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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1. Work Done and Energy Transferred

In physics, 'work' has a very specific meaning. Work is done whenever a force causes an object to move. If you push against a wall and it doesn't move, you have done no work, even though you might feel tired! The amount of work done is directly linked to the amount of energy transferred. For example, when you lift a book, you do work against gravity, and the chemical energy from your muscles is transferred to the book as gravitational potential energy. Work done and energy transferred are both measured in the same unit: the joule (J). One joule of work is done when a force of one newton moves an object by one metre.

Work Done (J) = Force (N) × distance moved in the direction of the force (m)

W = F × d

Key term

Work Done: The energy transferred when a force moves an object over a distance.

Examiner insight

Examiners require you to state that the distance moved must be in the direction of the force for work to be done. Marks are often awarded for correctly stating the formula and showing the substitution.

Common pitfall

Forgetting to convert distances from centimetres or kilometres into metres before using the work done formula. All units must be in their standard SI form.

Worked example 12 marks

A shopper pushes a trolley with a constant force of 50 N over a distance of 20 m. Calculate the work done by the shopper.

  1. 1

    Step 1: Identify the formula needed. Work Done = Force × distance.

  2. 2

    Step 2: List the known values. Force (F) = 50 N, distance(d) = 20 m.

  3. 3

    Step 3: Substitute the values into the formula. W = 50 N × 20 m.

  4. 4

    Step 4: Calculate the result. W = 1000 J.

  5. 5

    Answer: The work done is 1000 joules.

Recap

  • Work is only done when a force causes an object to move.
  • The distance moved must be in the same direction as the applied force.
  • Work done is a measure of energy transferred.
  • The unit for both work and energy is the joule (J).
  • The formula for work done is W = F × d.

Quick check

  1. If you lift a 10 N bag up by 2 m, how much work have you done?2 marks
  2. What is the definition of one joule?1 mark

2. Energy Stores and Transfers

Energy isn't 'used up'; it's stored and moved around. We can think of energy being held in different 'stores'. When something happens, energy is transferred from one store to another. There are 8 main energy stores you need to know: Kinetic (movement), Gravitational Potential (height), Chemical (in food, fuels, batteries), Elastic Potential (in stretched or squashed objects), Thermal (heat), Nuclear (in atomic nuclei), Electrostatic (in electric charges), and Magnetic (in magnets and electromagnets). Energy can be transferred between these stores in four main ways: by mechanical work (a force moving something), by electrical work (currents flowing), by heating (due to a temperature difference), or by radiation (like light or sound waves).

Key term

Energy Store: A system or object that contains energy which can be transferred to do work.

Fun fact

The chemical energy in a single AA battery, if converted with 100% efficiency, could lift an apple to the top of the world's tallest building, the Burj Khalifa, more than 10 times.

Worked example 13 marks

A battery-powered toy car accelerates from rest along a flat floor. Describe the main energy transfers taking place.

  1. 1

    Step 1: Identify the initial energy store. The energy starts in the battery.

  2. 2

    This is Chemical Energy.

  3. 3

    Step 2: Identify the main final energy store. The car is moving, so it has kinetic energy.

  4. 4

    This is Kinetic Energy.

  5. 5

    Step 3: Describe the transfer. The energy is transferred electrically from the battery to the motor, which then does mechanical work to turn the wheels.

  6. 6

    Step 4: Consider any 'wasted' energy. As the car moves, some energy is transferred to the surroundings due to air resistance and friction in the motor and wheels.

  7. 7

    This becomes Thermal Energy and Sound Energy.

  8. 8

    Final Answer: Chemical energy in the battery is transferred to Kinetic energy in the car, with some energy being dissipated as Thermal and Sound energy.

Recap

  • Energy is held in various stores, such as kinetic, potential, chemical, and thermal.
  • Energy is moved between stores via transfer pathways like mechanical work, electrical work, heating, or radiation.
  • A falling apple transfers energy from a gravitational potential store to a kinetic store.
  • A burning match transfers energy from a chemical store to thermal and light stores.
  • A light bulb transfers energy from an electrical pathway to light and thermal stores.

Quick check

  1. Name the energy store associated with a stretched rubber band.1 mark
  2. Name the main energy transfer that occurs when you switch on a kettle.1 mark

3. Calculating Kinetic and Potential Energy

Two of the most important energy stores in mechanics are Gravitational Potential Energy (GPE) and Kinetic Energy (KE). GPE is the energy an object has because of its height in a gravitational field. The higher it is, the more GPE it has. The formula is GPE = mass × gravitational field strength × height. Kinetic energy is the energy an object has because it is moving. The faster it moves and the more mass it has, the more kinetic energy it has. The formula is KE = ½ × mass × velocity². Notice that the velocity is squared, which means doubling an object's speed quadruples its kinetic energy!

Gravitational Potential Energy (J) = mass (kg) × gravitational field strength (N/kg) × height (m)

GPE = mgh

Kinetic Energy (J) = ½ × mass (kg) × velocity² ((m/s)²)

KE = ½mv²

Key term

Kinetic Energy: The energy an object possesses due to its motion.

Examiner insight

For KE calculations, marks are often lost for forgetting to square the velocity. Always write out v² separately in your working to avoid this mistake.

Common pitfall

Confusing mass (in kg) with weight (in N). Remember to use mass in both the GPE and KE formulas. If you are given a weight, you must first divide by g to find the mass.

Worked example 12 marks

A 60 kg person climbs a flight of stairs to a height of 5 m. Calculate the gravitational potential energy they gain. (Take g = 10 N/kg).

  1. 1

    Step 1: Identify the formula. GPE = mgh.

  2. 2

    Step 2: List the known values. m = 60 kg, g = 10 N/kg, h = 5 m.

  3. 3

    Step 3: Substitute the values. GPE = 60 kg × 10 N/kg × 5 m.

  4. 4

    Step 4: Calculate the result. GPE = 3000 J.

  5. 5

    Answer: The person gains 3000 J of GPE.

Worked example 23 marks

A cricket ball of mass 0.16 kg is travelling at 40 m/s. Calculate its kinetic energy.

  1. 1

    Step 1: Identify the formula. KE = ½mv².

  2. 2

    Step 2: List the known values. m = 0.16 kg, v = 40 m/s.

  3. 3

    Step 3: Substitute the values. KE = ½ × 0.16 kg × (40 m/s)¹.

  4. 4

    Step 4: Calculate the velocity squared first. 40² = 1600.

  5. 5

    Step 5: Complete the calculation. KE = 0.5 × 0.16 × 1600 = 128 J.

  6. 6

    Answer: The kinetic energy of the ball is 128 J.

Recap

  • Gravitational Potential Energy (GPE) depends on mass, height, and gravity.
  • Kinetic Energy (KE) depends on mass and speed.
  • The formula for GPE is mgh.
  • The formula for KE is ½mv².
  • Always remember to square the velocity (v) in the kinetic energy equation.
  • The unit for both GPE and KE is the joule (J).

Quick check

  1. What happens to an object's KE if its speed is tripled?1 mark
  2. Calculate the GPE of a 2 kg book on a shelf 1.5 m high. (g = 10 N/kg)2 marks

4. The Principle of Conservation of Energy

This is one of the most fundamental laws in all of science. The Principle of Conservation of Energy states that energy cannot be created or destroyed, only transferred from one store to another. In a 'closed system' (where no energy can get in or out), the total amount of energy is always constant. In the real world, energy often seems to be 'lost', for example, when a bouncing ball eventually stops. The energy hasn't been destroyed; it has been transferred to less useful stores. In the case of the ball, each bounce transfers some energy to a thermal store (heating the ball and the floor) and a sound store. This dissipated energy spreads out into the environment and is difficult to use again.

Total Energy Before = Total Energy After

Energy Input = Useful Energy Output + Wasted Energy

Key term

Conservation of Energy: The principle that energy cannot be created or destroyed, but only changed from one form to another.

Examiner insight

When describing energy transfers, clearly state the initial energy store, the transfer process, and all the final energy stores, explicitly mentioning any 'wasted' energy like heat or sound.

Worked example 14 marks

A 0.5 kg apple falls from a branch 3 m above the ground. Assuming no air resistance, what is its speed just before it hits the ground? (Take g = 10 N/kg).

  1. 1

    Step 1: Apply the principle of conservation of energy. The GPE at the top will be converted into KE at the bottom.

  2. 2

    So, GPE lost = KE gained.

  3. 3

    Step 2: Calculate the initial GPE. GPE = mgh = 0.5 kg × 10 N/kg × 3 m = 15 J.

  4. 4

    Step 3: This GPE is converted to KE. So, the KE just before impact is 15 J.

  5. 5

    Step 4: Use the KE formula to find the speed. KE = ½mv², so 15 J = ½ × 0.5 kg × v².

  6. 6

    Step 5: Rearrange the formula to solve for v². 15 = 0.25 × v², so v² = 15 / 0.25 = 60.

  7. 7

    Step 6: Find v by taking the square root. v = √60 ≈ 7.75 m/s.

  8. 8

    Answer: The apple's speed is approximately 7.75 m/s.

Recap

  • Energy is always conserved; it cannot be created or destroyed.
  • Energy is transferred from one store to another.
  • In real systems, some energy is always transferred to 'wasted' or less useful stores, usually thermal energy.
  • This dissipated energy spreads out into the surroundings.
  • We can equate GPE lost to KE gained for falling objects (if we ignore air resistance).

Quick check

  1. A light bulb is supplied with 100 J of electrical energy and produces 15 J of light energy. How much energy is wasted as heat?1 mark

5. Power and Efficiency

Power is the rate at which work is done or energy is transferred. A more powerful machine can do the same amount of work in less time. The unit of power is the watt (W), where 1 watt is equal to 1 joule of energy transferred per second. Efficiency is a measure of how good a device is at transferring energy into the form we want. No device is 100% efficient; some energy is always wasted, usually as heat. Efficiency is calculated by dividing the useful energy (or power) output by the total energy (or power) input. It has no units and is given as a decimal (e.g., 0.8) or a percentage (e.g., 80%). A Sankey diagram is a special type of flow chart where the width of the arrows is proportional to the amount of energy. It's a great way to visualise efficiency, with the straight arrow showing useful energy and the curving arrow showing wasted energy.

Power (W) = Work Done (J) / time taken (s)

P = W / t

Power (W) = Energy Transferred (J) / time taken (s)

P = E / t

Efficiency = (Useful Energy Output / Total Energy Input)

Efficiency = (Useful Power Output / Total Power Input)

Key term

Power: The rate at which work is done or energy is transferred, measured in watts (W).

Common pitfall

Mixing up energy and power. Remember, power is the 'how fast' (rate), while energy is the 'how much' (total amount).

Worked example 14 marks

A crane lifts a 1000 N load through a vertical height of 15 m in 30 s. The motor has an electrical power input of 600 W. Calculate the efficiency of the motor.

  1. 1

    Step 1: Calculate the useful work done by the crane. Work Done = Force × distance = 1000 N × 15 m = 15000 J.

  2. 2

    Step 2: Calculate the useful power output. Power = Work Done / time = 15000 J / 30 s = 500 W.

  3. 3

    Step 3: Identify the total power input. The question states this is 600 W.

  4. 4

    Step 4: Calculate the efficiency. Efficiency = Useful Power Out / Total Power In = 500 W / 600 W.

  5. 5

    Step 5: Give the answer as a decimal or percentage. Efficiency = 0.833... or 83.3%.

  6. 6

    Answer: The efficiency of the motor is 83.3%.

Worked example 23 marks

A car engine has a power input of 80 kW from the fuel. A Sankey diagram shows that 60 kW is wasted as heat and sound. What is the useful power output and the car's efficiency?

  1. 1

    Step 1: Apply conservation of energy. Total Input = Useful Output + Wasted Output.

  2. 2

    Step 2: Rearrange to find useful output. Useful Output = Total Input - Wasted Output.

  3. 3

    Step 3: Substitute values. Useful Power Output = 80 kW - 60 kW = 20 kW.

  4. 4

    Step 4: Calculate efficiency. Efficiency = Useful Power Out / Total Power In = 20 kW / 80 kW.

  5. 5

    Step 5: Calculate the result. Efficiency = 0.25 or 25%.

  6. 6

    Answer: The useful power output is 20 kW and the efficiency is 25%.

Recap

  • Power is the rate of energy transfer, measured in watts (W).
  • 1 W = 1 J/s.
  • Efficiency measures how much of the input energy is converted to useful output energy.
  • Efficiency can be calculated using either energy or power.
  • Efficiency is a ratio with no units, often expressed as a percentage.
  • Sankey diagrams visually represent energy transfers and efficiency.

Quick check

  1. An engine does 2000 J of work in 4 seconds. What is its power output?2 marks
  2. A motor is 75% efficient. If it is supplied with 400 J of energy, how much useful work does it do?2 marks

6. Renewable and Non-Renewable Resources

Energy resources are the sources we use to generate electricity and power our world. They are broadly classified into two groups: non-renewable and renewable. Non-renewable resources are finite; they are used up much faster than they are formed and will eventually run out. The main examples are fossil fuels (coal, oil, and natural gas) and nuclear fuels (like uranium). Renewable resources are those that are replenished naturally on a human timescale or will not run out as a result of being used. Examples include solar, wind, hydroelectric, geothermal, and biomass. Most of the energy we use on Earth, including both renewable and fossil fuels, originates from the Sun. The Sun's energy drives the weather for wind and rain (hydroelectric), and it was the source of energy for the ancient plants and animals that became fossil fuels.

Key term

Renewable Energy: Energy from a source that is not depleted when used or is replenished within a human lifetime.

Examiner insight

Be precise with definitions. A good definition for a renewable resource is one that 'is replenished naturally' or 'will not run out as a result of being used'.

Worked example 13 marks

Classify the following energy resources as either renewable or non-renewable: Coal, Wind, Uranium, Solar, Natural Gas.

  1. 1

    Step 1: Consider each resource. Coal is a fossil fuel and is finite. -> Non-renewable.

  2. 2

    Step 2: Wind is caused by weather patterns driven by the Sun and will not run out. -> Renewable.

  3. 3

    Step 3: Uranium is a mineral mined from the Earth and is finite. -> Non-renewable.

  4. 4

    Step 4: Solar energy comes directly from the Sun and will not run out. -> Renewable.

  5. 5

    Step 5: Natural Gas is a fossil fuel and is finite. -> Non-renewable.

  6. 6

    Answer: Renewable: Wind, Solar. Non-renewable: Coal, Uranium, Natural Gas.

Recap

  • Energy resources are either renewable or non-renewable.
  • Non-renewable resources are finite and will run out, e.g., fossil fuels and nuclear fuel.
  • Renewable resources are replenished naturally and will not run out, e.g., solar, wind, and hydro.
  • The Sun is the original source of energy for most resources on Earth.
  • Choosing energy resources involves balancing reliability, cost, and environmental impact.

Quick check

  1. Give one reason why fossil fuels are described as non-renewable.1 mark
  2. Name two renewable energy resources.1 mark

7. Focus on Non-Renewable Resources

Non-renewable resources, primarily fossil fuels and nuclear fuel, are the world's main source of energy because they are reliable and have a high energy density. In a typical thermal power station, a fuel is used to generate heat. For fossil fuels (coal, oil, gas), the fuel is burned (combustion). For nuclear fuel (uranium), atoms are split (fission). This heat is used to boil water, creating high-pressure steam. The steam is then directed at the blades of a turbine, causing it to spin. The spinning turbine is connected to a generator, which converts the mechanical energy of rotation into electrical energy.

Fossil Fuels:

  • Advantages: Reliable (can generate power 24/7), high energy density, relatively cheap to build power stations.
  • Disadvantages: Release carbon dioxide (a greenhouse gas) causing climate change, release sulfur dioxide causing acid rain, they are finite and will run out.

Nuclear Fuel:

  • Advantages: No greenhouse gas emissions during operation, extremely high energy density (a small amount of fuel produces a lot of energy), reliable.
  • Disadvantages: Produces hazardous radioactive waste that is difficult and expensive to store for thousands of years, high cost of building and decommissioning plants, risk of catastrophic accidents.

Key term

Generator: A device that converts mechanical energy into electrical energy, typically by rotating a coil of wire in a magnetic field.

Common pitfall

Stating that nuclear power is 'clean' or 'environmentally friendly'. While it doesn't produce greenhouse gases, the long-term storage of radioactive waste is a major environmental problem.

Worked example 13 marks

Describe the basic stages of generating electricity in a coal-fired power station.

  1. 1

    Step 1: The coal (chemical energy store) is burned to release heat (thermal energy).

  2. 2

    Step 2: The heat is used to boil water into high-pressure steam.

  3. 3

    Step 3: The steam is forced through a turbine, causing it to spin (kinetic energy).

  4. 4

    Step 4: The turbine is connected to a generator, which spins and produces electricity (electrical energy).

Worked example 22 marks

State one environmental advantage and one environmental disadvantage of using nuclear power compared to fossil fuels.

  1. 1

    Advantage: Nuclear power does not produce carbon dioxide or other greenhouse gases, so it does not contribute to global warming.

  2. 2

    Disadvantage: Nuclear power produces radioactive waste which remains dangerous for thousands of years and must be stored securely, posing a long-term environmental risk.

Recap

  • Thermal power stations use heat to make steam, which turns a turbine, which spins a generator.
  • Fossil fuels are burned to produce heat.
  • Nuclear fission is used to produce heat in a nuclear reactor.
  • Fossil fuels are reliable but produce greenhouse gases.
  • Nuclear power is reliable and produces no CO2, but creates radioactive waste.

Quick check

  1. What is the name of the process that releases energy from uranium in a power station?1 mark
  2. What gas, which contributes to acid rain, is released when some fossil fuels are burned?1 mark

8. Focus on Renewable Resources

Renewable energy resources offer an alternative to fossil fuels, helping to reduce pollution and combat climate change. Here's how the main types work:

  • Solar: Photovoltaic cells (solar cells) convert sunlight directly into electricity. Solar panels use sunlight to heat water. Adv: No pollution, free energy source after setup. Disadv: Only works when sunny (intermittent), requires a large area for significant power output.
  • Wind: Wind turns large blades connected to a turbine and generator. Adv: No pollution, low running costs. Disadv: Intermittent (only works when windy), can be noisy and considered a visual blight, can be a danger to birds.
  • Hydroelectric Power (HEP): A dam is built to trap water, creating a reservoir. The water is allowed to flow down through turbines to generate electricity. Adv: Very reliable, can be switched on quickly, low running costs. Disadv: High initial cost, floods large areas of land destroying habitats, can be affected by drought.
  • Geothermal: In volcanic regions, cold water is pumped down to hot rocks deep underground. It turns to steam, which rises to turn turbines. Adv: Reliable and consistent, no fuel costs, small footprint on land. Disadv: Only possible in specific geological locations.
  • Wave & Tidal: The movement of sea water is used to turn turbines. Tidal barrages work like HEP dams across estuaries, while wave machines float on the surface. Adv: Predictable (tides), no pollution. Disadv: High construction and maintenance costs due to corrosive seawater, can disrupt marine ecosystems.

Key term

Turbine: A machine with blades that is made to revolve by a fast-moving flow of water, steam, gas, or air, used to drive a generator.

Examiner insight

For questions on energy resources, a balanced answer that discusses both advantages and disadvantages for a specific resource, linked to the context of the question, scores highest.

Fun fact

The energy from the Sun that hits the Earth in a single hour is more than the entire world consumes in a year. The challenge is capturing it effectively.

Worked example 13 marks

A small, remote island community has strong, consistent winds but limited land space and no rivers. Suggest the most suitable renewable energy resource for them and give two reasons for your choice.

  1. 1

    Step 1: Identify the most suitable resource based on the description. The mention of 'strong, consistent winds' points directly to wind power.

  2. 2

    Step 2: Give the first reason. Wind turbines would be suitable because the island has a reliable source of wind.

  3. 3

    Step 3: Give the second reason. As a remote island, a self-sufficient source like wind is ideal, reducing the need to import expensive fuel.

  4. 4

    Step 4: Acknowledge the constraint. While land space is limited, offshore wind turbines could be an option.

  5. 5

    Answer: The most suitable resource is wind power. Reason 1: The island has strong and consistent winds. Reason 2: It provides energy independence for a remote location.

Recap

  • Solar power uses sunlight to generate electricity or heat water.
  • Wind power uses moving air to turn turbines.
  • Hydroelectric power uses falling water to turn turbines.
  • Geothermal power uses heat from the Earth to create steam.
  • The main disadvantage of solar and wind is their intermittency (they are not always available).
  • The choice of renewable resource often depends on the geography of the location.

Quick check

  1. What is the difference between a solar cell and a solar panel?2 marks
  2. State one advantage and one disadvantage of hydroelectric power.2 marks

End-of-chapter exercise

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

  1. A box of mass 5 kg is lifted from the floor onto a shelf that is 1.2 m high. Calculate the work done on the box. (Take g = 10 N/kg)3 marks
  2. A 1200 kg car is travelling at a steady speed of 20 m/s. Calculate its kinetic energy.2 marks
  3. An electric motor has a useful power output of 400 W. It is used for 50 seconds. If the motor is 80% efficient, calculate the total energy supplied to the motor.4 marks
  4. Describe the energy transfers that occur when a bungee jumper jumps from a platform, from the moment they jump until they reach the lowest point of their first bounce.3 marks
  5. Explain the difference between a renewable and a non-renewable energy resource, giving one example of each.3 marks
  6. A 2 kg stone is dropped from the top of a 45 m high cliff. By calculating its potential energy at the top, determine its speed just before it hits the sea below. You may ignore air resistance. (Take g = 10 N/kg)4 marks
  7. Describe the main stages of how electricity is generated in a nuclear power station. State one major advantage and one major disadvantage of this method.4 marks
  8. A car's engine provides a driving force of 800 N. The car travels at a constant speed of 25 m/s. Calculate the useful power output of the engine.3 marks
  9. Compare the use of wind power and hydroelectric power for generating electricity on a large scale. Include two advantages or disadvantages for each.4 marks
  10. A 100 W lamp is supplied with 5000 J of electrical energy. For how long was the lamp switched on? If it produces 800 J of light energy in this time, what is its efficiency?4 marks

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