Cambridge IGCSE0972

Energy, work and power

Physics 0972 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. 1Doing Work and Storing Energy
  2. 2Potential and Kinetic Energy
  3. 3Power and Efficiency
  4. 4Energy Resources and Generation

1. Doing Work and Storing Energy

In physics, 'work' has a very specific meaning. Work is done whenever a force causes an object to move. It is a measure of energy transfer. If you push a box across the floor, you are doing work on the box, transferring energy to it. The amount of work done depends on the size of the force and the distance the object moves. We calculate it using the formula: Work done = Force × distance. Since work is a transfer of energy, both are measured in the same unit: the joule (J). Energy isn't just 'used up'; it's stored in different ways. Key energy stores include: Kinetic (movement), Gravitational Potential (height), Chemical (in fuels, food, batteries), Elastic Potential (in stretched or compressed objects), and Thermal (heat).

W = F × d

Key term

Work Done (W): The energy transferred when a force moves an object over a distance, measured in joules (J).

Examiner insight

Examiners look for clear substitution of values into the correct formula. Always write down the formula you are using to secure the first mark.

Common pitfall

Forgetting that the distance in 'W = F × d' must be measured in metres and the force in newtons. Always convert units like cm or kN before calculating.

Worked example 12 marks

A shopper pushes a trolley with a constant horizontal force of 50 N over a distance of 15 m. Calculate the work done on the trolley.

  1. 1

    Step 1: Identify the formula. Work done = Force × distance (W = F × d).

  2. 2

    Step 2: Identify the given values. Force (F) = 50 N, distance(d) = 15 m.

  3. 3

    Step 3: Substitute the values into the formula. W = 50 N × 15 m.

  4. 4

    Step 4: Calculate the result. W = 750 J. The work done is 750 joules.

Worked example 23 marks

A crane does 20,000 J of work to lift a crate. If the force exerted by the crane is 4,000 N, how high was the crate lifted?

  1. 1

    Step 1: Start with the formula for work done. W = F × d.

  2. 2

    Step 2: Rearrange the formula to find the distance (d). d = W / F.

  3. 3

    Step 3: Identify the given values. Work done (W) = 20,000 J, Force (F) = 4,000 N.

  4. 4

    Step 4: Substitute the values into the rearranged formula. d = 20,000 J / 4,000 N.

  5. 5

    Step 5: Calculate the result. d = 5 m. The crate was lifted 5 metres high.

Recap

  • Work is done when a force causes displacement.
  • The formula for work done is W = F × d.
  • Work done and energy are both measured in joules (J).
  • Doing work is a method of transferring energy from one store to another.
  • Energy can be held in various stores, such as kinetic, potential, and chemical.

Quick check

  1. How much work is done if a force of 25 N moves an object 4 m?1 mark
  2. What is the unit of energy?1 mark

2. Potential and Kinetic Energy

Objects can store energy due to their position or motion. Kinetic Energy (KE) is the energy an object has because it is moving. The faster it moves or the more mass it has, the more kinetic energy it has. Gravitational Potential Energy (GPE) is the energy an object has because of its height in a gravitational field. Lifting an object gives it GPE. This stored energy can be converted back into other forms, for example, into kinetic energy if the object is dropped. This illustrates a fundamental rule: the Principle of Conservation of Energy. This principle states that energy cannot be created or destroyed, only transferred from one store to another. In a closed system, the total amount of energy remains constant.

KE = ½ × m × v²

GPE = m × g × h

Key term

Principle of Conservation of Energy: Energy cannot be created or destroyed, only transferred from one store to another or transformed from one form to another.

Examiner insight

In conservation of energy problems, clearly stating the energy conversion (e.g., GPE lost = KE gained) shows the examiner your understanding of the physics principle and will likely score a mark.

Common pitfall

Forgetting to square the velocity (v) when calculating kinetic energy. The most common mistake is calculating ½ × m × v instead of ½ × m × v².

Worked example 12 marks

A car with a mass of 1200 kg is travelling at a speed of 20 m/s. Calculate its kinetic energy.

  1. 1

    Step 1: Write down the formula for kinetic energy. KE = ½mv².

  2. 2

    Step 2: Identify the given values. Mass(m) = 1200 kg, velocity(v) = 20 m/s.

  3. 3

    Step 3: Substitute the values into the formula. KE = ½ × 1200 kg × (20 m/s)¹.

  4. 4

    Step 4: Calculate the result. KE = 600 × 400 = 240,000 J (or 240 kJ).

Worked example 22 marks

A 2 kg book is lifted from the floor and placed on a shelf 1.5 m high. Calculate the gravitational potential energy it gains. (Assume g = 10 N/kg).

  1. 1

    Step 1: Write down the formula for GPE. GPE = mgh.

  2. 2

    Step 2: Identify the given values. Mass(m) = 2 kg, height(h) = 1.5 m, gravitational field strength(g) = 10 N/kg.

  3. 3

    Step 3: Substitute the values into the formula. GPE = 2 kg × 10 N/kg × 1.5 m.

  4. 4

    Step 4: Calculate the result. GPE = 30 J.

Worked example 34 marks

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

  1. 1

    Step 1: Apply the Principle of Conservation of Energy. The GPE at the top is converted into KE at the bottom. So, GPE lost = KE gained.

  2. 2

    Step 2: Write the formulas for each side of the equation. mgh = ½mv².

  3. 3

    Step 3: Notice that mass(m) is on both sides, so it can be cancelled out. gh = ½v².

  4. 4

    Step 4: Rearrange the formula to make v² the subject. v² = 2gh.

  5. 5

    Step 5: Substitute the known values. v² = 2 × 10 N/kg × 3 m = 60.

  6. 6

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

Recap

  • Kinetic energy is the energy of motion (KE = ½mv²).
  • Gravitational potential energy is the energy stored by height (GPE = mgh).
  • Energy is conserved; it changes from one form to another but the total amount stays the same.
  • For a falling object, GPE is converted into KE.
  • Mass must be in kg, velocity in m/s, and height in m for these formulas.

Quick check

  1. What happens to an object's GPE as it is lifted higher?1 mark
  2. If a car doubles its speed, by how many times does its kinetic energy increase?1 mark

3. Power and Efficiency

Power is the rate at which work is done or energy is transferred. A more powerful engine can do the same amount of work in less time. Power is measured in watts (W), where 1 watt is equal to 1 joule of energy transferred per second. In any real-world process, not all the energy you put in comes out as useful energy; some is always wasted, usually as heat. Efficiency is a measure of how good a device is at converting input energy into useful output energy. It's calculated as a ratio, often expressed as a percentage. An efficiency of 100% is impossible due to unavoidable energy losses. Sankey diagrams are flow charts that show how energy is transferred in a process. The width of the arrows is proportional to the amount of energy. The straight arrow shows useful energy output, while arrows that curve away show wasted energy.

P = W / t (Power = Work done / time)

P = E / t (Power = Energy transferred / time)

Efficiency = (Useful energy output / Total energy input)

Efficiency = (Useful power output / Total power input)

Key term

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

Examiner insight

When calculating efficiency, your answer must be a value between 0 and 1 (or 0% and 100%). If you get a value greater than 1, you have likely divided the numbers the wrong way around.

Common pitfall

Confusing energy with power. Power is a rate. A high-power device uses a lot of energy *quickly*, while a low-power device might use the same total energy, but over a much longer time.

Worked example 13 marks

An electric motor lifts a 500 N weight through a height of 4 m in 10 s. What is the useful power output of the motor?

  1. 1

    Step 1: First, calculate the work done by the motor. Work done (W) = Force × distance = 500 N × 4 m = 2000 J.

  2. 2

    Step 2: Now, use the formula for power. Power (P) = Work done / time taken.

  3. 3

    Step 3: Substitute the values. P = 2000 J / 10 s.

  4. 4

    Step 4: Calculate the result. P = 200 W. The useful power output is 200 watts.

Worked example 22 marks

A light bulb is supplied with 6000 J of electrical energy. It converts 900 J of this into light energy. What is its efficiency?

  1. 1

    Step 1: Identify the useful energy output and total energy input. Useful energy output = 900 J (light). Total energy input = 6000 J (electrical).

  2. 2

    Step 2: Write down the formula for efficiency. Efficiency = (Useful energy output / Total energy input).

  3. 3

    Step 3: Substitute the values. Efficiency = 900 J / 6000 J.

  4. 4

    Step 4: Calculate the result. Efficiency = 0.15.

  5. 5

    Step 5: (Optional but good practice) Express as a percentage. 0.15 × 100% = 15%.

Worked example 34 marks

A car engine has a total power input of 80 kW. Its useful power output to the wheels is 20 kW. Draw a Sankey diagram to represent this energy transfer and calculate the engine's efficiency.

  1. 1

    Step 1: Calculate the wasted power. Wasted Power = Total Input - Useful Output = 80 kW - 20 kW = 60 kW.

  2. 2

    Step 2: Draw the Sankey diagram. Draw an arrow from left to right representing the total input power (80 kW). Draw a smaller straight arrow continuing to the right for useful output (20 kW). Draw a thicker arrow curving downwards for wasted power (60 kW). The width of the input arrow should equal the sum of the widths of the two output arrows.

  3. 3

    Step 3: Calculate the efficiency. Efficiency = (Useful power output / Total power input).

  4. 4

    Step 4: Substitute the values. Efficiency = 20 kW / 80 kW = 0.25 or 25%.

Recap

  • Power is the rate of energy transfer, measured in watts (W).
  • 1 Watt means 1 Joule of energy is transferred every second.
  • Efficiency measures how much of the input energy is converted into useful output energy.
  • No device is 100% efficient; some energy is always wasted, usually as heat.
  • Sankey diagrams visually represent energy transfers, with arrow widths proportional to the energy amount.

Quick check

  1. An engine does 5000 J of work in 20 seconds. What is its power?1 mark
  2. An appliance has a useful power output of 40 W and a total power input of 50 W. What is its efficiency?1 mark

4. Energy Resources and Generation

Most of the electricity we use is generated in power stations. These rely on various energy resources, which can be classified as either non-renewable or renewable. Non-renewable resources (like fossil fuels - coal, oil, gas - and nuclear fuel) are finite and will eventually run out. They are often burned to release chemical or nuclear energy. Renewable resources (like solar, wind, hydroelectric, and geothermal) are naturally replenished and will not run out. A typical thermal power station works by burning a fuel to heat water, creating high-pressure steam. This steam turns a turbine, which is connected to a generator that produces electricity. The choice of energy resource involves balancing factors like cost, reliability, and environmental impact. Fossil fuels are reliable but produce greenhouse gases, contributing to climate change. Nuclear power produces no greenhouse gases but creates radioactive waste. Renewables are clean but can be unreliable (e.g., wind doesn't always blow). Ultimately, the Sun is the original source of most energy on Earth, driving weather patterns (wind, rain for hydro) and creating the ancient biomass that formed fossil fuels.

Key term

Non-Renewable Resource: An energy source that exists in finite quantities and is consumed much faster than it can be formed, such as fossil fuels and nuclear fuels.

Fun fact

The energy in a single lightning bolt is enough to power a 100W lightbulb for about 3 months, but capturing and storing this energy is incredibly difficult and currently impossible on a large scale.

Worked example 14 marks

Describe the main energy transfers that occur in a coal-fired power station to generate electricity.

  1. 1

    Step 1: Start with the fuel. Coal stores Chemical energy.

  2. 2

    Step 2: The coal is burned, converting Chemical energy into Thermal energy (heat).

  3. 3

    Step 3: The thermal energy boils water to make high-pressure steam. The steam has Thermal energy and Potential energy.

  4. 4

    Step 4: The steam expands and rushes past a turbine, making it spin. The steam's energy is converted into Kinetic energy in the turbine.

  5. 5

    Step 5: The spinning turbine turns a generator, which converts the Kinetic energy into Electrical energy.

Worked example 22 marks

State one advantage and one disadvantage of using wind power to generate electricity.

  1. 1

    Advantage: Wind is a renewable resource, so it will not run out. It also produces no greenhouse gases or air pollutants during operation.

  2. 2

    Disadvantage: Wind is not constant, so power generation is intermittent and unreliable. Some people also consider wind farms to be noisy and a visual eyesore.

Recap

  • Energy resources are either renewable (won't run out) or non-renewable (finite).
  • Fossil fuels (coal, oil, gas) are non-renewable and produce CO₂ when burned.
  • Nuclear fuel is non-renewable but produces no CO₂; its waste is a major issue.
  • Renewable resources like solar and wind are clean but can be unreliable.
  • Most power stations use a fuel to turn water into steam, which spins a turbine connected to a generator.
  • The Sun is the ultimate source for most of our energy resources.

Quick check

  1. Name two non-renewable energy resources.1 mark
  2. What device in a power station converts kinetic energy into electrical energy?1 mark

End-of-chapter exercise

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

  1. A person pulls a box with a horizontal force of 200 N across a floor for a distance of 8 m. Calculate the work done.2 marks
  2. A 60 kg student climbs a flight of stairs with a vertical height of 5 m. Calculate the gravitational potential energy they gain. (Use g = 10 N/kg).2 marks
  3. A 0.4 kg ball is thrown with a velocity of 15 m/s. What is its kinetic energy?2 marks
  4. An electric kettle has a power rating of 2500 W. How much energy does it transfer in 2 minutes?3 marks
  5. A microwave oven has a power input of 1200 W. In 30 seconds, it supplies 18,000 J of energy to the food. Calculate the efficiency of the microwave.4 marks
  6. State two advantages and two disadvantages of using nuclear power compared to using fossil fuels for generating electricity.4 marks
  7. A 1500 kg car is travelling at a constant speed of 30 m/s along a flat road. The engine provides a forward force of 800 N to counteract air resistance and friction. Calculate the useful power output of the engine.3 marks
  8. A 1 kg rock is dropped from a 20 m high cliff. By calculating its GPE at the top and assuming all of this converts to KE, find its speed just before it hits the ground. Ignore air resistance. (Use g = 10 N/kg).4 marks
  9. An electric motor is used to lift a 200 kg crate of bricks to a height of 12 m in 24 s. The motor is 75% efficient. Calculate the electrical power supplied to the motor. (Use g = 10 N/kg).5 marks
  10. Describe the sequence of energy conversions that allows a hydroelectric power station to generate electricity, starting from the water stored in the reservoir.3 marks

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