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Energy
BA Design for Industry Year 3
John Errington MSc
What is energy?
• You can’t see it or feel it
– a charged battery
doesn’t look more
‘energetic’ than a flat
one.
• Energy has the ability to
do work
• It is measured in
Joules.
Energy is conserved:
• Energy can not be lost.
• It can be stored,
changed from one form
to another, even
‘wasted’.
• All other forms of
energy eventually end
up as heat.
Energy has the ability to do work
Work is done in changing
the energy level of an
object
–Pushing it makes it move
& gives it kinetic energy
–Lifting it against gravity
raises its potential energy
–Heating it raises its
temperature (heat energy)
Examples:
Accelerating a car: petrol is
burnt in the engine. The
chemical energy stored in the
fuel is used up making the car
go faster.
Raising a load: electricity is
used to make the lift motor
turn.
Heating your food: charcoal
burnt on a barbeque heats
and cooks your sausages.
What has most energy?
1.
A 5kg weight 1m above the floor (PE)
2.
A 41g golf ball travelling at 40 m/s (KE)
3.
A jam doughnut
4.
A spring compressed 0.1 m by a force of 20kg.
5.
A cup of coffee (black, no sugar)
6.
A Duracell D cell
7.
A bicycle wheel spinning at 10 rps.
Potential energy
Potential energy is energy something
has because of the state it is in.
Easy example: You do work lifting your
briefcase from the floor to the desk.
You have ‘used up’ some energy to do
that. The briefcase has gained energy.
PE = mgh m=mass g=gravity h=height
PE Calculation
The briefcase weighs 5kg and the desk is
1m high. In lifting it to the desktop you
have done work in fighting gravity.
The briefcase now has a potential energy
(relative to the floor) of
PE = 5kg * g * 1m = 5 * 9.81 * 1
PE = 49 Joules.
Kinetic Energy
To make things move we need to do work
– i.e. use energy.
So moving things have energy called kinetic
energy
Ek = ½ mv2
where m = mass, v = velocity
KE calculation
A golf ball with a mass of 45g = 0.045 kg
travels at 40 metres per second.
Its KE is = 0.5 * 0.045 * 40 * 40
KE = 36 joules
( Remember Ek = ½ m v2 )
KE of rotating body
The kinetic energy stored in a flywheel is E = ½ I ω2
Where
I = moment of inertia of the flywheel, given by
I = k M r2 M = mass; r = radius; k = inertial constant (depends on shape)
k = 1 for wheel loaded at rim; k = 0.5 for cylinder
ω is the angular velocity of rotation given by
ω = 2 π * speed in revs per second so
ω = 2 π * 60 * speed in rpm
You can see that to store the maximum energy in a flywheel
we need a shape where most of the mass is at the edge;
and to spin it very fast.
Example of flywheel
A bicycle is travelling at 30mph and has a wheel of radius
21cm and mass 200g. How much energy is stored?
1. Work out speed of rotation of wheel
(convert miles per hour to metres per second)
30mph = 30 / 2.24 mps = 13.4 mps
Circumference of wheel is C = 2 * .21 * pi = 1.32 m
13.4mps / 1.32m = 10 rps
2. Calculate moment of inertia
I = kMr2 = 1 * .2 * 10 * 10 = 20 kg m2 (k = 1 for bicycle wheel)
3.
Now calculate stored energy
ω = 2 π * speed in rps = 2 π * 10 = 63 radians per second
E = ½ I ω2 = ½ * 20 * 63 * 63 = 39630 Joules.
Conservation of energy
• The total amount of energy in a closed
system remains constant
• The energy we use in lifting the briefcase
is the same as the potential energy it has
on the desk.
• If it falls off its kinetic energy just before it
lands is the same.
Falling briefcase
Before moving PE = 49 Joules
So before landing KE = 49 joules
But KE = ½ m v2
49 = 0.5 * 5kg * v2
v2 = 49 / 0.5 * 5kg = 19.6
v = 4.4 metres per second
What happens when it hits the floor?
– It stops
– Its potential energy is zero
– Its kinetic energy is zero
• Where has the energy gone?
Waste heat
• Heat energy is the least useful form of energy
• All other forms of energy tend to be degraded to heat.
• Heat energy is hard to confine, and tends to spread out
until everything is at the same temperature.
• Heat engines work on temperature differences
Fallen briefcase
• Some energy will appear as sound
• Some energy may be used in breaking things
and deforming the plastic
• Some energy will be restored to the briefcase as
it bounces up again
• Eventually all the energy not used up in breaking
things will appear as heat.
• 49 J is enough energy to raise the temperature
of a kg of water by about 0.01 degrees C.
Energy of a hot body
The amount of energy required to raise the
temperature of 1kg of water by 1 degree C is a
kilocalorie. (1kcal = 4000J)
So a cup of coffee (0.12 litre = 0.12kg) heated from
room temperature at 20 deg C to 60 deg C
(careful, its hot!) has
Eheat = (60 – 20) * 0.12 kcal = 4.8 kcal
Eheat = 4.8 * 4000 = 19,000J
Energy of a doughnut
• Food energy is measured in ‘Calories’
(actually kilocalories kcal)
• A jelly (jam) doughnut has about 250 kcal
• 1 kcal = 4180 joules, so
• 1 JD = 1 Megajoule.
This is the same energy as a 10kg mass at a
height of 10,000m., or e.g. to accelerate a 350kg
car to 70 mph.
Energy stored in a stretched spring
• Work is done in stretching or compressing a
spring from its rest length
• So a deformed spring has Potential Energy
• The force exerted by the spring is
proportional to the change in length x
i.e.
Fx  x
(Hooke’s law)
• The amount of work done is force * distance
Energy stored in a spring
The force Fx exerted by a spring stretched by an amount x is
Fx = ks x where ks is the spring constant.
The energy stored is the average force F * distance
stretched, x
F = ½ (Fx + F0)
and F0 = 0
i.e.
Ex = ½ Fx x
or
Ex = ½ ks x * x
Force
Force is measured in Newtons
The force exerted by gravity on a mass
of 1 kg is 9.81 Newtons
In holding a small apple you are exerting a
force of about 1N
Spring energy example
A spring exerts a force of 20kg (200N) when
compressed by 0.1m. What is the energy stored in
the spring at this point?
Use Ex = F x
The force is 0 N for no compression and 200N at
0.1m compression
Average force F = (F0 + Fx) / 2 = 100N
Ex = 100 * 0.1 = 10 J
Converting energy
How fast could this spring drive a model car
weighing 100g (0.1 kg)?
Stored energy = 10 J
10 = ½ m v2
10 = 0.5 * 0.1 * v2
200 = v2 v = 14 metres per second
( Assuming 100% conversion efficiency )
Energy in stretched rubber band
Rubber is a cross-linked polymer.
In its rest condition the links are
very disorganised. When
stretched the links become more
regular, and so have less entropy.
This means there is a strong
tendency for the rubber to return
to its original state when released.
A significant amount of the energy
put in in stretching it is released
as heat when the band is
released.
Entropy?
• Entropy is a measure of how organized
something is.
• Take a set of billiard balls and put them in
the triangle. They are highly organized –
high entropy.
• Put the billiard balls in your rucksack and
shake it about. They are now randomly
distributed – low entropy.
• Everything tends to a state of low entropy.
Stretching a rubber band
stretching a rubber band
1.4
1.2
force in kg
1
0.8
0.6
0.4
0.2
0
0
10
20
30
length of band
40
50
Initially the band
stretches very easily
Then a stage is reached
where it obeys Hookes
law (20 – 40 on chart)
Finally the molecules
are very straight and
the band becomes hard
to stretch any further –
it will snap if too much
force is applied
Rubber band energy example
For a simple calculation ignore the early part
of the graph as little energy is used here.
To stretch from
0.2m = 0.1kg to 0.4m = 0.7kg
requires an average force of
F = (0.1 + 0.7) * 9.81 / 2 N = 4N
Energy is ½ (0.4 – 0.2) * 4 = 0.4J
Energy stored in a battery
A Duracell ‘D’ cell provides a terminal voltage of 1.5V. It has a
nominal capacity of 15.6 Ah at 10 ohms for 120 hours i.e. it can
supply 0.156 A for 100h
The maximum available stored energy is
E (watt hours) = volts * amp – hours
E = 1.5 * 15.6 = 23.4 watt hours
Now 1 watt = 1 joule per second, so 1Wh = 3,600J
Energy in joules is 23.4 * 3,600 = Eb = 84,240 J
(or 1/12 of a jelly doughnut)
NOTE THIS ENERGY CAN NOT ALL BE RELEASED IN A SHORT
TIME!
What has most energy?
1.
A 5kg weight 1m above the floor (PE)
50J
2.
A 41g golf ball travelling at 40 m/s (KE)
36J
3.
A jam doughnut (chemical energy)
1MJ
4.
A spring compressed 0.1 m by a force of 20kg.
10J
5.
A cup of coffee (black, no sugar) (thermal)
19kJ
6.
A Duracell D cell (electrical)
85kJ
7.
A bicycle wheel spinning at 10 rps
40kJ
Conversion efficiency
Whenever energy is converted from one form to
another there will be losses. For example when
the spring propels the vehicle:
most energy will be converted to kinetic energy
some energy will be lost as heat, through friction
– in the spring
– in the drive
– In moving the air
The proportion of energy that does useful work is
the conversion efficiency
Rate of release of energy
The amount of energy stored is not the only
consideration in choosing an energy source for a
project. Another important factor is how quickly
the energy can usefully be released.
In general the more slowly energy is released the
more effective is the conversion efficiency.
Most batteries can only deliver their maximum
energy over a long time (>10h)
Some systems are much better at releasing
energy quickly (examples – explosives, springs)
Releasing energy in a spring
Suppose we take a tension spring 0.1m long and
extend it to 0.2m with a force of 30N
The stored energy is Ex = F x Joules
F = average force = Fx / 2 = 15N
x = 0.2 – 0.1 = 0.1m
Ex = 15 * 0.1 = 1.5 Joules
If the spring is released the energy is used in many
different ways
Some ways energy is released
If the energy in the spring is used externally by releasing it
in a controlled way most of the stored energy can be
recovered. (e.g. clock)
If the spring is released in an uncontrolled way none of the
stored energy will be recovered, and the energy will be
dissipated through:
• Accelerating the spring
• Overcoming air friction
• Changing the shape of the spring
• Heating the spring
• Setting up vibrations in the spring
Accelerating the spring
If the spring has a mass of 0.1kg we can work out how it
will accelerate when released.
The stored energy of 1.5J is converted to kinetic energy
Ek = ½ m v2 where v is the average velocity of the spring.
1.5 = ½ * 0.1 * v2 so v2 = 30 v = 5.5
Now one end of the spring is moving, the other stationary,
so the average speed is half the speed of the free end.
Thus the free end will be accelerated to about 11m/sec.
( This is the same result as we would have for a free object weighing 0.05kg so
we can use the effective mass for the spring as ½ its real mass )
Partitioning energy transfer
If the free end of the spring is attached to a car with a mass of 0.2kg the same
equations can be applied.
1.5J = ½ m v2 or v2 = 1.5 / 0.5 * m
The total mass is 0.2 (car) + 0.05 (effective mass of spring)
v2 = 1.5 / 0.5 * 0.25 whence
v2 = 12 so v = 3.4 m/s
The car now has an energy of
Ek = ½ m v2 = 0.5 * 0.2 * 12 = 1.2J
and so 1.5 – 1.2J = 0.3J is dissipated in the spring.
The conversion efficiency is energy used / energy stored
= 1.2 / 1.5 = 0.8 or 80%
Other energy sources
The same principle applies to other energy stores.
For example a 1.2V NiMH battery is rated 1.8
Amp-hours at its “0.1C” rate. This means that the
energy will be released evenly over 10 hours.
If we try to release the energy much more quickly
the current is reduced owing to the internal
resistance of the cell. This causes the cell to get
hot, wasting energy. If overstressed (>10C) the
cell may be degraded, destroyed, or even explode.
Limit to available energy from battery during rapid discharge
energy output of NiMH AA cell vs discharge time
8000
6000
5000
4000
3000
2000
1000
0
1
10
100
1000
discharge time in seconds
10000
100000
Watt seconds = Joules
7000
Energy of a charged capacitor
A capacitor works like a battery. It doesn’t store
very much charge, but it can be charged and
discharged very quickly. The energy of a charged
capacitor is E = ½ C V2
where C = capacitance, V = voltage
A 5F capacitor charged to 2.3V has a stored
energy of 21J and typically can deliver 3A for 4
seconds.
This is enough to accelerate a 500g car to 9m/sec
Summary
• Energy (Joules) comes in many different forms
• Energy is conserved
• Chemical energy sources are often more potent
than other forms. (except fission / fusion)
• Equations to work out how much energy
• Conversion of energy
– Slowly for better efficiency
• Choose appropriate energy source for its
application
Examples of Energy storage
Energy storage methods:
Electrochemical:
Batteries
Fuel cells
Electrical:
Capacitor
Superconducting magnetic energy storage (SMES)
Mechanical:
Compressed air energy storage (CAES)
Flywheel energy storage
Hydraulic accumulator
Hydroelectric energy storage
Spring
http://www.all-science-fair-projects.com/science_fair_projects_encyclopedia/Energy_storage