Cambridge Lower Secondary CheckpointStage 9

Physics: Forces and energy

Science Stage 9 Chapter Notes

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Physics: Forces and energy
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In this chapter

  1. 1Work Done by a Force
  2. 2Understanding Energy Stores and Transfers
  3. 3Calculating GPE and Kinetic Energy
  4. 4The Principle of Conservation of Energy
  5. 5Power: The Rate of Energy Transfer
  6. 6Calculating Energy Efficiency

1. Work Done by a Force

In physics, 'work' has a very specific meaning. Work is done whenever a force causes an object to move. The amount of work done is a measure of the energy that has been transferred. To calculate work done, you multiply the size of the force by the distance the object moves in the direction of the force. For example, pushing a box across the floor involves doing work against friction. The formula is Work done (in Joules) = Force (in Newtons) × distance moved in the direction of the force (in metres).

W = F × d

Key term

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

Examiner insight

Examiners look for the distance to be measured in the same direction as the force, and for the correct units (Joules for work, Newtons for force, metres for distance).

Common pitfall

Forgetting that no work is done if the object does not move, no matter how large the force is.

Fun fact

Even if you hold a heavy weight above your head and feel tired, in physics terms, you are doing no work on the weight because it isn't moving.

Worked example 12 marks

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

  1. 1

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

  2. 2

    Step 2: Identify the given values. F = 50 N and 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. The work done is 1000 Joules.

Recap

  • Work is done when a force causes displacement.
  • Work done is a measure of energy transfer, measured in Joules (J).
  • The formula for work done is W = F × d.
  • No work is done if the object does not move (d=0).
  • The distance must be measured in the direction of the force.

Quick check

  1. If you push against a solid wall with a force of 100 N but it doesn't move, how much work have you done on the wall?1 mark

2. Understanding Energy Stores and Transfers

Energy is never 'used up'; it's just moved around. We think of energy as being kept in different 'stores' and moved between them via 'transfer pathways'. The main energy stores are: Kinetic (movement), Gravitational Potential (height), Chemical (food, fuel, batteries), Elastic Potential (stretched/squashed objects), Thermal (hot objects), Magnetic, Electrostatic, and Nuclear. Energy is transferred from one store to another by: Mechanical work (a force moving something), Electrical work (charges moving), Heating, or Radiation (light and sound waves).

Key term

Energy Store: A system or object that contains energy, such as the chemical store in a battery or the kinetic store of a moving car.

Examiner insight

Students who can correctly identify the initial and final energy stores, as well as the transfer pathway, in a given scenario score highly.

Common pitfall

Describing energy as being 'created' or 'destroyed' instead of transferred from one store to another.

Worked example 13 marks

A battery-powered torch is switched on. Describe the energy transfers that take place.

  1. 1

    Step 1: Identify the initial energy store. The energy is initially stored in the battery as chemical energy.

  2. 2

    Step 2: Identify the transfer pathway. When the torch is on, an electric current flows. This is an electrical work transfer.

  3. 3

    Step 3: Identify the final useful energy store/transfer. The electrical energy is transferred to the bulb, which emits light. This is a radiation transfer.

  4. 4

    Step 4: Identify any wasted energy. The bulb also gets hot, so some energy is transferred to the thermal store of the bulb and surroundings. So, the full transfer is: Chemical store -> Electrical work -> Light (useful) + Thermal energy (wasted).

Recap

  • Energy is stored in various forms: kinetic, potential, chemical, thermal, etc.
  • Energy is transferred between stores via work, heating, or radiation.
  • The total amount of energy is always conserved in any process.
  • Describing energy changes involves naming the stores and the transfer pathways.

Quick check

  1. What is the main energy store in a compressed spring?1 mark
  2. Name the four main ways energy can be transferred between stores.2 marks

3. Calculating GPE and Kinetic Energy

Two of the most important energy stores are related to height and movement. Gravitational Potential Energy (GPE) is the energy an object has because of its position in a gravitational field, i.e., its height above the ground. The higher it is, the more GPE it has. We calculate it using: GPE = mass × gravitational field strength × height. Kinetic Energy (KE) is the energy an object has because it is moving. The faster it moves, the more KE it has. We calculate it using: KE = ½ × mass × velocity².

GPE = m × g × h

KE = ½ × m × v²

Key term

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

Examiner insight

Marks are often awarded for correctly squaring the velocity term (v²) in the kinetic energy equation, as this is a very common source of error.

Common pitfall

Forgetting to square the velocity (v) when calculating kinetic energy, or using weight instead of mass when calculating GPE.

Fun fact

Doubling the speed of a car quadruples its kinetic energy (because of the v² term), which is why speed limits have such a big impact on road safety.

Worked example 13 marks

A book with a mass of 1.5 kg is on a shelf 2.0 m above the floor. Calculate its gravitational potential energy. (Take g = 9.8 N/kg).

  1. 1

    Step 1: Identify the formula for GPE. GPE = m × g × h.

  2. 2

    Step 2: Identify the given values. m = 1.5 kg, h = 2.0 m, g = 9.8 N/kg.

  3. 3

    Step 3: Substitute the values into the formula. GPE = 1.5 kg × 9.8 N/kg × 2.0 m.

  4. 4

    Step 4: Calculate the result. GPE = 29.4 J.

Worked example 23 marks

A cyclist and their bike have a combined mass of 80 kg and are travelling at a speed of 10 m/s. Calculate their kinetic energy.

  1. 1

    Step 1: Identify the formula for kinetic energy. KE = ½ × m × v².

  2. 2

    Step 2: Identify the given values. m = 80 kg, v = 10 m/s.

  3. 3

    Step 3: Substitute the values into the formula. KE = 0.5 × 80 kg × (10 m/s)¹.

  4. 4

    Step 4: Calculate the result. KE = 0.5 × 80 × 100 = 4000 J.

Recap

  • Gravitational Potential Energy (GPE) is the energy stored by an object due to its height.
  • Kinetic Energy (KE) is the energy an object has due to its motion.
  • GPE depends on mass, gravitational field strength, and height.
  • KE depends on mass and the square of the velocity.
  • Both GPE and KE are measured in Joules (J).

Quick check

  1. If you double the height of an object, what happens to its GPE?1 mark
  2. If you double the speed of an object, what happens to its KE?1 mark

4. The Principle of Conservation of Energy

This is one of the most fundamental laws in all of physics. The Principle of Conservation of Energy states that energy cannot be created or destroyed, it can only be transferred from one form to another. In any energy transfer, the total energy before is always equal to the total energy after. In a 'closed system' (where no energy can get in or out), the total energy is constant. In real-world situations, some energy is often transferred to a 'wasted' store, usually as thermal energy due to friction or air resistance. This makes the useful energy output less than the total energy input.

Total energy input = Useful energy output + Wasted energy output

Key term

Conservation of Energy: The principle that the total energy of an isolated system remains constant over time.

Examiner insight

Clear explanations that account for 'wasted' energy (usually as heat due to friction or air resistance) in real-world systems are highly rewarded.

Common pitfall

Ignoring 'wasted' energy transfers. When a question asks for a description of energy changes, you must account for where all the energy goes, including dissipated heat and sound.

Worked example 13 marks

A ball is dropped from a height of 2 m. It bounces back up to a height of 1.5 m. Use the principle of conservation of energy to explain why it does not return to its original height.

  1. 1

    Step 1: Describe the initial energy. At the start, the ball has gravitational potential energy (GPE).

  2. 2

    Step 2: Describe the energy transfer as it falls. As the ball falls, its GPE is converted into kinetic energy (KE).

  3. 3

    Step 3: Describe the energy transfer during the bounce. When the ball hits the ground, some of its kinetic energy is transferred into thermal energy (heating the ball and the ground) and sound energy.

  4. 4

    Step 4: Explain the result. Because some energy was 'lost' as heat and sound, there is less energy available to be converted back into GPE on the rebound. Therefore, the ball cannot return to its original height.

Recap

  • Energy can never be created or destroyed, only transferred.
  • The total energy in a closed system remains constant.
  • In real-world systems, some energy is always dissipated as 'wasted' energy.
  • This 'wasted' energy is usually in the form of thermal energy due to friction or air resistance.

Quick check

  1. A pendulum swings back and forth. At which point in its swing is its kinetic energy at a maximum?1 mark

5. Power: The Rate of Energy Transfer

Power is a measure of how quickly work is done or how quickly energy is transferred. A more powerful device can transfer the same amount of energy in less time than a less powerful one. The unit of power is the Watt (W), named after the Scottish engineer James Watt. One Watt is equal to one Joule of energy transferred per second. The main formulas are: Power = Work done / time taken, and Power = Energy transferred / time taken.

P = W / t

P = E / t

Key term

Power: The rate at which energy is transferred or the rate at which work is done.

Examiner insight

Examiners expect students to be able to rearrange the power equation (P=E/t) to solve for energy (E=P×t) or time (t=E/P).

Common pitfall

Confusing power with energy. Energy is the total amount of 'stuff' to do work (measured in Joules), while power is how fast you use that stuff (measured in Joules per second, or Watts).

Fun fact

A fit human can generate about 100 W of power over a sustained period, enough to power a bright light bulb. In short bursts, like sprinting, they can produce over 1000 W (1 kW).

Worked example 13 marks

A lift motor does 300,000 J of work to raise a lift in 25 seconds. Calculate the power output of the motor.

  1. 1

    Step 1: Identify the correct formula. Power (P) = Work done (W) / time taken (t).

  2. 2

    Step 2: Identify the given values. W = 300,000 J, t = 25 s.

  3. 3

    Step 3: Substitute the values into the formula. P = 300,000 J / 25 s.

  4. 4

    Step 4: Calculate the result. P = 12,000 W. This can also be written as 12 kW.

Recap

  • Power is the rate of energy transfer or the rate of doing work.
  • Power is measured in Watts (W).
  • One Watt is equivalent to one Joule per second (1 W = 1 J/s).
  • The formula for power is P = E / t or P = W / t.

Quick check

  1. An engine transfers 5000 J of energy in 10 seconds. What is its power?2 marks

6. Calculating Energy Efficiency

In any energy transfer, not all the input energy ends up in the desired useful store. Some is always 'wasted' or dissipated, usually as heat to the surroundings. Efficiency is a measure of how good a device is at transferring energy into a useful form. It is calculated as the ratio of the useful energy output to the total energy input. Efficiency has no units. It can be written as a decimal (e.g., 0.75) or as a percentage (e.g., 75%). An efficiency of 1.0 or 100% would mean no energy is wasted, which is impossible in practice.

Efficiency = Useful energy output / Total energy input

Efficiency (%) = (Useful energy output / Total energy input) × 100

Efficiency = Useful power output / Total power input

Key term

Efficiency: A measure of how much of the energy supplied to a device is transferred into a useful form.

Examiner insight

Candidates should be able to use both the energy and power versions of the efficiency equation and express the answer as a decimal or percentage as required by the question.

Common pitfall

Calculating an efficiency greater than 1 (or 100%). This is a sign you have divided the numbers the wrong way round (e.g., input / useful output).

Fun fact

The human body is about 25% efficient at converting chemical energy from food into mechanical work. The other 75% becomes thermal energy, which is why you get hot when you exercise.

Worked example 12 marks

An electric motor changes electrical energy into kinetic and thermal energy. 65% of the electrical energy is changed to useful kinetic energy. Calculate the percentage of electrical energy changed to wasted thermal energy.

  1. 1

    Step 1: Recall the conservation of energy. Total energy input = Useful energy output + Wasted energy output.

  2. 2

    Step 2: Express this in percentages. 100% = Percentage useful + Percentage wasted.

  3. 3

    Step 3: Substitute the known value. 100% = 65% + Percentage wasted.

  4. 4

    Step 4: Rearrange and solve. Percentage wasted = 100% - 65% = 35%. The percentage changed to thermal energy is 35%.

Worked example 23 marks

A light bulb is supplied with 200 J of electrical energy. It produces 40 J of light energy. Calculate its efficiency.

  1. 1

    Step 1: Identify the formula for efficiency. Efficiency = Useful energy output / Total energy input.

  2. 2

    Step 2: Identify the values. Useful energy output = 40 J (light). Total energy input = 200 J (electrical).

  3. 3

    Step 3: Substitute the values. Efficiency = 40 J / 200 J.

  4. 4

    Step 4: Calculate the result. Efficiency = 0.2. To express as a percentage, multiply by 100: 0.2 × 100 = 20%.

Recap

  • Efficiency measures how well a device converts input energy into useful output energy.
  • Efficiency can be calculated using energy or power.
  • Efficiency has no units and is expressed as a decimal or a percentage.
  • No device is 100% efficient; some energy is always wasted, usually as heat.

Quick check

  1. A machine has a total energy input of 500 J and a useful energy output of 400 J. What is its efficiency?2 marks

End-of-chapter exercise

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

  1. A weightlifter lifts a 1200 N barbell 2.0 m into the air. Calculate the work done by the weightlifter.2 marks
  2. A 60 W light bulb is left on for 30 seconds. How much electrical energy does it convert?2 marks
  3. A 70 kg person climbs a flight of stairs with a vertical height of 5.0 m. Calculate the gain in their gravitational potential energy. (g = 9.8 N/kg)3 marks
  4. A 0.5 kg ball is thrown with a velocity of 20 m/s. Calculate its kinetic energy.3 marks
  5. Describe the main energy transfers that occur when a moving car uses its brakes to stop. Start from the kinetic energy of the car.3 marks
  6. An electric motor has a power input of 500 W. It is used to lift a load, doing 1500 J of useful work in 5.0 s. Calculate the efficiency of the motor.4 marks
  7. A 2.0 kg rock is dropped from the top of a 40 m high cliff. Assuming all its gravitational potential energy is converted into kinetic energy, calculate its speed just before it hits the ground. (g = 9.8 N/kg)4 marks
  8. Person A (mass 60 kg) and Person B (mass 80 kg) both run up a 4.0 m high flight of stairs. Person A takes 5.0 s and Person B takes 7.0 s. Who is more powerful? Show your calculations. (g = 9.8 N/kg)5 marks
  9. An electric kettle with a power rating of 2200 W is used to heat 1.5 kg of water. It takes 3 minutes to raise the water's temperature by the desired amount, transferring 396,000 J of thermal energy to the water. Calculate the total energy supplied to the kettle and its efficiency.4 marks
  10. A solar panel with an area of 2 m² receives solar energy at a rate of 800 W/m². The panel has an efficiency of 20% in converting this solar energy to electrical energy. The electrical energy is then used to power a water pump that lifts 50 kg of water per minute from a well that is 10 m deep. Calculate the efficiency of the water pump. (g = 9.8 N/kg)6 marks

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