EnergyBA 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 inertiaI = kMr2 = 1 * .2 * 10 * 10 = 20 kg m2 (k = 1 for bicycle wheel)

3. Now calculate stored energyω = 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 bodyThe 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

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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 energyThe 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 releasedIf 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 springIf 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

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Energy of a charged capacitorA 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