School Physics notes: Energy store conversions, work done, power calculations

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TYPES OF ENERGY and ENERGY STORES - examples explained

IGCSE AQA GCSE Physics Edexcel GCSE Physics OCR GCSE Gateway Science Physics OCR GCSE 21st Century Science Physics Doc Brown's school physics revision notes: GCSE physics, IGCSE physics, O level physics,  ~US grades 8, 9 and 10 school science courses or equivalent for ~14-16 year old students of physics

and examples of types of energy, work done, power & energy store calculations

(a) Introduction to energy

(b) Types of energy and types of energy stores and calculations

(d) Introduction to work done calculations, power and wasted energy

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(a) Introduction to energy

The concept of energy emerged in the 19th century - The idea was used to explain the work output of steam engines and then generalised to understand other heat engines.

We now know energy can exist in many forms and this became a key tool for understanding chemical reactions and biological systems.

The Law of conservation of energy states that energy cannot be created but only changes from one form to another. In other words you can't use up energy, you can only change it from one form to another.

You can consider this as transferring energy from one store to another.

You need to know what the different forms of energy stores, types of energy and examples of energy conversions and transfers between energy stores.

In which different types of energy can exist?

You should be able to give brief description of examples of the different  forms of energy and their interconversion.

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(b) Types of energy and types of energy stores and calculations

There are many types of energy and energy stores - an alphabetical reminder list and links to notes on each of the types.

You can't analyse an energy transfer situation if you don't know your types of energy and types of energy store!

The types of energy and energy stores you need to know about are listed below.

You need to read pages (a) to (i) before proceeding any further!

(a) Chemical potential energy stores  * (b) Elastic potential energy stores

(c) Electrical energy and electrostatic energy stores  *  (d) Gravitational potential energy stores

(e) Kinetic energy stores  *  (f) Nuclear energy stores  *  (g) Thermal energy stores

(h) Light energy  *  (i) Sound energy  *  (j) Magnetic energy stores

You also need to be able to:

distinguish between a type of energy associated with a type of energy resource,

(e.g. fossil fuels are source of chemical energy, rainwater is a resource - collected behind a dam forms GPE store and it provides kinetic energy when allowed to flow).

in general be able to describe transfer of energy from one type of energy store to another type,

know how to analyse and describe a series of energy store conversions to produce electricity,

and do all sorts of energy transfer calculations, and examples have been included in pages (a) to (i).

.. see also Conservation of energy, energy transfers-conversions gcse physics revision notes on energy

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(c) Examples of types of energy store conversions in systems

Energy can be transferred between energy stores in four principal ways

1. By heating - the transfer of thermal energy from a hotter material/object to a cooler material/object.

You can only have a net heat flower from a higher temperature to a lower temperature region.

2. By radiation of a wave - sound wave vibrations transfer energy and electromagnetic radiation.

There seven types of EM radiation including microwaves, infrared and visible light.

Infrared radiation is referred to as thermal radiation - its a means of net transfer of thermal energy from a higher to a lower temperature material.

3. Flow of electrically - energy is transferred by electrical charge (electrons) moving around an electrical circuit down a potential difference i.e. moving from a higher to a lower potential energy, releasing energy in the process e.g. in the form of heat or light.

See also Usefulness of electricity and energy transfer for lots of examples starting with electricity

4. Mechanically - anything  that is moved by a force acting on it involves a mechanical transfer of energy - anything rotating, pushed, squashed or pulled etc.

The law of conservation of energy

No matter the nature of an energy store or an energy store transfer, the following law applies ...

Energy can be (i )stored, (ii) changed from one form to another and (iii) dissipated, but the total energy of a closed system is constant and you cannot create or destroy energy

There is no net change in total energy, no matter what energy transfers take place.

Dissipated usually means wasted energy like heat spreading out to increase the thermal energy store of the surroundings.

In the 19th century scientist began to realise that mechanical work generated heat, and so concluded that there was a connection between them e.g. heat is generated by friction when a mechanical device does work.

Work done in joules = force in newtons x distance through which force acts,

which means the same amount of work transfers the same amount of energy, but not all usefully.

Electrical heating elements transfer energy from an electrical energy store to the thermal energy store of the material being heated e.g. oil in a heater, water in a kettle.

Moving objects have kinetic energy. If you want to slow a moving object down you must reduce its kinetic energy store e.g. car brakes by operating a force. In doing so work must be done and heat from friction is released to increase the thermal energy store of the surroundings.

Whenever you get an increase in temperature of a system, energy must be transferred from one energy store to another.

A system is the physical components involved with the energy transfer conversion. e.g. your hand and winding up a clock, a car engine, your muscles being used to lift a weight, a photocell, an electrical appliance, objects colliding.

A closed system is a collection of objects you treat on their own and energy can be transferred between different energy stores of the system, but not between energy stores outside of the system - in other words no energy leaves or enters the defined closed system.

e.g. a hot drink standing on the table - the system includes the surroundings too, because thermal energy is readily transferred to the surrounding air - its an 'open' system..

However, if the hot drink is in a well insulated thermos flask, then this can be considered a closed system.

When a system changes it involves an energy transfer. Energy might be transferred into or out of a system between the different components of a system or between different types of energy stores.

You can transfer energy mechanically when a force is applied to do work e.g. winding up a clock, dragging a heavy box across the floor.

You can transfer energy electrically when work is done by moving charge e.g. an electrical heater, electric motor.

When you raise the temperature of a material (e.g. from a flame, electrical supply, electromagnetic radiation) you increase the thermal energy store of that material.

When your vocal chords vibrate you are transferring kinetic energy into sound energy

Know and understand that energy can be transferred usefully from one form to another, or stored, or dissipated, but energy cannot be created or destroyed.

This is the law of conservation of energy.

Another way of expressing this law to say energy is never lost but transferred between different energy stores often involving different objects or materials.

However, energy is only useful if it can be converted from one form to another.

Be careful in using the term energy loss!

The phrase 'energy loss' is used in the context of energy transfer when not all the energy is transferred into a useful form e.g. some energy from a car fuel is 'lost' in the friction of moving parts, i.e. some chemical energy ends up as heat or sound rather than kinetic energy to move the car.

Examples - from a suitable energy source ==> useful form of energy (plus waste in most cases)

Energy is usually transferred by radiation, electricity flow, heating or doing work in a mechanical sense.

When a gun fires chemical energy is converted into heat energy, sound energy, light energy and mainly kinetic energy. When the bullet embeds itself into some material the kinetic energy of movement is converted into some sound energy, but mainly heat energy. Some of the energy is wasted but most of the chemical energy stored in cartridge is converted to the useful kinetic energy of the bullet. Photovoltaic solar panels convert light energy into electrical energy. If this electrical energy is used to charge up a battery then you increase chemical energy store of the battery. We use a large number of electrical devices in the home eg

TV converts electrical energy into useful light and sound, but some waste heat

A charged mobile phone battery converts chemical energy into electrical energy, which in turn is converted into useful light and sound energy.

In the charging process you are increasing the energy store of the mobile phone battery. Wind turbines convert kinetic energy into electrical energy

The kinetic energy store of the wind is decreased, whereas that of the turbine blades is increased, initially an energy transfer involving the same type of energy store.

The start of making a cup of tea is a system. You use an electrical heating element in the kettle base to boil water by transferring energy to water via the conversion of electrical energy to thermal energy. The water increases in temperature and therefore its thermal energy store is increased. The water and heating element constitute a system.

Whenever an electrical current flows in a circuit, work is done against the resistance of the wire. This is all to do with the behaviour of the electrons moving due to an electrical potential difference.

It doesn't seem the same as say, pushing a lever to operate the machine, but you are applying a force to move the lever against a mechanical resistance. In fact the work done or energy transferred is equal to the force applied x the distance through which the force operates (see calculations further down the page).

When the car of a 'big dipper' fun ride is raised to the top of a loop using an electric motor you are converting electrical energy mechanically into the car's kinetic energy store.

As the car increases in height its gravitational potential energy store (GPE) increases.

When the car rolls down the other side its GPE store decreases and its kinetic energy store increases.

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(d) Introduction to work done calculations, power and wasted energy

If an object begins to move or changes how it moves (change in speed or direction) then a force must be involved.

If a force acts on an object, then work is being done on the object increasing its energy store - this must involve an energy transfer.

If an object exerts a force or transfers energy in some way, work is done by this object and energy is transferred from its energy store.

If there is no friction and a force is applied to an object, the work done on the object will equal the energy transferred to the object's kinetic energy store.

However, if an object is already moving and experiences a resistive force of friction slowing it down, the energy transferred from its kinetic energy store is equal to the work done against the object's motion.

The energy can be transferred usefully i.e. doing useful work, but some energy might (often) be wasted - often dissipated to the surroundings as heat due to friction.

The energy transferred, usefully or wastefully, is often referred to, and equal to, work done.

When dealing with the action of a resultant force acting through a linear distance in the direction of the force, you can calculate the work done with a very simple formula. When ever you or a machine moves something work is done

Work done (J) = energy transferred = force (N) x distance (m)

W (J) = F (N) x d (m)

The distance equals the length of the line of action through which the force acts.

(work done  might be denoted by E or W for the energy of work done, but remember the unit for power is the watt, W, so take care!)

If you apply a force of one newton through a linear distance of one metre, you do one joule of work.

one joule of work done = a force of one newton x one metre distance, 1 J = 1 Nm

Imagine a force of 1 newton acting through a distance of 1 metre, 1 joule of work is done = 1 joule of energy transferred.

(note that newton metres (Nm) = joules (J)  = work done = energy transferred)

The distance must be along the line of action of the force.

You need an energy source to keep applying any force for any length of time.

Whenever work is done e.g. mechanically or electrically, energy is transferred from one energy store to another.

See Power is the rate at which energy is transferred or 'used up' - work done!

In other words power is the rate of doing work.

The unit of power is the watt, W.

power (W) = energy transferred (J) / time taken (s)

power (W) = work done (J) / time taken (s)

P (W) = E (J) / t (s)

{and don't forget: work done (J) = force (N) x distance (m), which you need to solve some power problems}

A power rating of one watt means one joule of energy is transferred per second,

or, 1 joule of work is done in 1 second.

The joule is the unit of energy and the watt is the unit of power (W).

one watt = one joule of energy is transferred per second, 1 W = 1 J/s

A 1 kW electric heater converts 1000 J of electrical energy  ==> heat energy every second

(1 kW = 1000 W  =  1000 J/s)

See

The power of a machine or any other device is the rate at which it transfers energy.

A powerful machine doesn't necessary mean a bigger force is generated, it just means a lot of energy is transferred in a short time (or a lot of work done in a short time).

The more work done/energy transferred in a given time, the greater the power.

The shorter the time taken to transfer energy/do work, the greater the power generated.

Conversely, by using gears and a low powered electric motor, you can generate a relatively big force. So, don't confuse power and force - use the terms appropriately.

See

However, no mechanical device or electrical appliance is 'perfect' and energy is lost e.g. by thermal energy by friction or sound from unwanted vibrations, heat loss from circuit wires etc., but it is still part of the total work done - it just isn't all useful!

Therefore you should know and understand that when energy is transferred only part of it may be usefully transferred as useful energy or useful work, the rest is ‘wasted’ to the surroundings

You should know and understand that wasted energy is eventually transferred to the surroundings, which will become warmer AND ...

... the wasted energy becomes increasingly spread out and so becomes less useful.

For more on wasted energy see:

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(e) More examples of energy stores, energy transfers and doing work

Doing work in a mechanical sense is just another set of examples of energy transfer e.g. from one energy store to another.

This usually involves doing useful work, but the final energy store destination might have no further use.

For example when you burn fuel in a car engine the energy changes are as follows.

fuel + oxygen (chemical energy store) ==> hot gases (thermal energy store) ==> car moves (kinetic energy store)

In the process some of the original chemical energy store of the system is lost through friction and sound.

BUT, all the energy from the chemical energy store ends up as thermal energy to warm up the surroundings. Therefore the thermal energy store of the environment is increased but its now of no use whatsoever!

The waste of energy increases (but necessarily!) when you apply the brakes. Mechanical work is being done in the process - work is being done against the force of friction. The friction effect of the brake pad on the brake disc converts kinetic energy into thermal energy. The kinetic energy store of the car decreases (fortunately!) and the thermal energy store of the brake pad + disc increases. Eventually as the braking system cools down the heat energy is transferred to increase the thermal energy store of the surroundings - wasted or degraded energy!

If a vehicles crashes into a stationary object, the contact force causes energy to be mechanically transferred from the vehicle's kinetic energy store to elastic potential energy store of the crushed vehicle parts, the thermal energy stores of the vehicle, object crashed into and the surrounding air (including some sound energy too - which also ends up as thermal energy!).

When you lift an object up you are doing work against the effects of gravity.

The chemical energy stored in your muscles is decreased as some of it used to lift the object-weight which on gaining height increases its gravitational potential energy store.

In fact the work you do (J) equals the weight of the object (N) x vertical distance lifted (m)

When you kick a ball up in the air, three energy stores should be fairly obvious to you.

chemical energy store of muscles ==> kinetic energy store of ball ==> gravitational potential energy store of ball

AND, when the ball falls (ignoring a bit of lost sound energy)

gravitational potential energy store of ball ==>`kinetic energy store of ball ==> thermal energy store of the ground

For more examples see

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(f) Examples of simple mechanical work done calculation questions

and Examples of simple power calculation questions How to solve 'work done' problems.

The formula for work done is quite simple:

work done in joules = force in newtons x distance in metres along the line through which the force acts

work done (J) = force (N) x distance through which force acts (m)

E  = F x d

In real situations of energy transfers involving mechanical work, I'm afraid friction effects accompany the useful work done.

Moving parts rubbing against each other causes friction and rise in temperature - kinetic energy store ==> thermal energy store of machine and surroundings.

Note that the force can be the weight of an object acting in a vertical direction ... see the page on ... How to solve power problems - just a few simple 'mechanical' examples here..

Power is the rate at which energy is transferred, that is the rate at which work is done.

power in watts = (work done = energy transferred) ÷ time taken

P (W) = E (J) / t (s)

Power P in Watts, Energy E in Joules, time t in seconds

The power rating of 1 watt is equal to a work rate of 1 joule of energy transferred per second

See also FORCES 3. Calculating resultant forces using vector diagrams and work done

Examples of problem solving using the 'work done' and 'work rate = power' formulae

In every case watch the units e.g. W/kW, J/kJ/MJ, min/secs etc. so take care!

Q1 If you drag a heavy box with a force of 200 N across a floor for 3 m,

(a) what work is done?

work done = 200 x 3 = 600 J

(b) If you do the job in 5 seconds, what was your power rating in doing this task?

power (W) = work done (J) / time taken (s)

your power = 600 / 5 = 120 W  (just over the power of 100 W light bulb!)

Q2 (a) If a machine part does 500 J of work moving linearly 2.5 m, what force was applied by the machine?

work done = force x distance, rearranging,  force (N) = work done (J) ÷ distance (m)

force = 500 ÷ 2.6 = 200 N

(b) If an electric motor transfers 12.0 kJ of useful energy in 3.0 minutes.

Calculate the power output of the motor.

work done = energy transferred = 12 x 1000 = 12,000 J, time taken = 3 x 60 = 180 s

power = work done / time = 12,000 / 180 = 66.7 W (3 sf)

(c) An appliance has a power rating of 1.2 kW.

How many kJ of energy is transferred in 8.0 minutes?

1.2 kW = 1200 watts, time = 8 x 60 = 480 seconds

P = E / t, rearranging gives E = P x t

energy transferred = 1200 x 480 = 576 000 J = 576 kJ

Q3 A machine applies a force of 200 N through a distance of 2.5 m in 2.0 seconds.

What is the power of the machine?

work done = force x distance = 200 x 2.5 = 500 ?

power = work done / time taken = 500 / 2.0 = 250 J/s = 250 W

Q4 A 500 kg express skyscraper lift moves non-stop up a total height of 100 m.

(a) If the force of gravity = 9.8 N/kg, calculate the weight of the lift.

weight = mass x g

= 500 x 9.8 = 4900 N

(b) Calculate the work done by the lift motor.

work = force x distance

the force exerted by the lift motor must be at least equal to the weight of the lift due to gravity

therefore work done = 4900 x 100 = 490000 J 490 kJ 0.490 MJ

(c) If the lift ascent time is 20 seconds, what is the power of the lift motor?

power = work done / time taken

power = 490000 / 20 = 24500 W 24.5 kW

(d) What assumptions has been made for calculations (b) and (c)?

Both (b) and (c) calculations ignore the extra work done in overcoming any forces of friction.

Q5 Part of a machine requires a continuous force of 500 N from a motor to move it in a linear direction.

(a) How much work is done in moving it a distance of 50 m?

work done = force x distance = 500 x 50 = 25000 J (25 kJ)

(b)  If the power of the machine is 5.0 kW, how long will it take to move the machine part the 50 m distance?

power = work done / time taken

time taken = work done / power

time = 25000 / 5000 = 5.0 s (stand clear!)

Q6 A machine has to move a conveyor belt at a rate of 30 m/min.

The system is designed to use 6 kJ/min of electrical energy to move the conveyor belt along.

What is the minimum force the motor must produce to move the conveyor belt along?

(i) power = rate of energy transfer = energy transferred (J) / time taken (s)

power = 6000 / 60 = 100 W (100 J/s)

(ii) 30 m/min ≡ 30 / 60 = 0.5 m/s

so in one second, the energy transferred is 100 J and the distance moved is 0.5 m.

work = force x distance

force = work / distance = 100 / 0.5 = 200 N

(iii) If you are smart, you can solve the problem directly, because both bits of data involved 'per minute'.

So you can just say force = work / distance = 6000 / 30 = 200 N !!!

BUT, always work logically in your own comfort zone, the data might not always be so kind!

Q7 A toy model car has a clockwork motor, whose spring can store 8.75 J of elastic potential energy.

On release the clockwork motor can deliver a continuous force of 2.5 N.

How far will the car travel in one go?

energy store = total work done = force x distance

distance = energy store / force = 8.75 / 2.5 = 3.5 m

Q8 A sliding object moving across a very rough surface has 5.0 J in its kinetic energy store.

If the object experiences a constant resistive force of friction of 25 N, calculate in cm how far the object travels before coming to a halt.

energy transferred = kinetic energy = resistive force x distance to come to a halt

E = KE = F x d,  5.0 = 25 x d, d = 5.0/25 = 0.20 m = 20 cm

Q9 A small electric motor uses 120 J of electrical energy in 3.0 minutes.

Calculate the power of the electric motor.

Energy transferred = 120 J, time = 3 x 60 = 180 s

P = E / t  =  120/180  = 0.67 W (2 sf)

Q10 A 45.5 kg mass is hoisted up vertically 15.5 m.

If the gravitational field force is 9.8 N/kg, calculate the work done to the nearest joule.

weight = force = mass x gravity = 45.5 x 9.8 = 445.9 N

This force acts through the vertical height the object is lifted.

work done = force x vertical distance = 445.9 x 15.5 = 6911.45

work done = 6911 J

Q11 A small electric motor operating a water pump for a garden ornament does 6.5 kJ of work in 3.0 minutes.

Calculate the power of the pump.

Work done = 6.5 x 1000 = 6500 J

Time taken = 3 x 60 = 180 s

Power = work done / time taken = 6500 / 180 = 36.11 = 36 W (2 sf).

Q12 An electrical appliance transfers 8000 J of energy in 1 minute and 40 seconds.

Calculate the power of the appliance.

power = energy transferred / time = 8000 / 100 = 80 W

Q13 A person weighing 600 N strides up 20 steps, each one 20 cm high, in 10 seconds.

(a) Calculate the work done.

Each step is 20 cm = 0.20 m, total height = 20 x 0.20 = 4.0 m

Work done (J) = force (N) x distance (m)

Work done = 600 x 4.0 = 2400 J

(b) calculate the average power the person generates in the process of ascending the 20 steps.

power (W) = work done (J) / time taken (s)

power = 2400 / 10 = 240 W

(c) If the person stands still on the 20th step, what is the person's power?

Since no force is acting through a distance, in a mechanical sense, the power is zero, but ....

YES. Your body must be still releasing energy through respiration to maintain the tension in your muscles to keep you upright, otherwise you would flop down in a heap!

Q14  (you might not have dealt with all aspects of Q14 yet)

Imagine a car of 1000 kg travelling at 20 m/s doing an emergency stop in a distance of 25 m - the braking distance.

Calculate the average braking force produced by the driver when pressing on the brake pedal.

To solve this question you to use several formulae.

(a) Calculate the kinetic energy of the car.

KE = 0.5 mv2 = 0.5 x 1000 x 202 = 200 000 J

(b) What work must be done to bring the car to a halt? Explain your answer.

If the kinetic energy of the car is 200 000 J, then 200 000 J of work must be done to bring the KE of the car to zero i.e zero velocity.

(c) Calculate the average braking force required.

Work (J) = force (N) x distance (m)

work = 200 000 J and the braking distance was 25 m

force = work / distance = 200 000 / 25 = 8000 N average braking force.

Q15 A large car is travelling at 120 km/hour and the engine provides a constant driving force of 1500 N.

(a) How far does the car travel in 1 second?

1 km = 1000 m, 1 hour = 60 x 60 = 3600 s

speed (m/s) = distance (m) / time (s)

speed of vehicle = 120 x 1000 / 3600 = 33.33 m/s

so, in one second the vehicle moves 33.3 m (3 sf)

(b) From your answer to (b) calculate the power of the engine.

You have to do a little 'think' connecting two equations.

work = force x distance and power = energy transferred / time

i.e. energy transferred = work done = force x distance

power (W) = work done / time = force (N) x distance (m) / time (s)

power = 1500 x 33.33 / 1 = 50 000 W or 50 kW (3 sf)

In other words the distance / time in the equation is quite simply the speed of 33.3 m/s, get it OK?

See also electrical energy used, power and cost of electricity calculations gcse physics revision notes

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Energy resources, and transfers, work done and electrical power supply revision notes index

Types of energy & stores - examples compared/explained, calculations of mechanical work done and power

Chemical  * Elastic potential energy  * Gravitational potential energy

Kinetic energy store  *  Nuclear energy store  *  Thermal energy stores  * Light energy  * Sound energy

Renewable energy (1) Wind power and solar power, advantages and disadvantages gcse physics revision notes

See also Renewable energy - biofuels & alternative fuels, hydrogen, biogas, biodiesel gcse chemistry notes

Greenhouse effect, global warming, climate change, carbon footprint from fossil fuel burning gcse chemistry

The Usefulness of Electricity gcse physics electricity revision notes

and The 'National Grid' power supply, mention of small scale supplies, transformers gcse physics notes aqa gcse 9-1 physics: Know that a system is an object or group of objects. There are changes in the way energy is stored when a system changes. For example: an object projected upwards, a moving object hitting an obstacle, an object accelerated by a constant force, a vehicle slowing down, bringing water to a boil in an electric kettle., Throughout this section on Energy you should be able to : describe all the changes involved in the way energy is stored when a system changes and calculate the changes in energy involved when a system is changed by: heating  IGCSE revision notes types of energy KS4 physics Science notes on types of energy GCSE physics guide notes on types of energy for schools colleges academies science course tutors images pictures diagrams for types of energy science revision notes on types of energy for revising physics modules physics topics notes to help on understanding of types of energy university courses in physics careers in science physics jobs in the engineering industry technical laboratory assistant apprenticeships engineer internships in physics USA US grade 8 grade 9 grade10 AQA GCSE 9-1 physics science revision notes on types of energy GCSE notes on types of energy Edexcel GCSE 9-1 physics science revision notes on types of energy for OCR GCSE 9-1 21st century physics science notes on types of energy OCR GCSE 9-1 Gateway  physics science revision notes on types of energy WJEC gcse science CCEA/CEA gcse science               Website content © Dr Phil Brown 2000+. All copyrights reserved on revision notes, images, quizzes, worksheets etc. Copying of website material is NOT permitted. Exam revision summaries & references to science course specifications are unofficial.

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