ENERGY, WORK AND POWER
1. ENERGY , E
Energy is defined as the ability to do physical work.
S.I. unit: Joule (J)
FORMS AND SOURCES OF ENERGY
FORMS
SOURCES
Heat energy
fires
RENEWABLE/N
ONRENEWABLE
NR
Light energy
sun, stars, light bulbs, burning fires
NR
Sound energy
vibrating objects
NR
Chemical
energy
Electrical
energy
Kinetic energy
Food, fossil fuels (coal and gas)
NR
batteries, H.E.P and Nuclear Power
Stations
moving objects
NR
Potential
energy
Nuclear energy
objects above Earth surface
NR
atoms (atomic nuclei)
NR
Solar energy
sun
R
Geothermal
energy
Wind energy
molten rocks underground
R
wind
R
Wave energy
water waves at sea
R
NR
PRINCIPLE OF CONSERVATION OF ENERGY
States: Energy cannot be created or destroyed but changed from one form to another.
Energy input
‘machine’ converts
(transducer)
equal energy output
CONSERVATION OF ENERGY IN VERTICAL MOTION
WHEN AN OBJECT IS THROWN VERTICALLY UPWARDS ITS VELOCITY
DECREASES THEREFORE ITS KINETIC ENERGY ALSO DECREASES.AS THE
OBJECT RISES ITS HEIGHT ABOVE THE GROUND INCREASES AND THEREFORE
ITS GRAVITATIONAL POTENTIAL ENERGY ALSO INCREASES.
When the object falls its kinetic energy increases as the gravitational potential energy
decreases. At every point of its motion the sum of kinetic energy and gravitational potential
energy is constant; Ek + Ep = constant.
This concept is used in energy changes or conversions: energy changing from one form to
another.
ENERGY CONVERSIONS
Energy flow diagrams are used to show energy changes that occur. Some examples are given
below.
(a) A bulb torch illuminating a room
Chemical Energy
Electrical energy
Light Energy + Heat Energy
(b) An apple falling from a tree
Potential Energy
Energy
Kinetic Energy
Heat Energy + Sound
(c) A singer singing into a microphone
Sound Energy
Electrical Energy
Kinetic Energy + Sound Energy
(d) An initially moving car suddenly brought to rest
………… Energy
Heat Energy + ……………… Energy
(e) Production of electricity from a hydroelectric power station
Potential Energy
(from head of water)
Kinetic Energy
(rotating turbine)
Electrical Energy
(f) Production of electricity in a power station using coal
Chemical Energy
Heat Energy
Kinetic Energy + Electrical Energy
(turn water into
(rotating turbine)
steam)
(g) A simple pendulum
Potential Energy
(at extreme left)
Kinetic Energy
(at centre)
Potential Energy
(at extreme right)
NB: The pendulum eventually stops at the middle position because all the energy becomes
gradually lost due to air resistance opposing its motion. This does not show that energy of
the pendulum is destroyed!
There are many examples of energy conversions, which we experience in our everyday life.
For the examples listed below draw energy flow diagrams:
(i) Footballer kicking a ball
(ii) Charging a car battery
(iii) A radio speaker producing music
(iv) Solar Panels used in our homes
(v) Swimmer diving from a platform
It is also important to note that every energy conversion is designed to produce useful energy,
which can be made use of in special ways like for lifting, data transfer, growth, storage,
deceleration and many others.
SOURCES OF ENERGY IN BOTSWANA
SOURCE
Sun
Firewood
Coal
Natural gas
ADVANTAGES
-Renewable
-Abundant and clean
-Cheap and easy to
find
-Can be used to
produce electricity in
power stations
-People get paid for
mining
-Clean and easy to
use
DISADVANTAGES
-Changes with weather
-Expensive (solar panels)
-Non-renewable and dirty to use
-Causes deforestation
-Produces CO2 which causes
pollution and Global warming
-Non-renewable
-Produces Carbons which causes
pollution and Global warming
-Non-renewable
-Causes pollution and Global
warming
Oil (petrol, diesel,
paraffin)
-Easy and clean to use
Wind
-Renewable
-Abundant and clean
-Non-renewable
-Produces CF’s which causes
pollution and Global warming
-Machinery used is expensive
N.B: In columns two and three the responses should be based on the Social, Economic
and Environmental factors.
Fill in the blanks in this article about Global Warming. Use the terms given below.
Some gases such as -------------------- from industries accumulate in the atmosphere leading to
an ------------------------ in temperature. These gases trap long wavelength
----------------------- radiation emitted by the Earth. This is known as the -------------effect, and is believed to cause ------------------------------ . Global warming causes a
rise in temperature of the oceans, which leads to ---------------- in the sea level.
[Greenhouse, Nitrogen, solar, rise, fall, infrared, carbon dioxide, increase, decrease, Global
Warming]
A. KINETIC ENERGY, Ek
Kinetic Energy is defined as energy due to motion of objects or energy possessed by all
moving objects.
It depends on the mass and velocity of the object.
S.I. unit: Joule (J)
To calculate kinetic energy of a body we use the formula:
Kinetic Energy = ½ x mass x velocity x velocity
In symbols, Ek = ½ mv2
where m is the mass of the object in kg
v is the velocity of the object in ms-1
Examples
(a) Calculate the kinetic energy of a car of mass 1000 kg moving at a speed of 20 ms-1.
Answer
m = 1 000 kg, v = 20 ms-1, Ek = ?
Using Ek = ½ mv2
= ½ x 1 000 kg x 20 ms-1 x 20 ms-1
= 2 000 J
(b) A body of mass 100 g is moving with a velocity of 5 ms-1. Calculate its Ek.
Answer
m = 100 g, v = 5 ms-1, Ek = ?
= (100/1 000) kg
= 0.1 kg
Using Ek = ½ mv2
= ½ x 0.1 kg x (5 ms-1)2
= 1.25 J
(c) A moving object has a mass of 0.4 kg and 80 J of kinetic energy. Calculate the
object’s velocity.
Answer
m = 0.4 kg, Ek = 80 J, v = ?
Using Ek = ½ mv2
80 J = ½ x 0.4 kg x v2
80 J = 0.2 kg x v2
v2= 80 J/0.2 kg
v = ±v(80 J/0.2 kg)
v = ± 20 ms-1
The velocity of the moving object is 20 ms-1.
B. GRAVITATIONAL POTENTIAL ENERGY, Ep
Potential Energy is defined as the energy a body possesses due to its position with
respect to the Earth.
It depends on the weight and height of a body above the Earth.
S.I. unit: Joule (J)
To calculate potential energy of a body we use the formula:
Potential Energy = mass x acceleration due to gravity x height above the Earth
In symbols:
Ep = mgh
where m is measured in kg
g is 10 ms-2 or 10 Nkg-1
h is measured in meters, m
Examples
(a) A boy of mass 45 kg, fearing dogs climbs to the top of a 3 m tall tree.
(i) What form of energy does he gain as he climbs?
(ii) Calculate the amount of energy he gains.
Answer
(i) Ep
(ii) m = 45 kg, g = 10 Nkg-1, h = 3 m, Ep = ?
Using Ep = mgh
= 45 kg x 10 Nkg-1x 3 m
= 1350 J
(b) Peter let a stone of mass 200 g fall from a tower that is 20 m tall till it hit the ground.
(i) What type of energy does the stone possess when at the top of the tower?
(ii) Calculate the amount of energy it has at the top of the tower.
(iii) What form of energy does the stone gain as it falls?
(iv) Calculate the amount of PE when the stone has fallen by 15 m.
(v) State the kinetic energy of stone on hitting the ground. Support your answer with a
reason.
(vi) What is the speed of stone on hitting the ground?
(vii) Use energy flow diagram to show energy changes that take place.
Answer
(i)
Ep
(ii)
m = 200 g,
= (200/1000) kg
= 0.2 kg
g = 10 N/kg, h = 20 m, Ep =?
Using Ep = mgh
= 0.2 kg x 10 N/kg x 20 m
= 40 J
(iii) Ek
h = 20 m – 15 m
= 5 m;
Ep =?
Using Ep = mgh
= 0.2 kg x 10 N/kg x 5 m
= 10 J
NB: The Ek = 40 J – 10 J (from the PCE)
= 30 J
(v) Ek = 40 J
From the PCE, the entire Ep has been converted to Ek.
(iv)
(vi) Ek = 40 J, m = 0.2 kg, v =?
Using Ek = ½ mv2
v = ±v(2KE/m)
= ±v[(2 x 40 J)/0.2 kg]
= ± 20 ms-1
The velocity of the stone is 20 ms-1.
(vii) Potential Energy
Kinetic energy
Sound energy + Heat energy
WORK, W
Work is defined as a product of a force and a distance in the direction of force.
S.I. unit: Joule (J)
To calculate work done, the mathematical expression is used:
Work Done = Force x distance moved in the direction of force
In symbols:
W=Fxs
Relation between Work and Energy
For an object to do a piece of work, it must have energy that is actually used up. A good
example is of a man who becomes tired after pushing a box on a floor. No energy means no
work is possible.
WORK DONE = ENERGY
However, not any energy spent means work is done! Carrying 100 kg of cement on the head
without changing the vertical height make a person tired although NO WORK IS DONE.
(i) What is the reason for this unfortunate situation?
(ii) Give other examples of cases as that mentioned above.
Examples on calculating the work done by forces
(i) What is the amount of work done if 100 N is applied to push a box across a horizontal
floor for a distance of 3 m?
Answer
F = 100 N, s = 3 m, W =?
Using W = F x s
= 100 N x 3 m
= 300 J
(ii) A boy of mass 50 kg climbs a tree to a height of 5 m. Calculate the amount of work
done in this process.
Answer
m = 50 kg, g = 10 Nkg-1, s = height = 5 m, F = ?, W = ?
Using F = mg
F = 50 kg x 10 Nkg-1
= 500 N
But
W = F x s **
Then
W = 500 N x 5 m
= 2500 J
Note that in ** above,
W = mgh
The Work Done in a vertical direction is equal to Potential Energy.
POWER, P
Power is defined as the rate at which, work is done.
or
Rate at which energy is being used (supplied).
Mathematical expression:
Power = Work Done/ Time taken
or
Power = Energy transfer/ Time taken
In symbols:
P = W/t or E/t
S.I. unit: Watt (W)
where 1W = 1J/1s
Multiple units: kilowatts (kW); 1 kW = 1 000 W
Megawatts (MW); 1MW = 1 000 000 W
Examples
(a) A man loading a truck lifts a box of mass 100 kg through a height of 1.6 m in 4 s.
(i)
Calculate the amount of work done by the man.
(ii)
What is the power of this man?
Answer
(i) m = 100 kg, g =10 Nkg-1, h = 1.6 m, W =?
Using W = mgh
= 100 kg x 10 Nkg-1 x 1.6 m
= 1 600 J
(ii) W = 1 600 J, t = 4 s, P =?
Using P = W/t
= 1 600 J/4 s
= 400 W
(b) A crane, A, lifts a load of 400 kg through a vertical height of 10 m in 4 s. Another
crane, B, lifts 300 kg through 15 m vertically in 5 s. Which crane uses more power?
(Answer: PA = 10 000 W; PB = 9 000 W; Crane A uses more power than crane B)
(c) A trailer was pulled by a car with a horizontal force of 3 000 N so that it moved a
distance of 100 m in 1minute on a horizontal road. Calculate the average power
exerted by the car on the trailer.
(Answer: P = 5 000 W)
EFFICIENCY OF ENERGY CONVERSIONS
Generally refers to the conversions of energy to other forms at a minimum loss.
Efficiency, η, is defined as the ratio of output energy to input energy, multiplied by 100%.
Mathematical expression
Efficiency, η = Output Energy x 100 %
or Power Output x 100 %
Input Energy
Power Input
Consider the diagram below;
The intension was to produce only light from the bulb but along with light produced, heat
was unintentionally produced. This means that some of the electrical energy ended up
producing some form of energy that was not intend to produce. In this case if the bulb only
produced light, then it would be 100% efficient.
UNFORTUNATELY THERE IS NO KNOWN MACHINE (ENERGY CONVERTER)
THAT IS 100% EFFICIENT.
EXAMPLES
1.A machine lifts a load of 500 N through a vertical height of 2 m in 5 seconds.
(a) What type of energy does the load gain?
(b) How much work does the machine do?
(c) How much power does the machine develop?
(d) The machine has an efficiency of 40%. Determine how much energy was supplied
to the machine.
2. An athlete in a race exerts a force of 100 N for a distance of 200 m and in the process
uses 500 000 J.
(a) What is the efficiency of the athlete?
(b) State where the rest of the energy goes?