TYPES OF ENERGY - examples explained

and work done, power and energy store calculations

Doc Brown's Physics Revision Notes

Suitable for GCSE/IGCSE Physics/Science courses or their equivalent

 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 or type of energy there are.

 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.

  • There are many types of energy and energy stores - an alphabetical reminder list

    • Chemical energy and chemical energy stores

      • Chemical energy is 'stored' or 'bound up' in chemical elements/compounds by virtue of their chemical structure. They can release energy when they react eg burning hydrocarbon fuels like petrol from crude oil, metabolising foods like fats and carbohydrates, discharging a charged car battery containing sulfuric acid solution and lead electrodes.

      • Since chemical energy is a form of stored energy e.g. a battery or tank of fuel, it does nothing until it is released and converted into another form of energy.

      • INDEX of energy changes-transfers in chemical reactions notes

    • Elastic potential energy and elastic potential energy stores

      • This is energy stored when some material is stretched or compressed and the energy released when the constriction is released eg the wound up spring of a clockwork clock, a pulled elastic rubber band, stretched coiled metal spring, the compressed spring in a an animal trap, stretched bow  before the arrow is released.

      • Since elastic potential energy is a form of stored energy, it does nothing until it is released and converted into another form of energy.

      • The amount of elastic potential energy stored in a stretched spring can be calculated using the equation:

        • elastic potential energy = 0.5 × spring constant × (extension)2,    Ee = 1/2 k e2

        • (assuming the limit of proportionality has not been exceeded)

        • elastic potential energy, Ee, in joules, J

        • spring constant, k, in newtons per metre, N/m

        • extension or compression, e, in metres, m

  • Electrical energy and electrostatic energy stores

  • Gravitational potential energy (GPE) and gravitational potential energy stores

    • Here an object or material possesses a gravitational potential energy store by virtue of its higher position and can then fall or flow down to release the GPE e.g. winding up the weights on a clock, water stored behind a dam that can flow down through a turbine generator.

    • Any object falling is converting its GPE store into kinetic energy (eg skier) and any object raised in height gains GPE (eg cable car). You doing work against the weight of an object or material due to the attraction of the gravitational field of the Earth.

    • Since gravitational energy is a form of stored energy, it does nothing until it is released and converted into another form of energy.

    • The greater the weight of an object or material or the greater the height it is raised, the greater is the gravitational potential energy store created.

    • GPE is also greater, the greater the strength of the gravitational field. Raising the same object to the same height on Mars or the Moon will not increase the GPE of the object as much as on Earth because the strength of gravity is less on these smaller bodies of smaller mass than Earth.

    • The amount of gravitational potential energy gained by an object raised above ground level can be calculated using the equation:

      • gravitational potential energy (GPE).= mass × gravitational field strength × height

        • Egpe = m g h

      • gravitational potential energy (gpe), Egpe, in joules, J

      • mass, m, in kilograms, kg;

      • gravitational field strength, g, in newtons per kilogram, N/kg

      • height, h, in metres, m

      • In any calculation the value of the gravitational field strength (g) will be given, on the Earth's surface it is 9.8 N/kg.

      • When an object or material falls its gravitational potential energy store is decreased as the GPE is converted into kinetic energy.

      • When an object in air or flowing water is falling you always get some heat loss from friction forces, thereby increasing the thermal energy store of the surroundings.

      • If you ignore the frictional heat losses due to air resistance the sum of GPE + KE is a constant.

      • So, when a stationary object is then dropped from a height, at the point of impact on the ground, the maximum amount of kinetic energy equals the original amount of gravitational potential energy (based on the height from which the object is dropped). This is quite handy to know in solving certain kinds of problems.

  • Kinetic energy or movement energy (KE) and kinetic energy stores

    • Any moving object has kinetic energy and KE energy must be removed from the object to slow it down e.g. braking a moving car, fired bullet embedding in material on impact.

    • The greater the mass or the greater the speed of an object, the greater its kinetic energy store.

    • The kinetic energy of a moving object can be calculated using the equation:

      • kinetic energy (KE) = 0.5 × mass × (speed)2

      • Eke = 1/2 m v2

      • kinetic energy, Eke, in joules, J; mass, m, in kilograms, kg; speed, v, in metres per second, m/s

  • Light energy (parts of the electromagnetic spectrum, like visible light, microwaves and infrared etc.)

    • Light is an example of electromagnetic radiation and the energy is carried by photons. All luminous sources by definition give out light eg the sun, light bulb, candle, fire etc. When light impacts on any material, the energy is absorbed eg sunlight shining on plant leaves in photosynthesis, light falling on the retina of our eyes.

      • Note that invisible infrared radiation is converted directly into heat when absorbed by a surface eg warmth feeling in sunlight, standing by a fire, a toaster. All objects radiate infra-red radiation. The hotter the object the greater the intensity of infrared emitted - the greater the energy store transfer.

    • See Electromagnetic radiation, types, properties and uses

  • Nuclear energy and nuclear energy stores

    • This is energy associated with the structure of atomic nuclei. This is the energy released when atoms undergo a nuclear reaction eg radioactive decay and fission reactions when larger atoms split to form smaller atoms and fusion is when smaller atoms come together to form a larger atom, but this also releases huge amounts of nuclear energy e.g. hydrogen ==> helium in a star like our Sun.

    • All these processes release huge amounts of nuclear energy and the energy from fission can be harnessed to power steam turbine generators to drive generators producing electricity. It is hoped one day that nuclear fusion will provide the energy, but not practical at the moment!

    • See Nuclear Physics Notes

  • Sound energy

  • Thermal energy (heat energy) and thermal energy stores

Examples of energy store conversions in systems

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.

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, 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 heat. 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).


Wasted energy

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.


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 heat 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. Work is being done in the process. The friction effect of the brake pad on the brake disc converts kinetic energy into heat. 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!


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


Examples of simple mechanical work done 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 in the line through which the force acts

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


Q1.1 If you drag a heavy box with a force of 200 N across a floor for 3 m, what work is done?

work done = 200 x 3 = 600 J


Q1.2 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




Examples of simple power calculation questions

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)

1 watt is equal to a work rate of 1 joule per second


Q2.1 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




See also electrical energy used, power and cost of electricity calculations

Examples of stored energy calculation questions

How to solve potential energy problems.

How to solve kinetic energy store problems.


Q3.1 A bullet with a mass of 10.0 g is travelling with an initial speed of 400 m/s.

(a) What is the bullet's Intial kinetic energy store?

Eke = 1/2 m v2 , 10 g 10/1000 = 0.01 kg

Eke = 0.5 x 0.01 x 4002

Eke = 800 J of kinetic energy

(b) If the bullet embeds itself in a wooden plank, by how much will the planks thermal energy store be increased?

All of the 800 J of kinetic energy will end up as heat. There will be some loss due to friction (air resistance) and sound energy, but most of the 800 J will end up as heat energy in the plank.


Q3.2 A car of mass 1200 kg is travelling at a steady speed of 30.0 m/s.

(a) What is the kinetic energy store of the car?

Eke = 1/2 m v2 , 10 g 10/1000 = 0.01 kg

Eke = 0.5 x 1200 x 302

Eke = 540,000 J of kinetic energy (5.4 x 105J, 0.54 MJ)

(b) If on slowing down the kinetic energy of the car is halved, what speed is it then doing?

Eke = 1/2 m v2 , rearranging:   v2 = 2Eke / m,  so v = √(2Eke / m),  KE = 540,000/2 = 270,000 J

v = √(2 x Eke / m) = √(2 x 270,000 / 1200) = 21.2 m/s (3 s.f.)


Q3.3 The chemical potential energy store of a 100 g rocket, on firing, gives it an initial kinetic energy store of 200 J.

Calculate the initial vertical velocity of the rocket.

Eke = 1/2 m v2 , rearranging:   v2 = 2Eke / m,  so v = √(2Eke / m)

m = 100 g ≡ 100 / 1000 = 0.1 kg

v = √(2 x Eke / m) = √(2 x 200 / 0.10) = 63.2 m/s (3 s.f.)


Q3.4 A projectile is required to impart a kinetic energy blow of 5000 J at a speed of 500 m/s.

What mass of projectile is required?

Eke = 1/2 m v2 , rearranging:   m = 2 x Eke / v2

m = 2 x Eke / v2 = 2 x 5000 / 5002 = 0.040 kg (40 g)


How to solve gravitational potential energy store problems

Q4.1 An 80.0 kg person climbs up flights of steps to a vertical gained height of 9.00 m.

(a) Calculate the increase in the person's gravitational energy store (gravity force = 9.8 N/kg).

Egpe = m g h

GPE store gain = 80 x 9.8 x 9.0 = 7056 J (7.06 kJ)

(b) What is the work done by the person in climbing the stairs?

work = force x distance, force = weight = 90 x 9.8 = 784 J

work = 784 x 9.0 = 7056 J

Note: This is the same answer as (a) because the GPE formula is essentially expressing a force acting through a specified distance.

(c) How high would you have to climb to work off a 45.0 g bar of chocolate with a calorific value of 30.0 kJ/g?

Total energy in the chocolate bar chemical energy store = 45 x 30 x 1000 = 1350000 J

This will be converted to the person's gravitational potential energy store, therefore ..

GPE = m g h = 1350000 J

so h = 1350000 / (m x g) = 1350000 / 784 = 1720 m (to 3 s.f. and higher than Ben Nevis in Scotland)

Note: A typical active adult needs 9000 kJ/day. An elderly person with a sedentary lifestyle might only need 5000 kJ/day. A very active teenager might need 12000 kJ/day. The calculation does make the point that a single bar of chocolate does provide a good 'chunk' of you daily energy needs. Of course if you snack a lot on high calorie foods you will put on weight if it isn't 'burnt off'! The calorific value of fat is ~37 kJ/g and carbohydrates typically ~17 kJ/g.


Q4.2 If a 5.00 kg 'weight' is dropped from a height of 10.0 m above the ground, at what speed will it hit the ground?

The GPE of the 'weight' is easily calculated from the formula GPE = m g h     (and g = 9.80 N/kg)

GPE = 5 x 9.8 x 10 = 490 J

As the weight falls its gravitational potential energy store is depleted as its kinetic energy store increases.

Therefore, at the point of impact, all the GPE is converted to kinetic energy, so we use the KE equation to get v.

Eke = 1/2 m v2 , rearranging:   v2 = 2Eke / m,  so v = √(2Eke / m)

v = √(2Eke / m) = √(2 x 490 / 5.0) = 14.0 m/s

Note (i): You can actually simplify the calculation because you don't actually need to know the mass of the weight.

initial Egpe = final Eke = m g h = 1/2 m v2 , the m's cancel out,

so  g x h = 1/2 x v2  and  v = √(2 x g x h) = √(2 x 9.8 x 10) = 14.0 m/s (3 s.f.)

Note (i): All these calculations ignore air resistance, so some KE is lost as heat, so the final speed is actually just a bit less than the theoretical calculations above.




See also FORCES 2. Mass and the effect of gravity force on it - weight, (mention of work done and GPE


How to solve elastic potential energy store problems

Q5.1 A spring with spring constant of 5.00 N/m is stretched for 10.0 cm.

How much energy is stored in the elastic potential energy store of the spring.

Eepe = 1/2 k e2,  10.0 cm ≡ 10.0 / 100 = 0.10 m

Eepe = 0.5 x 5.0 x 0.102

Eepe = 0.025 J


Q5.2 A car suspension spring has a spring constant of 2000 N/m.

If the elastic potential energy store of the spring is 50 J, how far is the spring compressed?

Eepe = 1/2 k e2,  rearranging gives e2 = 2Eepe / k,  e = √(2Eepe / k)  and  e = the compression

e = √(2Eepe / k) = √(2 x 50 / 2000) = √0.063 = 0.224 m  (22.4 cm, 3 s.f.)


Q5.3 It takes 5.0 J of work to stretch a spring 20 cm.

How much extra work must be done to stretch it another 20 cm?

(i) You need to work out the spring constant.  20 cm ≡ 20 / 100 = 0.20 m

Eepe = 1/2 k e2,  rearranging gives k = 2Eepe / e2

k = (2 x 5.0) / (0.20 x 0.20) = 250 N/m

(ii) Then work out the total work to stretch the spring a total of 40 cm.

The total work done on the spring equals its elastic potential energy store when fully stretched 40 cm (which is 0.40 m). Since you now know the spring constant, you use the same equation again, but solving for the total elastic potential energy.

Eepe = 1/2 k e2 = 0.5 x 250 x 0.402 = 20 J

(iii) You then subtract (i) from (ii) to get the extra work done.

Therefore the extra work done = 20 - 5 = 15 J




See also Elasticity and energy stored in a spring calculations


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

Types of energy, comparison with examples explained, energy stores, mechanical work done & power calculations

Energy resources and their uses - a general survey more details in gcse physics revision notes below

Renewable energy (1) Wind power and solar power, advantages and disadvantages

Renewable energy (2) Hydroelectric power and geothermal power, advantages and disadvantages

Renewable energy (3) Wave power and tidal power, advantages and disadvantages

Biofuels, renewables and non-renewables, advantages and disadvantages

Generating electricity and the 'National Grid' power supply, mention of small scale supplies

Energy transfer and efficiency - calculations and Sankey diagrams

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

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