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Physics: Energy

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Physics: Energy
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1. Energy and Its Conservation

In physics, energy is the capacity to do work. It's what makes things happen – from a ball rolling down a hill to the Sun shining. The standard unit for energy is the Joule (J). The single most important rule in this topic is the Principle of Conservation of Energy. This principle states that energy cannot be created or destroyed, only transferred from one form to another. For example, when you switch on a lamp, electrical energy is not 'used up'; it is transferred into light energy and thermal energy (heat). The total amount of energy before and after the transfer remains exactly the same.

Key term

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

Examiner insight

Examiners often test the Principle of Conservation of Energy in questions about energy transfers, so always be ready to state it clearly and apply it to the situation described.

Common pitfall

Stating that energy is 'lost' or 'used up'. You must always specify where the energy has been transferred to, for example, 'transferred to the surroundings as thermal energy'.

Worked example 14 marks

A battery-powered toy car is switched on and moves across the floor. It eventually slows down and stops. Describe the energy transfers that take place, from switching it on to stopping, according to the Principle of Conservation of Energy. [4 marks]

  1. 1

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

  2. 2

    Step 2: Describe the first transfer. The chemical energy is transferred into electrical energy in the wires.

  3. 3

    Step 3: Describe the main useful transfer. The electrical energy is transferred by the motor into kinetic energy (movement) of the car.

  4. 4

    Step 4: Account for the 'lost' energy. As the car moves, energy is also transferred to the surroundings as thermal energy due to friction with the floor and air resistance, and as sound energy. When the car stops, all the initial chemical energy has been transferred to these stores.

Recap

  • Energy is the capacity to do work, measured in Joules (J).
  • The Principle of Conservation of Energy states that energy is never created or destroyed.
  • Energy is transferred from one store to another.
  • In any energy transfer, the total energy remains constant.

Quick check

  1. What is the unit of energy?1 mark
  2. State the Principle of Conservation of Energy.1 mark

2. Energy Stores and Pathways

To make sense of energy transfers, we think of energy as being held in different 'stores'. When something happens, energy is transferred from one store to another along a 'pathway'. There are 8 main stores you need to know:

  1. Kinetic: The energy of a moving object.
  2. Gravitational Potential (GPE): Energy stored by an object due to its height in a gravitational field.
  3. Chemical: Energy stored in the bonds between atoms, found in food, fuels, and batteries.
  4. Elastic Potential: Energy stored when an object is stretched or compressed, like in a spring or rubber band.
  5. Thermal: The internal energy of an object due to the motion of its particles – what we feel as 'heat'.
  6. Nuclear: Energy stored in the nucleus of an atom.
  7. Magnetic: Energy stored in the magnetic field between magnets.
  8. Electrostatic: Energy stored between charged objects.

Energy moves from one store to another via one of four pathways:

  • Mechanical Working: A force moving an object (e.g., pushing a box).
  • Electrical Working: Charges moving due to a potential difference (e.g., a current in a circuit).
  • Heating: Energy transferred due to a temperature difference.
  • Radiation: Energy transferred as waves (e.g., light from the sun or sound from a speaker).

Key term

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

Fun fact

A single lightning bolt can contain enough energy to power a 100-watt light bulb for more than three months!

Worked example 13 marks

A person fires a stone from a catapult. Identify the main energy stores and transfers, starting from the stretched catapult to the stone flying through the air. [3 marks]

  1. 1

    Step 1: The stretched catapult contains elastic potential energy.

  2. 2

    Step 2: When released, this elastic potential energy is transferred to the stone as kinetic energy.

  3. 3

    Step 3: As the stone flies upwards, its kinetic energy is transferred into gravitational potential energy. Some energy is also transferred to the surroundings as thermal energy due to air resistance.

Recap

  • Energy is held in stores, such as kinetic, potential, chemical, and thermal.
  • Energy is transferred between stores via pathways: mechanical, electrical, heating, or radiation.
  • A falling object transfers gravitational potential energy to kinetic energy.
  • A battery transfers chemical energy via an electrical pathway.

Quick check

  1. Name the energy store associated with a moving car.1 mark
  2. Name the energy store in a stretched rubber band.1 mark

3. Kinetic Energy (KE)

Kinetic energy is the energy of motion. Any object that is moving has kinetic energy. The amount of kinetic energy an object has depends on two things: its mass(m) and its velocity (v). A heavier object or a faster object will have more kinetic energy. The relationship is described by the formula: Kinetic Energy = ½ × mass × velocity². Notice that the velocity is squared, which means that doubling the velocity of an object quadruples its kinetic energy. This is why high-speed crashes are so much more destructive.

KE = ½ × m × v²

Key term

Kinetic Energy (KE): The energy an object possesses due to its motion, measured in Joules (J).

Examiner insight

Marks are often awarded for showing the correct substitution into the formula, so write it out clearly even if your final answer is wrong.

Common pitfall

Forgetting to square the velocity (v) in the kinetic energy equation. This is the most frequent calculation error.

Worked example 13 marks

A car of mass 1200 kg is travelling at a velocity of 20 m/s. Calculate its kinetic energy. [3 marks]

  1. 1

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

  2. 2

    Step 2: Substitute the known values into the formula. KE = ½ × 1200 kg × (20 m/s)²

  3. 3

    Step 3: Calculate the final answer with units. KE = 600 × 400 = 240,000 J (or 240 kJ).

Worked example 24 marks

A ball has a kinetic energy of 50 J and a mass of 0.4 kg. Calculate its velocity. [4 marks]

  1. 1

    Step 1: Write down the formula. KE = ½ × m × v²

  2. 2

    Step 2: Rearrange the formula to make v the subject. 2 × KE = m × v² => v² = (2 × KE) / m => v = √((2 × KE) / m)

  3. 3

    Step 3: Substitute the values. v = √((2 × 50 J) / 0.4 kg)

  4. 4

    Step 4: Calculate the final answer. v = √(100 / 0.4) = √250 = 15.8 m/s (to 3 s.f.).

Recap

  • Kinetic energy is the energy of a moving object.
  • The formula for kinetic energy is KE = ½ × m × v².
  • Kinetic energy is measured in Joules (J).
  • Mass (m) is in kilograms (kg) and velocity (v) is in metres per second (m/s).
  • Doubling the velocity of an object increases its kinetic energy by a factor of four.

Quick check

  1. A 2 kg object moves at 10 m/s. What is its kinetic energy?2 marks

4. Gravitational Potential Energy (GPE)

Gravitational Potential Energy (GPE) is the energy an object stores because of its position in a gravitational field. When you lift an object, you do work against gravity, and this work is stored as GPE. If you let go, this stored energy is converted into kinetic energy as the object falls. The amount of GPE an object has depends on its mass (m), the strength of the gravitational field it is in (g), and its vertical height(h) above a reference point. On Earth, g is approximately 9.8 N/kg (or often rounded to 10 N/kg in exams).

GPE = m × g × h

Key term

Gravitational Potential Energy (GPE): The energy an object possesses due to its position in a gravitational field, measured in Joules (J).

Examiner insight

Be prepared for questions that combine GPE and KE. You must be able to state that GPE lost equals KE gained (or vice versa) in the absence of friction.

Common pitfall

Using the distance moved along a slope instead of the vertical height change (h) when calculating GPE.

Worked example 13 marks

A book with a mass of 1.5 kg is lifted from the floor onto a shelf that is 2 m high. Calculate the gain in its gravitational potential energy. (Take g = 9.8 N/kg). [3 marks]

  1. 1

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

  2. 2

    Step 2: Substitute the known values. GPE = 1.5 kg × 9.8 N/kg × 2 m

  3. 3

    Step 3: Calculate the final answer with units. GPE = 29.4 J.

Worked example 24 marks

A 60 kg diver stands on a diving board 5 m above the water. They fall towards the water. Assuming no air resistance, what is their speed just before they hit the water? (Take g = 10 N/kg). [4 marks]

  1. 1

    Step 1: State the energy transfer. The diver's GPE at the top is converted into KE at the bottom. So, GPE lost = KE gained.

  2. 2

    Step 2: Write the equation for this transfer. m × g × h = ½ × m × v²

  3. 3

    Step 3: Simplify the equation (mass cancels out). g × h = ½ × v². Rearrange for v: v = √(2 × g × h)

  4. 4

    Step 4: Substitute values and calculate. v = √(2 × 10 N/kg × 5m) = √100 = 10 m/s.

Recap

  • GPE is energy stored due to an object's height.
  • The formula for GPE is GPE = m × g × h.
  • GPE is measured in Joules (J).
  • Mass (m) is in kg, gravitational field strength (g) is in N/kg, and height (h) is in metres (m).
  • When an object falls, its GPE is converted into KE.

Quick check

  1. Calculate the GPE gained by a 5 kg mass when lifted by 3 m. (Take g = 10 N/kg).2 marks

5. Work Done and Energy Transfer

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. For example, when you push a box across the floor, you are doing work on the box, and you are transferring energy to it (as kinetic energy and thermal energy due to friction). The amount of work done is calculated by multiplying the force applied by the distance the object moves in the direction of the force. Since work is a measure of energy transfer, it is also measured in Joules (J).

Work Done (W) = Force (F) × distance (d)

Key term

Work Done: The energy transferred when a force causes an object to move a certain distance in the direction of the force.

Examiner insight

Questions often link work done to a change in kinetic or gravitational potential energy. You must be able to state that the work done on an object equals the energy it gains.

Worked example 13 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. [3 marks]

  1. 1

    Step 1: Write down the formula for work done. Work Done = Force × distance

  2. 2

    Step 2: Substitute the known values. Work Done = 50 N × 20 m

  3. 3

    Step 3: Calculate the final answer with units. Work Done = 1000 J (or 1 kJ).

Worked example 24 marks

A crane lifts a 500 kg crate vertically by 12 m. Calculate the work done by the crane. (Take g = 10 N/kg). [4 marks]

  1. 1

    Step 1: Identify that the work is done against gravity. Therefore, the force required is the weight of the crate.

  2. 2

    Step 2: Calculate the weight of the crate. Force (Weight) = mass × g = 500 kg × 10 N/kg = 5000 N.

  3. 3

    Step 3: Use the work done formula. Work Done = Force × distance = 5000 N × 12 m.

  4. 4

    Step 4: Calculate the final answer. Work Done = 60,000 J (or 60 kJ). Note: This is equal to the GPE gained by the crate.

Recap

  • Work is done when a force moves an object.
  • Work done is equal to the energy transferred.
  • The formula for work done is W = F × d.
  • Work done is measured in Joules (J).
  • Force is in Newtons (N) and distance is in metres (m).

Quick check

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

6. Power: The Rate of Energy Transfer

Power is the rate at which energy is transferred, or the rate at which work is done. It's not just about how much energy is used, but how quickly it is used. For example, two kettles might use the same total energy to boil water, but the more powerful kettle will do it faster. The unit of power is the Watt (W), which is defined as one Joule of energy transferred per second (1 W = 1 J/s). A 100 W light bulb transfers 100 Joules of energy every second.

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

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

Key term

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

Common pitfall

Confusing energy and power. Energy is the total amount (in Joules), while power is how quickly that energy is used (in Joules per second, or Watts).

Fun fact

A human heart has a power output of about 1-5 Watts, while a Tour de France cyclist can sustain over 400 Watts for an hour.

Worked example 13 marks

An electric motor transfers 12,000 J of energy in 60 seconds. Calculate its power. [3 marks]

  1. 1

    Step 1: Write down the formula for power. Power = Energy transferred / time

  2. 2

    Step 2: Substitute the known values. Power = 12,000 J / 60 s

  3. 3

    Step 3: Calculate the final answer with units. Power = 200 W.

Worked example 25 marks

A lift with a total mass of 800 kg moves upwards a distance of 15 m in 30 s. Calculate the power output of the lift motor. (Take g = 10 N/kg). [5 marks]

  1. 1

    Step 1: First, calculate the work done. This is the GPE gained by the lift. GPE = m × g × h

  2. 2

    Step 2: Substitute values to find GPE. GPE = 800 kg × 10 N/kg × 15 m = 120,000 J. This is the work done.

  3. 3

    Step 3: Now use the power formula. Power = Work done / time

  4. 4

    Step 4: Substitute the work done and time. Power = 120,000 J / 30 s

  5. 5

    Step 5: Calculate the final answer. Power = 4000 W (or 4 kW).

Recap

  • Power is the rate of energy transfer or work done.
  • The unit of power is the Watt (W).
  • One Watt is equal to one Joule per second (1 W = 1 J/s).
  • The formula for power is P = E / t or P = W / t.
  • A more powerful device transfers energy more quickly.

Quick check

  1. An engine does 500 J of work in 10 s. What is its power?2 marks

7. Energy Efficiency and Dissipation

When energy is transferred, some of it is transferred to a useful energy store, but some is always transferred to less useful stores. This 'wasted' energy is said to be dissipated, which usually means it is transferred to the surroundings as thermal energy, making them warmer. For example, a light bulb is designed to produce light (useful energy), but it also gets hot (wasted thermal energy). Efficiency is a measure of how good a device is at transferring energy into the useful form. It is calculated as the ratio of the useful energy output to the total energy input. Efficiency can be given as a decimal (e.g., 0.8) or a percentage (e.g., 80%). No device is 100% efficient due to the dissipation of energy.

Efficiency = Useful energy output / Total energy input

Efficiency = Useful power output / Total power input

Key term

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

Examiner insight

When asked about improving efficiency, your answer should focus on reducing the wasted energy transfer, for example by using lubrication to reduce friction or insulation to reduce heat loss.

Common pitfall

Giving efficiency as a value greater than 1 or 100%. Efficiency can never be more than 100% due to the principle of conservation of energy.

Worked example 13 marks

A light bulb is supplied with 100 J of electrical energy. It converts 20 J into light energy. Calculate its efficiency. [3 marks]

  1. 1

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

  2. 2

    Step 2: Substitute the values. Efficiency = 20 J / 100 J

  3. 3

    Step 3: Calculate the final answer. Efficiency = 0.2. To express as a percentage, multiply by 100: 0.2 × 100 = 20%.

Worked example 24 marks

An electric motor has a power input of 500 W. It has a useful power output of 400 W.a) How much power is wasted?b) What is the efficiency of the motor? [4 marks]

  1. 1

    Parta) Step 1: Wasted power = Total power input - Useful power output.

  2. 2

    Parta) Step 2: Wasted power = 500 W - 400 W = 100 W.

  3. 3

    Partb) Step 1: Use the power efficiency formula. Efficiency = Useful power output / Total power input.

  4. 4

    Partb) Step 2: Substitute values. Efficiency = 400 W / 500 W = 0.8 or 80%.

Recap

  • Useful energy is the energy transferred for the intended purpose.
  • Wasted energy is energy that is dissipated, usually as heat, to the surroundings.
  • Efficiency measures how much input energy is converted to useful output energy.
  • The formula for efficiency is (useful output / total input).
  • Efficiency can be expressed as a decimal or a percentage.
  • No device can be more than 100% efficient.

Quick check

  1. A machine uses 200 J of energy and produces 50 J of useful energy. What is its efficiency?2 marks

End-of-chapter exercise

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

  1. Define power and state its SI unit.2 marks
  2. A 1500 kg car accelerates from rest to a speed of 30 m/s. Calculate the kinetic energy of the car at this speed.3 marks
  3. A student of mass 55 kg runs up a flight of stairs. The vertical height of the stairs is 4.5 m. Calculate the gravitational potential energy gained by the student. (Take g = 9.8 N/kg).3 marks
  4. A builder does 2500 J of work to lift a bag of cement a vertical distance of 10 m. Calculate the force the builder applied.3 marks
  5. An electric kettle has a power rating of 2.2 kW. It takes 2 minutes to boil a quantity of water. Calculate the total energy transferred by the kettle in this time.4 marks
  6. An apple of mass 0.2 kg falls from a branch 3 m above the ground. By considering the transfer of energy, calculate the speed of the apple just before it hits the ground. Assume air resistance is negligible. (Take g = 10 N/kg).4 marks
  7. An electric motor is used to lift a 200 kg load. The motor has a power input of 1.2 kW and is 75% efficient. Calculate the useful power output of the motor.3 marks
  8. Describe the main energy transfers that occur when a moving car brakes to a stop.3 marks
  9. A powerful engine can lift a 12,000 N load at a constant velocity of 1.5 m/s. Calculate the power output of the engine.4 marks
  10. A solar panel receives 60,000 J of energy from the sun every minute. It produces 150 W of useful electrical power. Calculate the efficiency of the solar panel.5 marks

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