY CONSUMED
Reading an Electric Meter
The electric meters in our homes measure the amount of electricity the households use. This is used to produce the bills.
The use of electric energy is shown on the meter as kilowatts – hour (kWh). The commercial unit of energy is kWh. That
is one kilowatt–hour is the electric energy used by 1 Kw appliance in one hour.
The total amount of energy is:
Energy
= Power x Time
(Joules) (J) = (watt) (w)
(second) (s)
Worked examples on Calculating the cost of electricity
1. A 2000W electric heater is used for 10 hours. What is the cost at ₦6.00 per kWh?
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Solution:
Energy used (kWh) = power (kW) x time (hours)
= 2 kW x 10 hours
= 20 kWh
Cost at ₦6.00 per kWh x 20kWh = ₦120.00
2. In 1 minute how much energy does a 100 W electric bulb transfer?
Energy = Power x time
POWER = 100WATT
TIME= 1 MINUTES = 60 SECONDS
Energy = POWER X TIME
100 X 60 =6000 J
ENERGY TRANSFER WHEN WORK IS DONE
Most mechanical and human activity represents an inter-change of energies from kinetic, potential and work done. For
example, when an object falls from above the ground the potential energy of the body is changed to kinetic energy.
Other forms of energy transfer include:
1. Electrical energy to sound energy: This occurs in radio and television.
2. Potential energy to heat energy: e.g. the potential energy you use in rubbing your palm is transferred into Kinetic
energy and heat energy is generated.
3. Chemical energy to mechanical energy: In motor vehicles, cars and trucks, fuel which contains chemical energy is
converted to heat energy and then to mechanical energy.
4. Solar to heat energy: When the energy (ray of light) from the Sun is concentrated on paper, the paper gets heated
and burns off.
5. Heat to light energy: When a piece of iron is heated in a flame for some time, it becomes red hot, and it glows.
6. Hydro-mechanical to electrical energy: In this type of conversion, falling water from a dam is used to turn the
turbine of a generator to produce electricity.
All the energy transfer described above affirms the law of conservation of energy which states that energy cannot be
created nor destroyed but is transferred or changed from one form of energy to the other.
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ASSIGNMENT ON WORK, ENERGY AND POWER
The simplest formula to calculate kinetic energy is_______
Calculate the potential energy possessed by an object weighing 20kg placed on a roof 40m above the ground. (Take
g = 10m/s).
A crane uses 2000 J of energy to lift 10 kg of water from a well. Calculate the depth of the well.
Given g = 10 m/s2
_________ and _________ have the same S.I. unit?
A pulley carries a bag weighing 40 kg from the ground floor to his class on the first floor that is
20m high. The work done by the boy is_______ [Take g=10m/s2]
Mechanical energy is a combination of ________
A. electrical and sound energy
B. magnetic and gravitational energy
C. thermal and kinetic energy
D. potential and kinetic energy
Solar energy is converted by plants in process of photosynthesis into________
A. chemical potential energy
B. potential energy
C. gravitational Potential Energy
D. kinetic energy
A toy train moves a distance of 20m with a constant force of 2N, the work done is________
Energy possessed by a body at rest is called _______
B Note: The step-by-step workings or calculations showing formulas used and how you arrived at your final answers
for numbers 2, 5 6, and 8 must be shown.
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