Energy, work and power Revision Notes

Kinetic energy is the energy an object possesses because of its motion. Any moving object, from a rolling ball to flowing water, stores energy kinetically.

The amount of kinetic energy (E_k) depends on the object's mass (m) and speed (v), calculated by the formula:

\[ E_k = \frac{1}{2} m v^2 \] where E_k is in joules (J), m in kilograms (kg), and v in metres per second (m/s). For example, a 2 kg ball moving at 3 m/s has kinetic energy: \[ E_k = \frac{1}{2} \times 2 \times 3^2 = 9 \text{ J} \]. This energy can be transferred or transformed, such as when the ball hits a wall and stops, transferring energy to the wall and surroundings.

• Depends on mass and velocity squared.
• Energy increases rapidly with speed.
• Examples: moving cars, flowing rivers, thrown stones.

Gravitational potential energy (GPE) is stored when an object is raised above a reference level, such as the ground. The higher the object, the more energy it stores due to Earth's gravity.

The change in gravitational potential energy when an object is lifted is given by:

\[ \Delta E_p = m g \Delta h \] where \( m \) is mass (kg), \( g \) is gravitational field strength (approximately 9.8 N/kg on Earth), and \( \Delta h \) is the change in height (m). For example, lifting a 5 kg box by 2 m stores: \[ \Delta E_p = 5 \times 9.8 \times 2 = 98 \text{ J} \]. This energy can convert back to kinetic energy if the object falls.

• Depends on mass, height, and gravity.
• Energy increases with height.
• Examples: water behind a dam, raised weights, climbers on a mountain.

Chemical energy is stored in the bonds between atoms and molecules. Fuels like petrol, food, and batteries contain chemical energy that can be released during chemical reactions.

For example, when wood burns, chemical energy converts to heat and light. Similarly, the body releases chemical energy from food during digestion to power muscles.

Chemical energy storage is vital for many processes, including metabolism, combustion, and battery operation.

• Stored in chemical bonds.
• Released or absorbed in chemical reactions.
• Examples: fuels, food, batteries.

Elastic energy is stored when materials are stretched, compressed, or bent, such as in springs or rubber bands. The energy is stored because the material resists deformation and tends to return to its original shape.

The amount of elastic energy stored depends on the force applied and the extent of deformation. For a spring obeying Hooke's law, elastic potential energy (E_e) is:

\[ E_e = \frac{1}{2} k x^2 \] where \( k \) is the spring constant (N/m) and \( x \) is the extension or compression (m). For example, stretching a spring with \( k = 100 \text{ N/m} \) by 0.05 m stores: \[ E_e = \frac{1}{2} \times 100 \times 0.05^2 = 0.125 \text{ J} \].

• Stored by deformation of elastic materials.
• Depends on force and displacement.
• Examples: stretched springs, compressed rubber balls.

Nuclear energy is stored in the nucleus of atoms, held by strong nuclear forces. This energy can be released during nuclear reactions such as fission (splitting nuclei) or fusion (combining nuclei).

For example, nuclear power plants release energy by splitting uranium nuclei, producing heat to generate electricity. The Sun’s energy comes from nuclear fusion of hydrogen nuclei.

Nuclear energy stores are extremely dense, meaning a small amount of material can release a large amount of energy.

• Stored in atomic nuclei.
• Released in nuclear reactions.
• Examples: nuclear reactors, the Sun.

Electrostatic energy is stored when electric charges are separated, creating an electric field. This energy is present in charged objects and capacitors.

For example, when you rub a balloon on your hair, electrons transfer, and the balloon stores electrostatic energy that can attract small pieces of paper.

The energy stored depends on the amount of charge and the distance between charges.

• Stored by separated electric charges.
• Depends on charge magnitude and distance.
• Examples: charged balloons, capacitors.

Energy is stored in different forms, such as kinetic, gravitational potential, chemical, thermal, and electrical energy. When energy moves from one store to another, it is called energy transfer. Understanding how energy transfers occur helps explain everyday phenomena and the operation of machines and devices.

Energy transfer always involves a process or mechanism that causes energy to move from one store to another. The total energy remains constant according to the conservation of energy principle, but the form and location of the energy change.

• Energy transfer changes the form or location of energy.
• Energy is conserved during transfer.
• Different processes transfer energy in different ways.

Mechanical work occurs when a force causes an object to move in the direction of the force. This transfers energy from one store to another, often from kinetic energy to gravitational potential energy or vice versa.

For example, when you lift a book from the floor to a shelf, your muscles do mechanical work on the book. Energy is transferred from the chemical energy store in your muscles to the gravitational potential energy store of the book.

The work done (W) by a force (F) moving an object through a distance (d) is calculated by the formula: W = F × d. The unit of work and energy is the joule (J). For instance, if you apply a force of 10 N to lift a book 2 m, the work done is W = 10 N × 2 m = 20 J, meaning 20 joules of energy have been transferred to the book’s gravitational store.

• Mechanical work involves force and displacement.
• Work done equals energy transferred.
• Example: lifting an object increases its gravitational potential energy.

Electrical work transfers energy through the movement of electric charges in a circuit. When charges move through a component like a resistor, energy is transferred from the electrical energy store to other forms, often thermal energy.

For example, in a toaster, electrical energy is transferred to thermal energy as the current passes through the heating element, causing it to heat up and toast the bread.

The energy transferred electrically can be calculated using the formula: E = V × Q, where E is energy in joules, V is potential difference in volts, and Q is charge in coulombs. Alternatively, power and time can be used: E = P × t, where power (P) is in watts and time (t) in seconds.

• Electrical work involves moving charges through a potential difference.
• Energy is often converted to thermal energy in resistors.
• Example: electrical energy heats a filament in a bulb.

Heating transfers energy from a hotter object to a cooler one, increasing the thermal energy of the cooler object. This transfer can occur via conduction, convection, or radiation.

For example, when a metal spoon is placed in hot water, thermal energy transfers from the water to the spoon by conduction, raising the spoon’s temperature.

Energy transfer by heating always occurs from higher to lower temperature until thermal equilibrium is reached.

• Heating transfers thermal energy between objects.
• Occurs via conduction, convection, or radiation.
• Example: warming hands near a fire by radiation.

Waves transfer energy without transferring matter. Mechanical waves, such as sound waves, transfer energy through vibrations in a medium like air or water. Electromagnetic waves, such as light, transfer energy through oscillating electric and magnetic fields and can travel through a vacuum.

For example, sound waves transfer energy from a vibrating speaker cone through air to your ear, allowing you to hear.

Light waves transfer energy from the Sun to Earth, enabling photosynthesis and warming the planet.

• Waves transfer energy without matter transfer.
• Mechanical waves need a medium; electromagnetic waves do not.
• Example: sound waves carry energy through air to your ear.

Energy is a quantity that can neither be created nor destroyed; it can only be transferred or transformed from one form to another. This fundamental principle is known as the conservation of energy.

In a closed system, where no energy enters or leaves, the total amount of energy remains constant over time. For example, when a pendulum swings, its energy continuously changes between kinetic energy (energy of motion) and gravitational potential energy (energy stored due to height), but the total energy stays the same, ignoring frictional losses.

Understanding this principle allows us to analyse how energy moves and changes form in physical processes.

• Energy cannot be created or destroyed.
• Energy can change form, e.g., kinetic to potential energy.
• Total energy in a closed system remains constant.

Consider a ball dropped from a height. Initially, it has gravitational potential energy due to its elevated position. As it falls, this potential energy converts into kinetic energy. Just before hitting the ground, the ball’s kinetic energy is at its maximum, and its potential energy is nearly zero.

If we ignore air resistance, the sum of kinetic and potential energy at any point during the fall remains constant, illustrating energy conservation.

In real situations, some energy may be lost as heat or sound due to air resistance or impact, but the total energy, including these forms, is still conserved.

• Energy transforms between stores during motion.
• Ignoring losses, total mechanical energy remains constant.
• Energy losses appear as heat, sound, or deformation.

Energy flow diagrams visually represent how energy is transferred and transformed in a system. They use arrows to show the direction and type of energy flow, with widths often proportional to the amount of energy.

For example, a flow diagram for an electric kettle might show electrical energy input, useful thermal energy output heating the water, and wasted energy lost to the surroundings as heat.

By interpreting these diagrams, we can identify how much energy is usefully transferred and how much is wasted, which is important for understanding efficiency and energy conservation in practical devices.

• Arrows represent energy transfers and transformations.
• Arrow width can indicate energy quantity.
• Useful and wasted energy flows are distinguished.
• Flow diagrams help analyse energy efficiency.

Imagine a 2 kg object dropped from a height of 5 m. Calculate the gravitational potential energy (GPE) at the start and the kinetic energy (KE) just before impact, assuming no energy losses.

Using the formula for GPE: E_p = mgh, where m = 2 kg, g = 9.8 m/s², h = 5 m, we get:

E_p = 2 × 9.8 × 5 = 98 J (joules). This is the energy stored due to height before the fall begins. Just before hitting the ground, this energy converts into kinetic energy: E_k = 98 J (assuming no losses). This shows energy conservation as total energy remains constant during the fall.

• Calculate GPE using E_p = mgh.
• At ground level, GPE converts to KE.
• Total mechanical energy remains constant if no losses.

Consider a simple energy flow diagram for a light bulb powered by electrical energy. The diagram shows electrical energy input, useful light energy output, and wasted heat energy.

If the electrical input is 100 J, and the useful light output is 20 J, then 80 J is wasted as heat.

This helps calculate efficiency: efficiency = (useful energy output / total energy input) × 100% = (20 / 100) × 100% = 20%. Understanding these flows helps improve device design to reduce wasted energy.

• Identify energy inputs and outputs in flow diagrams.
• Calculate efficiency from energy values.
• Recognise wasted energy reduces efficiency.

Kinetic energy is the energy an object possesses because of its motion. Any object moving with a velocity has kinetic energy, which depends on how much mass it has and how fast it is moving. For example, a moving car has kinetic energy, but a stationary car does not. This energy can be transferred or converted into other forms, such as heat or sound, when the object interacts with its environment.

• Kinetic energy relates to motion.
• It depends on mass and velocity.
• It is a scalar quantity measured in joules (J).

The kinetic energy (E_k) of an object is calculated using the formula:

E_k = 1/2 mv², where: m is the mass in kilograms (kg), and v is the velocity in metres per second (m/s).

This formula shows that kinetic energy increases linearly with mass but increases with the square of velocity. Therefore, doubling the velocity quadruples the kinetic energy, while doubling the mass only doubles the kinetic energy.

• E_k = 1/2 mv²
• m in kilograms (kg)
• v in metres per second (m/s)
• E_k in joules (J)

Consider a bicycle with a mass of 15 kg moving at 4 m/s. Calculate its kinetic energy.

Step 1: Identify values: m = 15 kg, v = 4 m/s. Step 2: Substitute into the formula: E_k = 1/2 × 15 × (4)² E_k = 0.5 × 15 × 16 E_k = 0.5 × 240 E_k = 120 J Step 3: State the answer with units: The kinetic energy is 120 joules.

This shows how to use the formula with correct substitution and units.

• Identify mass and velocity.
• Square the velocity before multiplying.
• Multiply by half the mass.
• Include units in the final answer.

Because velocity is squared in the formula, changes in velocity have a greater effect on kinetic energy than changes in mass. For example, if the velocity doubles, kinetic energy increases by a factor of four. If the mass doubles, kinetic energy only doubles.

Example: A 2 kg object moving at 3 m/s has kinetic energy: E_k = 1/2 × 2 × 3² = 1 × 9 = 9 J. If velocity doubles to 6 m/s: E_k = 1/2 × 2 × 6² = 1 × 36 = 36 J (four times greater). If mass doubles to 4 kg at 3 m/s: E_k = 1/2 × 4 × 3² = 2 × 9 = 18 J (twice as much).

• Velocity changes affect kinetic energy more than mass changes.
• Kinetic energy ∝ mass × velocity².
• Doubling velocity quadruples kinetic energy.
• Doubling mass doubles kinetic energy.

A frequent error is forgetting to square the velocity before multiplying by mass and 1/2. Another is mixing units, such as using grams instead of kilograms for mass or km/h instead of m/s for velocity, which leads to incorrect answers.

Always convert mass to kilograms and velocity to metres per second before calculation. Also, ensure the velocity is squared correctly.

Example of incorrect calculation: Using v = 5 m/s but calculating E_k = 1/2 × m × v = 1/2 × m × 5 instead of squaring 5 to get 25. This underestimates kinetic energy by a factor of 5.

• Always square velocity before multiplying.
• Use correct SI units: kg for mass, m/s for velocity.
• Convert units if necessary before calculation.
• Check calculations carefully.

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field, typically relative to a reference level such as the ground. When an object is raised to a higher position, work is done against gravity, and this work is stored as gravitational potential energy. Conversely, when the object falls, this stored energy converts to other forms, such as kinetic energy. Understanding how to quantify this energy change is essential for analysing energy transfers in mechanics.

• Energy stored due to position in a gravitational field.
• Depends on mass, height, and gravitational field strength.
• Reference level (zero potential energy) is arbitrary but must be consistent.

The change in gravitational potential energy (ΔE_p) when an object moves vertically is given by the product of its mass (m), the gravitational field strength (g), and the change in height (Δh).

Mass (m) is measured in kilograms (kg). It represents the amount of matter in the object.

Gravitational field strength (g) is the acceleration due to gravity, approximately 9.81 m/s² near Earth's surface. It quantifies the force per unit mass exerted by gravity downward. This value can vary slightly with location but is generally taken as 9.81 m/s² for calculations on Earth’s surface. Change in height (Δh) is the vertical displacement in metres (m). It is positive if the object moves upward and negative if it moves downward.

• ΔE_p = mgΔh calculates energy change due to vertical movement.
• m in kilograms, g in m/s², Δh in metres.
• Positive Δh means increase in potential energy; negative means decrease.

Consider a 2.0 kg book lifted from the floor to a shelf 1.5 m above. Calculate the increase in gravitational potential energy.

Step 1: Identify variables: m = 2.0 kg, g = 9.81 m/s², Δh = +1.5 m (upwards).

Step 2: Substitute into the formula: ΔE_p = mgΔh = 2.0 × 9.81 × 1.5 = 29.43 J (joules). Step 3: Interpret the result: The book’s gravitational potential energy increases by 29.43 J when lifted to the shelf.

• Use consistent units for mass, gravity, and height.
• Calculate product carefully to find energy change in joules.
• Positive result indicates energy stored in the object.

When an object is raised, work is done against gravity, increasing its gravitational potential energy. When it falls, the gravitational potential energy decreases, converting into kinetic energy or other forms. The sign of Δh determines whether energy is gained or lost in the gravitational store. This concept is crucial in energy conservation problems and understanding mechanical energy transformations.

• Positive Δh → increase in potential energy.
• Negative Δh → decrease in potential energy, energy released.
• Energy conservation links potential energy change to kinetic or other energy forms.

A common mistake is confusing the change in height (Δh) with the total height. Only the vertical displacement matters, not the absolute height unless referenced consistently.

Another error is using incorrect units or forgetting that g is approximately 9.81 m/s² on Earth. Using the wrong value for g leads to incorrect energy calculations.

It is also important to remember that ΔE_p represents a change in energy, not the total energy unless the initial energy is zero.

• Always use vertical displacement, not total height, for Δh.
• Use correct units and standard value for g unless otherwise specified.
• ΔE_p is change in energy, not absolute energy unless referenced.

Work is done when a force causes an object to move through a distance in the direction of the force. This mechanical work results in energy being transferred to or from the object or system.

Energy transfer means energy moves from one form or store to another or from one system to another. The amount of energy transferred is equal to the work done during the process.

In electrical processes, work done occurs when an electric current flows through a component, transferring energy from the electrical energy store to other forms such as heat, light, or kinetic energy.

• Work done = energy transferred.
• Mechanical work involves force and displacement.
• Electrical work involves current and voltage.

When a force F (in newtons) moves an object through a distance d (in metres) in the direction of the force, the work done W (in joules) is given by the formula:

\[ W = F \times d \] This work done transfers energy to the object, often increasing its kinetic or potential energy.

For example, lifting a book off the floor involves doing work against gravity, transferring energy to the book’s gravitational potential energy store.

• Work done (J) = Force (N) × Distance (m)
• Energy transferred increases kinetic or potential energy.
• Example: lifting an object increases gravitational potential energy.

In electrical circuits, work done is the energy transferred when charge moves through a potential difference.

The work done W (in joules) can be calculated using:

\[ W = V \times Q \] where V is the potential difference (volts) and Q is the charge (coulombs). Alternatively, using current I (amperes) and time t (seconds): \[ W = V \times I \times t \] This energy transfer powers devices, heats components, or produces light.

• Work done (J) = Potential difference (V) × Charge (C)
• Or Work done (J) = Voltage (V) × Current (A) × Time (s)
• Energy transferred powers electrical devices.

The principle of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed.

Work done in mechanical or electrical processes is exactly equal to the energy transferred between stores or systems.

For example, when a motor lifts a load, the electrical work done by the motor transfers energy from the electrical store to the gravitational potential energy store of the load.

• Energy is conserved during work processes.
• Work done equals energy transferred.
• Energy changes form but total energy remains constant.

A person pushes a box with a force of 50 N across a floor for 3 m. Calculate the work done and the energy transferred.

Using the formula: \[ W = F \times d = 50 \text{ N} \times 3 \text{ m} = 150 \text{ J} \]

Therefore, 150 joules of energy are transferred to the box, for example increasing its kinetic energy or overcoming frictional forces.

• Work done = 50 N × 3 m = 150 J
• Energy transferred = 150 J
• Units: newtons × metres = joules

Mechanical work occurs when a force causes an object to move in the direction of that force. This movement transfers energy from one object or system to another. If there is no displacement, or if the displacement is perpendicular to the force, no mechanical work is done.

For example, pushing against a stationary wall with a force does not do mechanical work because the wall does not move. Conversely, lifting a box off the ground involves work because the force applied (upwards) causes the box to move upwards.

• Work is energy transferred by a force moving an object.
• Displacement must be in the direction of the force for work to be done.
• No movement or movement perpendicular to force means no work done.

The amount of work done (W) by a force (F) moving an object through a distance (d) is calculated by the equation: W = F × d.

Here, W is work done measured in joules (J), F is the force in newtons (N), and d is the displacement in metres (m).

This formula assumes the force is constant and acts in the same direction as the displacement. If the force and displacement are at an angle θ, the work done is W = Fd cosθ, but this is beyond the core scope here.

• W = Fd where W is work (J), F is force (N), d is displacement (m).
• Work is scalar and measured in joules (J).
• Force and displacement must be in the same direction for this formula.

Mechanical work results in a change in the energy of the system. This can be expressed as W = ΔE, where ΔE is the change in energy.

For example, when lifting an object, work done increases its gravitational potential energy. When a force causes an object to accelerate, work done increases its kinetic energy.

This relationship emphasises that work is a means of transferring energy from one form or object to another.

• Work done equals the energy transferred: W = ΔE.
• Energy changes can be kinetic, potential, or other forms.
• Calculating work helps quantify energy transfer in mechanical processes.

Suppose a person pushes a box with a force of 50 N across a floor for 3 metres in the direction of the force. Calculate the work done.

Using W = Fd, substitute the values: W = 50 N × 3 m = 150 J.

Therefore, the person does 150 joules of work on the box, transferring energy to it, for example, increasing its kinetic energy or overcoming friction.

• Identify force and displacement in the same direction.
• Multiply force (N) by displacement (m) to find work (J).
• Check units and direction consistency.

If the force and displacement are not aligned, only the component of force in the direction of displacement does work.

If an object moves but the force applied is perpendicular (e.g., carrying a bag horizontally with an upward force), no mechanical work is done by that force.

Frictional forces can do negative work, removing energy from a system, often converting it to thermal energy.

• Work depends on force component along displacement.
• No work if force is perpendicular to movement.
• Friction can do negative work, reducing mechanical energy.

Fossil fuels such as coal, oil, and natural gas are formed from the remains of ancient plants and animals. They store chemical energy which is released by combustion (burning) to produce heat. This heat is commonly used to boil water, producing steam that drives turbines connected to electrical generators.

Biofuels are renewable fuels derived from recent organic matter like plants or animal waste. Examples include ethanol from sugarcane and biodiesel from vegetable oils. Like fossil fuels, biofuels release chemical energy through combustion, but they are considered more sustainable because their source materials can be regrown or replenished relatively quickly.

For example, a power station might burn coal to heat water in a boiler, producing steam at high pressure. The steam spins a turbine, which turns a generator to produce electricity. Similarly, a biofuel-powered generator might burn ethanol to produce heat for the same purpose.

• Fossil fuels release chemical energy by combustion to generate heat.
• Heat converts water to steam, which drives turbines for electricity.
• Biofuels are renewable and combusted similarly to fossil fuels.
• Both methods rely on thermal energy conversion.

Hydroelectric power uses the gravitational potential energy of water stored in reservoirs behind dams. When released, water flows downhill, turning turbines connected to generators.

Tidal energy exploits the rise and fall of sea levels caused by the gravitational pull of the moon and sun. Tidal barrages or underwater turbines convert this kinetic energy into electricity.

Wave energy captures the movement of surface waves on the ocean. Devices such as oscillating water columns or floating buoys convert wave motion into mechanical energy, which is then transformed into electrical energy by generators.

• Hydroelectric power converts potential energy of stored water into electricity.
• Tidal power uses predictable sea level changes to drive turbines.
• Wave energy captures kinetic energy from surface waves.
• All methods convert mechanical energy of moving water into electrical energy.

Geothermal energy taps heat stored beneath the Earth's surface, often near volcanic regions. Hot rocks heat underground water, producing steam that can be brought to the surface to drive turbines.

For example, in geothermal power plants, wells are drilled into hot rock formations. Steam or hot water is extracted and used to spin turbines connected to generators, producing electricity.

This method provides a reliable and continuous energy source, as the Earth's internal heat is constant and not weather-dependent.

• Geothermal energy uses Earth's internal heat to produce steam.
• Steam drives turbines to generate electricity.
• It is a stable, renewable energy source independent of weather.
• Requires drilling wells into hot underground reservoirs.

Nuclear fission involves splitting heavy atomic nuclei (such as uranium-235) into smaller nuclei, releasing a large amount of energy as heat.

In nuclear power plants, this heat is used to produce steam from water, which then drives turbines connected to electrical generators.

The process requires careful control using moderators and control rods to maintain a steady chain reaction and ensure safety.

• Nuclear fission splits heavy nuclei, releasing heat energy.
• Heat produces steam to drive turbines for electricity.
• Control rods regulate the fission chain reaction.
• Produces large amounts of energy with low fuel mass.

Solar energy can be converted directly into electricity using photovoltaic (PV) cells made of semiconductor materials. When sunlight hits these cells, it excites electrons, creating an electric current.

Alternatively, solar thermal systems use mirrors or lenses to concentrate sunlight to heat fluids, producing steam that drives turbines.

For example, rooftop solar panels use PV cells to power homes, while large solar thermal plants use concentrated sunlight to generate electricity on a larger scale.

• Photovoltaic cells convert sunlight directly into electricity.
• Solar thermal systems concentrate sunlight to produce steam.
• Solar energy is renewable and abundant during daylight hours.
• PV systems are scalable from small to large installations.

Wind turbines convert the kinetic energy of moving air into mechanical energy by rotating blades connected to a generator.

The generator then converts this mechanical energy into electrical energy.

Wind farms, consisting of multiple turbines, are often located in areas with consistent wind speeds, such as coastal regions or open plains.

• Wind turbines convert wind kinetic energy into electricity.
• Blades rotate a generator to produce electrical power.
• Wind energy is renewable but variable depending on weather.
• Wind farms maximize electricity generation by using many turbines.

Efficiency is a measure of how well energy is converted from one form to another during a transfer process. It is expressed as the ratio of useful energy output to total energy input, often shown as a percentage. A high efficiency means most of the input energy is usefully transferred, while a low efficiency means much energy is lost, usually as heat or sound.

For example, when an electric heater converts electrical energy into heat, nearly all the input energy becomes useful heat, so efficiency is close to 100%. In contrast, a petrol engine converts chemical energy into kinetic energy, but much energy is lost as heat and sound, so efficiency is lower.

• Efficiency = (Useful energy output / Total energy input) × 100%
• Efficiency indicates the effectiveness of energy conversion
• Efficiency is always less than or equal to 100%

Energy transfer processes are never perfectly efficient because some energy is always dissipated in forms that are not useful for the intended purpose. Common energy losses include friction, heat generation, sound, and deformation.

For instance, in mechanical systems, friction between moving parts converts some kinetic energy into heat, which is not useful for the system’s main function. Similarly, electrical resistance in wires converts electrical energy into heat, reducing efficiency.

These unavoidable losses mean that the useful energy output is always less than the total energy input.

• Energy losses occur due to friction, heat, sound, and other dissipative effects
• These losses reduce the useful energy output
• No real system achieves 100% efficiency

Efficiency can be calculated using energy values or power values. The general formula is:

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

or equivalently, using power: Efficiency = (Useful power output / Total power input) × 100%.

• Use consistent units for energy (joules) or power (watts)
• Express efficiency as a percentage
• Example: A motor uses 200 J of electrical energy and produces 150 J of mechanical energy. Efficiency = (150 J / 200 J) × 100% = 75%

Several factors influence the efficiency of energy transfer processes. These include:

Friction between moving parts, which converts kinetic energy into heat

Electrical resistance in circuits, causing energy loss as heat in wires and components - Air resistance and drag in moving objects, dissipating energy as sound and heat - Imperfect insulation, allowing heat to escape from systems - Mechanical deformation, where energy is used to permanently change shape rather than perform useful work

• Reducing friction and resistance improves efficiency
• Better insulation reduces heat loss
• Design improvements can minimise energy wasted as sound or deformation

Consider a light bulb: an incandescent bulb converts electrical energy into light and heat, but most energy is lost as heat, so efficiency is low (around 5-10%). In contrast, LED bulbs convert a higher proportion of electrical energy into light, achieving efficiencies above 20%.

In a car engine, chemical energy from fuel is converted into kinetic energy to move the vehicle, but much energy is lost as heat through the exhaust and engine cooling system, resulting in efficiencies typically around 25-30%.

• Incandescent bulbs have low efficiency due to heat loss
• LED bulbs are more efficient light sources
• Car engines have limited efficiency due to heat and friction losses

Solar radiation, the energy emitted by the Sun in the form of electromagnetic waves, is the fundamental source of energy for most processes and resources on Earth. This energy reaches the Earth’s surface and drives natural phenomena such as photosynthesis in plants, which forms the base of most food chains and biomass energy sources.

Solar energy also powers the water cycle by heating oceans and land, causing evaporation and precipitation, which in turn supports hydroelectric power and other water-based energy systems.

Because solar radiation fuels these processes, many renewable energy resources—such as wind, biofuels, and hydropower—are indirectly dependent on the Sun’s energy.

• Solar radiation provides energy for photosynthesis, supporting biomass fuels.
• It drives the water cycle, enabling hydropower and wave energy.
• Wind energy results from solar heating causing air movement.

Unlike solar-dependent resources, geothermal energy originates from heat stored within the Earth’s interior. This heat comes from the decay of radioactive elements and residual heat from the planet’s formation.

Geothermal energy is harnessed by tapping into hot rocks or steam reservoirs underground to generate electricity or provide heating.

Because it does not rely on solar radiation, geothermal energy is available continuously, independent of weather or time of day, making it a reliable energy source in suitable locations.

• Geothermal energy comes from radioactive decay and Earth's formation heat.
• It is extracted by drilling wells to access hot underground reservoirs.
• It provides a steady energy supply regardless of solar input.

Nuclear energy is produced by nuclear fission reactions in reactors, where heavy atomic nuclei split to release large amounts of energy.

This energy source is independent of solar radiation because it originates from the strong nuclear forces within atoms rather than from the Sun.

Nuclear power plants convert this energy into electricity, providing a significant portion of the world's energy supply without relying on solar input.

• Nuclear energy arises from splitting atomic nuclei (fission).
• It does not depend on solar radiation.
• Used in power plants to generate electricity.

Tidal energy is generated by the gravitational pull of the Moon and the Sun on Earth's oceans, causing regular rises and falls in sea level known as tides.

This energy source is independent of solar radiation because it is driven by gravitational interactions rather than solar heating.

Tidal power plants capture the kinetic and potential energy of moving water during tidal changes to produce electricity.

• Tidal energy results from gravitational forces, not solar radiation.
• It depends on the relative positions of the Moon, Sun, and Earth.
• It provides predictable and renewable energy from ocean tides.

Recognising that most energy resources depend on solar radiation helps understand the interconnectedness of Earth's energy systems.

Knowing the exceptions—geothermal, nuclear, and tidal energy—is important for energy planning and sustainability discussions, as these sources provide alternatives that are not limited by solar availability.

This distinction also aids in evaluating the reliability and environmental impact of different energy sources.

• Most energy resources are solar-driven, directly or indirectly.
• Geothermal, nuclear, and tidal energies are notable exceptions.
• Understanding these differences supports informed energy choices.

The Sun is a massive star that emits energy continuously in the form of light and heat. This energy originates from its core, where extremely high temperatures and pressures allow nuclear reactions to occur. Unlike chemical reactions, which involve electrons, these nuclear reactions involve changes in the nuclei of atoms, releasing much more energy per reaction.

• Energy from the Sun powers Earth's climate and ecosystems.
• The Sun's energy output is enormous and sustained over billions of years.

At the Sun's core, hydrogen nuclei (protons) collide with such force that they overcome their natural repulsion and fuse together. This fusion process combines hydrogen nuclei to form helium nuclei. During this process, a small amount of mass is converted into energy according to Einstein's equation, E=mc², where m is the mass lost and c is the speed of light.

This energy is released mainly as electromagnetic radiation (light) and thermal energy (heat), which eventually reaches Earth.

• Fusion combines four hydrogen nuclei into one helium nucleus.
• Mass difference between reactants and products converts to energy.
• Energy released sustains the Sun's radiation output.

The total mass of the helium nucleus produced is slightly less than the combined mass of the four original hydrogen nuclei. This 'missing' mass has been converted into energy. Because the Sun contains an enormous number of hydrogen nuclei undergoing fusion every second, the total energy released is immense.

This energy travels outward from the core through radiation and convection before escaping the Sun's surface as sunlight.

• Mass-energy equivalence explains energy release.
• Continuous fusion reactions maintain the Sun's brightness.
• Energy output is stable over long periods.

The energy produced by nuclear fusion in the Sun is fundamental to life on Earth. It drives photosynthesis in plants, influences weather and climate, and provides the energy source for many renewable energy technologies such as solar panels.

Understanding that the Sun's energy comes from fusion helps explain why the Sun shines steadily and why it has such a long lifespan compared to chemical energy sources.

• Solar energy supports ecosystems and human activities.
• Fusion energy is far more powerful than chemical energy.
• Solar energy is the primary energy source for most natural processes on Earth.

In summary, the Sun produces energy through nuclear fusion, where hydrogen nuclei fuse to form helium, releasing energy as light and heat. Detailed mechanisms of the fusion process are beyond this level, but recognising fusion as the Sun's energy source is essential for understanding energy in the universe.

• Fusion occurs in the Sun's core under extreme conditions.
• Hydrogen nuclei combine to form helium nuclei.
• Energy released sustains sunlight and heat.
• This energy supports life and natural processes on Earth.

Nuclear fission is a process in which the nucleus of a heavy atom, such as uranium-235 or plutonium-239, splits into two smaller nuclei. This splitting releases a considerable amount of energy. The energy comes from the conversion of some of the mass of the original nucleus into energy, as described by Einstein's equation E=mc².

In nuclear reactors, this energy release is harnessed to produce heat, which is then used to generate electricity. Although the detailed steps of how the nucleus splits are complex, it is sufficient to know that fission results in energy release.

• Heavy atomic nuclei split into smaller nuclei.
• Mass is converted into energy during fission.
• Energy released is harnessed in nuclear reactors.

When a nucleus undergoes fission, it releases energy mainly in the form of kinetic energy of the fission fragments and neutrons. This kinetic energy is transferred to the surrounding material as heat.

In a nuclear reactor, this heat energy is used to produce steam from water. The steam then drives turbines connected to electrical generators, producing electricity.

The process is controlled carefully to maintain a steady rate of fission and energy release, ensuring safe and continuous power generation.

• Fission releases kinetic energy converted to heat.
• Heat produces steam to drive turbines.
• Controlled reaction maintains steady energy output.

For this objective, it is not necessary to understand the detailed nuclear reactions, such as neutron absorption, chain reactions, or the exact splitting process.

The focus is on recognising that nuclear fission is a source of energy in reactors and that this energy can be harnessed for practical use.

This approach allows students to grasp the concept of nuclear energy without requiring advanced nuclear physics knowledge.

• Detailed nuclear reactions are beyond this scope.
• Key point is energy release from fission.
• Focus on practical energy use in reactors.

When a uranium-235 nucleus absorbs a neutron, it becomes unstable and splits into smaller nuclei, releasing about 200 million electron volts (MeV) of energy per fission event.

This energy is millions of times greater than the energy released in typical chemical reactions, such as burning fossil fuels.

This large energy release per atom makes nuclear fission a very powerful energy source.

• Uranium-235 fission releases ~200 MeV per event.
• Energy per fission far exceeds chemical reactions.
• Enables high energy density in nuclear fuel.

Nuclear reactors use control rods to absorb excess neutrons and regulate the fission rate, preventing the reaction from accelerating uncontrollably.

Coolants remove heat from the reactor core to transfer it safely to the steam generators.

Safety systems ensure that energy release is controlled and that the reactor operates within safe limits.

• Control rods regulate fission rate.
• Coolants transfer heat safely.
• Safety systems prevent uncontrolled reactions.

Efficiency is a measure of how well a system converts the energy or power supplied to it into useful output. It shows the effectiveness of energy transfer or transformation processes. Since some energy is often lost to the surroundings (for example, as heat, sound, or friction), efficiency helps quantify how much of the input energy is actually used for the intended purpose.

Efficiency is always expressed as a percentage, where 100% means all input energy is converted into useful output with no losses, which is practically impossible due to inevitable energy dissipation. Therefore, efficiency values are typically less than 100%.

• Efficiency indicates the effectiveness of energy conversion.
• It is expressed as a percentage.
• Efficiency values range from 0% to 100%.

Efficiency can be calculated by comparing the useful energy output to the total energy input. The formula is:

\[ \text{Efficiency} = \left( \frac{\text{Useful energy output}}{\text{Total energy input}} \right) \times 100\% \]

Here, 'useful energy output' is the amount of energy that performs the desired work or function, while 'total energy input' is the energy supplied to the system. Both quantities must be in the same units, typically joules (J).

• Efficiency = (Useful energy output / Total energy input) × 100%
• Energy values must be in joules (J)
• Efficiency is unitless but expressed as a percentage

Efficiency can also be calculated using power values, which represent the rate of energy transfer per unit time. The formula is:

\[ \text{Efficiency} = \left( \frac{\text{Useful power output}}{\text{Total power input}} \right) \times 100\% \]

Power values must be in the same units, usually watts (W). This method is useful when dealing with systems where energy transfer rates are more relevant than total energy amounts.

• Efficiency = (Useful power output / Total power input) × 100%
• Power values must be in watts (W)
• Useful for systems analysed by rates of energy transfer

A motor receives 500 J of electrical energy and delivers 400 J of mechanical energy to lift a load. Calculate the efficiency of the motor.

Step 1: Identify useful energy output = 400 J, total energy input = 500 J.

Step 2: Substitute into the formula: Efficiency = (400 J / 500 J) × 100% = 0.8 × 100% = 80%.

• Efficiency = (400 J / 500 J) × 100% = 80%
• The motor converts 80% of electrical energy into useful mechanical energy

A light bulb consumes electrical power of 60 W but only emits 15 W of visible light. Calculate the efficiency of the bulb in converting electrical power to visible light.

Step 1: Useful power output = 15 W, total power input = 60 W.

Step 2: Efficiency = (15 W / 60 W) × 100% = 0.25 × 100% = 25%.

• Efficiency = (15 W / 60 W) × 100% = 25%
• Only 25% of electrical power is converted to visible light; the rest is lost as heat

Power is a physical quantity that measures how fast work is done or energy is transferred. It is not just the amount of work or energy involved, but how quickly this happens. For example, lifting a heavy box slowly requires less power than lifting it quickly, even though the work done is the same.

Power is therefore defined as the rate of doing work or transferring energy, meaning the amount of work or energy transferred per unit time. This concept helps us understand the efficiency and performance of machines and processes.

• Power relates to speed of energy transfer, not just amount of energy.
• It is a scalar quantity measured in watts (W).
• 1 watt equals 1 joule of work done or energy transferred per second.

The two main equations for power are: P = W/t and P = E/t. Here, P stands for power, W for work done, E for energy transferred, and t for the time taken.

These formulas mean that power is calculated by dividing the total work done or energy transferred by the time over which this occurs. If the same amount of work is done in less time, the power is higher.

For example, if a machine does 100 joules of work in 5 seconds, its power output is P = 100 J / 5 s = 20 W.

• P = W/t where W is work done in joules and t is time in seconds.
• P = E/t where E is energy transferred in joules and t is time in seconds.
• Power is measured in watts (W), where 1 W = 1 J/s.

Work done and energy transferred are closely related concepts; work done on an object transfers energy to it. Power links these to time, showing how quickly this transfer happens.

For example, when you push a box across the floor, the work you do transfers energy to the box and the floor (mainly as heat due to friction). The power tells us how fast this energy transfer occurs.

Understanding this relationship helps in analysing mechanical systems, electrical devices, and other energy transfer processes.

• Work done equals energy transferred in mechanical processes.
• Power measures how fast this energy transfer or work occurs.
• Higher power means faster energy transfer or work done.

Consider a motor that lifts a 50 kg weight vertically by 10 metres in 4 seconds. Calculate the power output of the motor.

First, calculate the work done, which equals the change in gravitational potential energy: W = mgh, where m = 50 kg, g = 9.8 m/s², h = 10 m.

W = 50 × 9.8 × 10 = 4900 J (joules). Next, calculate power: P = W/t = 4900 J / 4 s = 1225 W (watts). The motor’s power output is 1225 watts, meaning it transfers energy at this rate while lifting the weight.

• Work done = mgh = 50 × 9.8 × 10 = 4900 J.
• Power = Work done / time = 4900 J / 4 s = 1225 W.
• Power indicates how quickly the motor transfers energy to lift the weight.

Power is measured in watts (W), where 1 watt equals 1 joule per second. Larger power values are often expressed in kilowatts (kW), where 1 kW = 1000 W.

In practical situations, power ratings help compare machines and devices. For example, a 100 W light bulb uses energy at a rate of 100 joules per second.

When measuring power experimentally, it is important to measure work or energy transferred accurately and record the time taken precisely to calculate power reliably.

• Power unit: watt (W) = joule/second (J/s).
• Kilowatt (kW) = 1000 watts, used for larger power values.
• Accurate measurement of work/energy and time is essential for correct power calculation.