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Cambridge IGCSE0625

Energy, work and power

Physics 0625 Chapter Notes

What this chapter covers

Energy, work and power - EnergyEnergy, work and power - WorkEnergy, work and power - Energy resourcesEnergy, work and power - Power
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In this chapter

  1. 1Energy stores
  2. 2Transferring energy between stores
  3. 3Conservation of energy
  4. 4Kinetic energy
  5. 5Gravitational potential energy
  6. 6Multi-stage transfers and wasted energy
  7. 7Work done is energy transferred
  8. 8The equation for work
  9. 9Which force, which distance
  10. 10Fossil fuels and biofuels
  11. 11Water, geothermal and nuclear
  12. 12Light and waves from the Sun
  13. 13Advantages and disadvantages
  14. 14Efficiency of energy transfer
  15. 15The Sun as the source
  16. 16Calculating efficiency
  17. 17Defining power
  18. 18Calculating power and its unit
  19. 19Using the equation: energy, power and time

1. Energy stores

Energy may be stored as kinetic, gravitational potential, chemical, elastic (strain), nuclear, electrostatic and internal (thermal).

Use the full name of the store. Write ‘gravitational potential’, not just ‘potential’.

A battery is a chemical store. There is no electrical store.

Examiner insight

“Candidates needed to know that energy is transferred between stores when electrical work is done but that there is no electrical store of energy.” “However, a reference to potential energy, without mention of ‘gravitational’ was insufficient for credit.”

Worked example 11 mark

A bicycle tyre contains air. The temperature of the air in the tyre increases. In which store does the energy stored increase?

A chemical store · B electrostatic store · C internal store · D nuclear store

  1. 1

    C: the internal store. [1]

2. Transferring energy between stores

Energy is transferred between stores. It can be transferred by forces (mechanical work done), by electrical currents (electrical work done), by heating, and by electromagnetic, sound and other waves.

When a candle burns, the chemical store of the candle decreases. Energy is transferred by light, and the thermal store of the surroundings increases.

For every transfer, name the store that decreases and the store that increases.

Examiner insight

“Only stronger candidates recognised that the chemical energy store in the candle decreased and was transferred by light and that the thermal energy store of the surroundings was increased.”

Worked example 11 mark

An electric car is travelling at constant velocity along a straight horizontal road. Which row shows the energy changes that are taking place?

energy store decreasingtransfer processenergy store increasing
Achemicalelectricalthermal
Bchemicalelectricalkinetic
Celectricalmechanicalkinetic
Delectricalmechanicalthermal
  1. 1

    The velocity is constant, so the kinetic store does not increase.

  2. 2

    A: chemical decreasing, electrical transfer, thermal increasing. [1]

3. Conservation of energy

The principle of the conservation of energy: energy cannot be created or destroyed. It is only transferred from one store to another.

A flow diagram shows the transfers as arrows. Follow each arrow and name the energy at its end. When energy is transferred to the surroundings, it is the thermal store of the surroundings that increases.

Examiner insight

“Weaker answers omitted a reference to both energy created and destroyed or made no mention of energy being transferred.” “Many candidates thought the energy transfer was from kinetic to gravitational (potential) and did not see that this was not possible as there was no change in height of the car.”

Worked example 12 marks

Figure 3.2 shows the energy transfer diagram for a solar panel charging a mobile phone. Complete the energy transfer diagram.

  1. 1

    chemical energy stored in battery [1]

  2. 2

    thermal / internal energy transferred to surroundings [1]

4. Kinetic energy

The kinetic energy of a moving object depends on its mass and its speed.

The speed is squared. Doubling the speed makes the kinetic energy four times bigger.

E_k = 1/2mv²

Examiner insight

“The most common errors were not squaring the numerical value of the velocity when substituted in the equation and not converting the mass in g into kg.” “Some candidates calculated a value for momentum instead of kinetic energy.”

Worked example 12 marks

A small aircraft travels at a constant speed of 60 m / s. The mass of the small aircraft is 820 kg. Calculate the energy E_k in the kinetic store of the aircraft.

  1. 1

    E_k = 1/2 × 820 × 60² [1]

  2. 2

    = 1.5 × 10⁶ J [1]

5. Gravitational potential energy

A change in gravitational potential energy depends on the mass, the acceleration of free fall g and the change in height.

Use g = 9.8 m/s². An energy given in kJ must be converted to J first.

As an object falls, its gravitational potential store decreases and its kinetic store increases. As an object rises, its gravitational potential store increases.

Δ E_p = mgΔ h

Examiner insight

“Although most candidates correctly calculated the change in gravitational potential energy (GPE) to be 350 J, many had the misconception that the GPE of the rock increases as it falls rather than decreases.” “Some weaker candidates omitted g (acceleration of free fall) from their equation while others gave an incorrect unit or omitted the unit from their answer.”

Worked example 13 marks

At height h, the balloon has gained 120 kJ of energy in the gravitational potential store. The mass of the balloon is 2.5 kg. Calculate the height h.

  1. 1

    Δ E_p = mgΔ h, so h = (Δ E_p)/mg [1]

  2. 2

    convert: 120 kJ = 120 000 J [1]

  3. 3

    h = (120 000)/(9.8 × 2.5) = 4900 m [1]

6. Multi-stage transfers and wasted energy

In a complex example, energy passes through several stores. Follow each transfer in turn.

When a ball is dropped, the gravitational potential store decreases and the kinetic store increases. When it hits the ground, energy is transferred to the internal (thermal) store and by sound.

If no energy is wasted, the gravitational potential energy lost equals the kinetic energy gained. A Sankey diagram shows transfers like these as arrows, as the flow diagram in section 3 does.

wasted energy = total energy in - useful energy out

Examiner insight

“Stronger answers accurately referred to precise energy transfers between stores.” “Most identified a form of waste energy but few gave an explanation of where this wastage occurred.”

Worked example 12 marks

A student uses an electric motor to turn a wheel. Explain one way in which energy is wasted as the electric motor turns the wheel.

  1. 1

    some input energy is transferred as thermal / internal energy [1]

  2. 2

    to the surroundings / air / the motor / the drive belt [1]

Recap

  • Stores: kinetic, gravitational potential, chemical, elastic (strain), nuclear, electrostatic, internal (thermal). There is no electrical store.
  • Energy is transferred by forces, electrical currents, heating and waves.
  • Energy cannot be created or destroyed. It is only transferred between stores.
  • Extended: E_k = 1/2mv², with the mass in kg and the speed squared.
  • Extended: Δ E_p = mgΔ h, with g = 9.8 m/s².
  • Extended: wasted energy = total energy in − useful energy out.

7. Work done is energy transferred

Mechanical work done is a way of transferring energy. When a force moves an object, energy moves from one store to another.

Mechanical or electrical work done is equal to the energy transferred.

work done = energy transferred

Examiner insight

“Few correct answers were seen, and many candidates did not seem to fully understand that work done = energy transferred.” “Candidates needed to understand that mechanical work done is equal to the energy transferred.”

Worked example 11 mark

Which process involves the transfer of energy by mechanical working?

A radiating thermal energy from a stationary object · B measuring the room temperature with a digital thermometer · C passing an electric current through a LED · D pushing a box along the floor

  1. 1

    D: pushing a box along the floor. [1]

8. The equation for work

Work done is force × distance moved in the direction of the force. It is measured in joules, J.

The work done is the energy transferred, so the same quantity can be written as a change in energy.

W = Fd = Δ E

Examiner insight

“A common approach seen was dividing the pulling force by the distance the trolley moved.”

Worked example 13 marks

The student pulls the trolley with a force of 24 N for a distance of 15 m in the direction of the force. Calculate the work done by the 24 N force.

  1. 1

    work done = force × distance (moved in direction of force) [1]

  2. 2

    = 24 × 15 [1]

  3. 3

    = 360 J [1]

9. Which force, which distance

The distance is measured in the direction of the force. When an object is lifted, the force is its weight and the distance is the vertical height.

Substitute the weight in newtons, not the mass in kilograms. Give the unit.

Examiner insight

“The majority of candidates did not use the correct equation to calculate work done as they used the mass of the 20 tiles instead of the weight of the 20 tiles.” “Some candidates who did realise that an equation or defining expression was required, did not refer to the distance moved being in the direction of the force and just gave force × distance as the answer.”

Worked example 14 marks

The weight of the block of ice is 650 N. The machine lifts the block of ice a vertical height of 1.2 m. Calculate the work done on the block of ice. Include the unit.

  1. 1

    work done = force × distance [1]

  2. 2

    = 650 × 1.2 [1]

  3. 3

    = 780 [1]

  4. 4

    unit: J (joule) [1]

Recap

  • Mechanical or electrical work done is equal to the energy transferred.
  • W = Fd = ΔE.
  • Work done = force × distance moved in the direction of the force.
  • Lifting: use the weight in newtons and the vertical height.
  • Work is measured in joules, J.

10. Fossil fuels and biofuels

Fossil fuels and biofuels store chemical energy. Burning the fuel gives thermal energy.

The thermal energy heats water in a boiler to make steam. The steam drives a turbine. The turbine drives a generator, and the generator produces the electrical power.

Examiner insight

“Weaker candidates often missed out one or two stages or compressed separate stages into one process.” “Common errors included failing to state that the biofuels are burnt to give the thermal energy used to boil water.”

Worked example 14 marks

Describe how a power station generates electrical power by burning fossil fuels.

  1. 1

    burning the fuel produces thermal energy [1]

  2. 2

    water is boiled to produce steam [1]

  3. 3

    steam drives the turbine [1]

  4. 4

    turbine drives the generator [1]

11. Water, geothermal and nuclear

Water held behind a hydroelectric dam has gravitational potential energy. Only a turbine and a generator are needed: the moving water turns the turbine and the turbine turns the generator. The water is not heated. Waves and tides also use moving water to turn a turbine.

Geothermal energy arises from the decay of radioactive elements in the Earth's core.

In a nuclear power station, a neutron is absorbed by a heavy nucleus. The nucleus splits and releases a large amount of energy. The energy heats water to make steam, and the steam drives a turbine connected to a generator.

Examiner insight

“Some candidates believed that hydroelectric power involves the heating of water to produce high pressure steam.” “It was important that the reference was to nuclei splitting and not atoms, isotopes or elements splitting.”

Worked example 13 marks

Nuclear fission is the process used to transfer energy in a nuclear reactor in a power station. Describe the process which occurs when heavy nuclei undergo fission in a power station.

  1. 1

    a neutron is absorbed by a (heavy) nucleus [1]

  2. 2

    the (heavy) nucleus splits into smaller daughter nuclei [1]

  3. 3

    large amounts of energy are released [1]

12. Light and waves from the Sun

Solar cells use light from the Sun to generate electrical power. Solar panels use infrared and other electromagnetic waves from the Sun to heat water.

The Sun is also the source of wind energy. The wind turns the turbine and the turbine turns the generator. No water is heated, so there is no boiler.

Examiner insight

“Candidates did not seem to recognise that the Sun is the source of wind energy.” “Weaker candidates believed that the generation of electricity always involves the heating of water to form steam which drives a turbine and consequently a generator.”

13. Advantages and disadvantages

A non-renewable resource has a limited supply and will run out. Fossil fuels and nuclear fuel are non-renewable. Biofuels are renewable because crops can be regrown. Wind and geothermal resources are also regarded as renewable. Tides are renewable because they are caused by the Moon, which is always present.

Solar cells only work when there is sunlight. Wind gives no electricity when there is no or little wind, and wind farms need a large area of land. Hydroelectric power is dependent on rainfall. Tides are very reliable and predictable. Nuclear power is available 24 hours per day and is not dependent on the Sun shining.

Burning fossil fuels emits carbon dioxide and causes atmospheric pollution. Biofuels make a much smaller contribution to global warming, but growing them means a loss of agricultural land for food production. Solar cells produce no greenhouse gases, and hydroelectric power does not contribute to global warming or produce acid rain. Nuclear waste is hazardous, difficult to store and must be stored for a long time. A leak of radiation is a danger.

Examiner insight

“Common answers which were not accepted included “cheap” or “pollution” without further explanation.” “Most candidates believed that wind is reliably available as well as being renewable.”

Worked example 12 marks

A solar panel is charging a mobile phone (cell phone). State one advantage and one disadvantage, apart from cost, of using the solar panel to charge the mobile (cell) phone instead of using a mains power supply to recharge the battery.

  1. 1

    advantage, any one: renewable energy source, can be used anywhere there is sunlight, does not produce greenhouse gases, or no atmospheric pollution [1]

  2. 2

    disadvantage, any one: energy output is small, or only works when there is sunlight [1]

14. Efficiency of energy transfer

In an energy transfer, some of the input energy becomes useful output energy and some is wasted. A transfer that is not 100% efficient wastes some of its input energy. A low efficiency means that only a small fraction of the input energy becomes useful output energy.

In an electric motor or a transformer, the wasted energy is transferred as thermal energy to the surroundings.

Examiner insight

“Most identified a form of waste energy but few gave an explanation of where this wastage occurred.” “Weaker candidates clearly knew what efficiency meant but missed out the need for the fact that much energy is wasted.”

Worked example 12 marks

A student uses an electric motor to turn a wheel. Explain one way in which energy is wasted as the electric motor turns the wheel.

  1. 1

    some of the input energy is transferred as thermal (internal) energy [1]

  2. 2

    to the surroundings, air, motor or drive belt [1]

15. The Sun as the source

Radiation from the Sun is the main source of energy for all our energy resources except geothermal, nuclear and tidal.

Energy is released by nuclear fusion in the Sun. Research is being carried out to investigate how fusion can produce electrical energy on a large scale.

Examiner insight

“Many stronger candidates chose the correct option but overall the responses from candidates were distributed across the four options, with weaker candidates incorrectly believing that the Sun is the main source of energy for a geothermal energy resource.” “However, many weaker candidates had the misconception that the Sun is not the main source of energy for oil.”

Worked example 11 mark

Which pair of energy resources is derived from the process of nuclear fusion in the Sun?

A fossil fuels and tidal · B geothermal and nuclear fuel · C nuclear fuel and tidal · D fossil fuels and waves

  1. 1

    D: fossil fuels and waves. [1]

16. Calculating efficiency

Put the useful output on top and the total input underneath. Use energies together or powers together. Multiply by 100% for a percentage.

efficiency = (useful energy output)/(total energy input) × 100%

efficiency = (useful power output)/(total power input) × 100%

Examiner insight

“Weaker candidates, who could have gained partial credit by correctly quoting the efficiency equation, often did not do so because they merely quoted output/input and did not mention energy or power.” “Others wrote down a formula for efficiency with input and output interchanged from their correct positions.”

Worked example 11 mark

A motor is used to lift different sized loads through the same vertical height. The power input to the motor is kept constant. The graph of time taken against load lifted is shown. Which statement about the efficiency of the motor is correct?

A It decreases as the load increases · B It increases as the load increases · C It stays the same as the load increases · D More information is needed to determine this.

  1. 1

    D: more information is needed to determine this. [1]

Recap

  • Fuel-burning and nuclear stations: thermal energy boils water, steam drives a turbine, the turbine drives a generator.
  • Hydroelectric, wave, tidal and wind: moving water or air turns a turbine. The turbine drives a generator.
  • Solar cells use light from the Sun. Solar panels use infrared and other waves to heat water.
  • Compare resources by renewability, availability, reliability, scale and environmental impact.
  • Low efficiency: only a small fraction of the input energy is useful. The rest is wasted, for example as thermal energy to the surroundings.
  • Extended: the Sun is the main source of energy for all resources except geothermal, nuclear and tidal.
  • Extended: efficiency = useful output ÷ total input × 100%, for energy or for power.

17. Defining power

Power is the work done per unit time. Power is also the energy transferred per unit time.

Work done is force × distance moved in the direction of the force. To find power you need two things: the work done and the time taken.

W = Fd

P = W/t

P = (Δ E)/t

Examiner insight

“Candidates needed to know that to determine power, the time taken for a task is required as well as the actual work done (force × distance).” “There was evidence that many candidates, especially weaker candidates, could not recall and combine the equations for power and work done.”

Worked example 11 mark

Which statement is correct?

A Energy is the power transferred per unit time · B Energy is the time transferred per unit power · C Power is the energy transferred per unit time · D Power is the time transferred per unit energy

  1. 1

    C: Power is the energy transferred per unit time. [1]

18. Calculating power and its unit

To calculate power, use power = energy ÷ time. Write the equation first, then put in the numbers. The time must be in seconds: 4.0 min is 240 s.

Power is measured in watts (W). J / s is also accepted. Energy is measured in joules, so energy and power do not have the same unit.

Examiner insight

“Most candidates appreciated that the rate of transfer of energy was the same as the power of the lamp and that it did not require a change of unit – the W being a perfectly satisfactory unit. J / s are also acceptable.” “A common error was to indicate that energy and power have the same unit, but not work.”

Worked example 12 marks

Water is heated as it flows through an electric shower. The energy required to heat 18 kg of the water is 1.7 × 10⁶ J. This energy is transferred to the water in 4.0 min. Calculate the power transferred to the water.

  1. 1

    time = 4.0 × 60 = 240 s

  2. 2

    P = (Δ E)/t = (1.7 × 10⁶)/240 [1]

  3. 3

    = 7100 W [1]

19. Using the equation: energy, power and time

Rearrange P = Δ E / t to find energy or time. Energy is power × time. Time is energy ÷ power. Convert before you substitute: kJ to J, kW to W, minutes to seconds.

In the question below, the power of the hotplate must be greater than the value calculated, because some energy is transferred to the surroundings.

E = Pt

t = (Δ E)/P

Examiner insight

“Other common mistakes were to divide power by time instead of multiplying, to give the amount of energy transferred or to substitute the time in minutes instead of in seconds.”

Worked example 12 marks

A pan of water is heated on a hotplate. The energy transferred to the water is approximately 49 kJ. The time taken for the temperature of the water to increase from 22 °C to 80 °C is 41 s. Calculate the minimum power of the hotplate.

  1. 1

    energy = 49 kJ = 49 000 J

  2. 2

    P = (Δ E)/t = (49 000)/41 [1]

  3. 3

    = 1200 W [1]

Recap

  • Power is the work done per unit time: P = W / t.
  • Power is the energy transferred per unit time: P = Δ E / t.
  • Work done = force × distance moved in the direction of the force.
  • Power is measured in watts (W). 1 W = 1 J / s.
  • Energy = power × time. Convert to J, W and s before substituting.

End-of-chapter exercise

Test yourself on the whole chapter. Work through these before moving on.

  1. A mobile phone is being charged. Name the energy store of the battery that increases.1 mark
  2. A box sits on a high shelf. Name the energy store that depends on the height of the box.1 mark
  3. A candle burns and gives out light. Name the store that decreases and the store of the surroundings that increases.2 marks
  4. Name the process that transfers energy when: (a) a person pushes a box along the floor (b) an electric current passes through a heater.2 marks
  5. A toy car slows down and stops on a flat table. State the energy transfer. Explain why it is not a transfer to the gravitational potential store.3 marks
  6. The diagram shows the energy transfers for a radio. Calculate the energy transferred to the surroundings as thermal energy.2 marks
  7. A trolley of mass 800 g moves at 3.0 m / s. Calculate its kinetic energy.3 marks
  8. A box gains 360 J of gravitational potential energy when it is lifted through a height of 3.0 m. Calculate the mass of the box.3 marks
  9. A catapult fires a stone of mass 40 g vertically upwards. When the catapult is released, its elastic (strain) store decreases by 5.0 J. Of this energy, 0.50 J is transferred to the thermal store of the surroundings. The rest is transferred to the kinetic store of the stone. (a) Calculate the speed of the stone as it leaves the catapult. (b) Air resistance is negligible. Calculate the height the stone rises above the catapult.6 marks
  10. A roller-coaster car of mass 450 kg passes point A at a speed of 4.0 m / s. Point A is 18 m above the ground. The car runs down to ground level and then climbs to point B, which is 11 m above the ground. Between A and B, 21 kJ of energy is transferred to the thermal store of the surroundings. Calculate the speed of the car at B.6 marks
  11. State what is equal to the mechanical work done on an object.1 mark
  12. A student pushes a box with a force of 35 N for a distance of 6.0 m in the direction of the force. Calculate the work done.2 marks
  13. A crane lifts a load of weight 1200 N through a vertical height of 8.5 m. Calculate the work done in kJ.3 marks
  14. A force of 40 N moves an object 25 cm in the direction of the force. Calculate the work done in J.2 marks
  15. A trolley is pushed with a force of 60 N. The work done on the trolley is 480 J. Calculate the distance the trolley moves in the direction of the force.3 marks
  16. A rope pulls a sledge a distance of 12 m in the direction of the rope. The work done by the rope is 900 J. Calculate the force in the rope.3 marks
  17. A porter holds a heavy case stationary above the ground for 30 s. Calculate the work done on the case while it is held still. Explain your answer.2 marks
  18. A motor lifts a load of weight 500 N through a vertical height of 3.0 m in a time of 10 s. Calculate the energy transferred to the load.3 marks
  19. A conveyor belt carries 20 roof tiles from the ground to a roof. Each tile has a mass of 2.5 kg and a weight of 24.5 N. The tiles travel 9.0 m along the sloping belt and rise a vertical height of 6.0 m. Calculate the work done against the weight of the 20 tiles.4 marks
  20. A sled on a fairground ride has 18 kJ of energy in its kinetic store when it reaches a level braking track. A first brake exerts a force of 400 N on the sled for the first 25 m. A second brake then stops the sled in a further 16 m. All of the 18 kJ is transferred by the work done by the two brakes. Calculate the force exerted by the second brake.5 marks
  21. A coal-fired power station has a boiler, a turbine and a generator. State the order in which the energy passes through them and what each does.3 marks
  22. Describe how a wind farm generates electrical power.3 marks
  23. Water is held behind a dam and then released to generate electrical power. (a) Name the energy store of the water behind the dam. (b) State which part turns the generator.2 marks
  24. A town takes its electrical power from a wind farm. A student says: ‘Wind is renewable, so the town will always have power.’ Explain why the student is wrong.2 marks
  25. A country plans to burn biofuels instead of coal. State one advantage and one disadvantage of using biofuels.2 marks
  26. A coal-fired power station is described as having a low efficiency. Explain what this means.2 marks
  27. (a) Name the process that releases energy in the Sun. (b) State what research into this process is trying to achieve. (c) Six energy resources are listed: oil, tidal, wind, geothermal, hydroelectric, nuclear fuel. Name the three that do not depend on the Sun as their main source of energy.5 marks
  28. In one minute, a solar cell receives 2400 J of light energy from the Sun and transfers 360 J of it to electrical energy. Its electrical power output is 6.0 W. Calculate the efficiency of the solar cell.2 marks
  29. A biofuel power station has a boiler, a turbine and a generator. Burning the fuel gives a power input of 400 MW to the boiler. The steam carries 340 MW from the boiler to the turbine. The turbine transfers 150 MW to the generator. The electrical power output of the generator is 144 000 kW. (a) Calculate the efficiency of the generator. (b) Calculate the efficiency of the whole power station. (c) Show by calculation which of the three parts wastes the most power.6 marks
  30. A hydroelectric power station must supply 54 MW of electrical power to a town. Its generator has an efficiency of 96%. Its turbine has an efficiency of 90%. (a) Calculate the power the turbine must transfer to the generator. (b) Calculate the power the moving water must transfer to the turbine. (c) Calculate the efficiency of the whole power station. (d) Calculate the total power wasted. Give your answer in kW.8 marks
  31. State the equation that links power, energy transferred and time.1 mark
  32. A lamp has a power of 40 W. State what this means in terms of energy and time.1 mark
  33. A lamp transfers 1800 J of energy in 30 s. Calculate its power.2 marks
  34. A motor does 4500 J of work in 1.5 minutes. Calculate its power.2 marks
  35. A heater has a power of 2.4 kW. Calculate the energy it transfers in 50 s.3 marks
  36. A machine transfers 7200 J of energy. Its power is 150 W. Calculate the time it takes.3 marks
  37. A student pushes a box with a force of 40 N for 12 m in the direction of the force. This takes 8.0 s. Calculate the power of the student.3 marks
  38. Machine A does 600 J of work in 20 s. Machine B does 900 J of work in 45 s. State which machine has the greater power. Show your working.3 marks
  39. A winch pulls a boat up a slipway. The winch has a power of 1.8 kW. It pulls the boat 27 m in the direction of its force in 1.5 minutes. Calculate the force the winch exerts on the boat.4 marks
  40. An athlete trains on a rowing machine. On each stroke she pulls the handle 1.25 m with a force of 320 N in the direction of movement. She makes 24 strokes every minute. (a) Calculate the work done in one stroke. (b) Calculate her power. (c) Calculate the time, in minutes, she takes to do 240 kJ of work at this power.7 marks

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