Energy Revision Notes

Energy is the capacity to do work or produce change and can be stored in different ways within physical systems. These stores represent where energy is held before it is transferred or transformed. Recognising the various forms of energy storage helps in understanding energy conservation and transfer in physics.

• Energy stores are scalar quantities measured in joules (J).
• Energy can be transferred between stores but the total energy remains constant (conservation of energy).

Kinetic energy is the energy an object possesses due to its motion. Any moving object has kinetic energy proportional to its mass and the square of its speed.

The formula for kinetic energy (E_k) is: E_k = ½ mv², where m is mass in kilograms (kg) and v is speed in metres per second (m/s).

This energy store increases as an object moves faster or has more mass.

• Example: A moving car, a thrown ball, or flowing water all have kinetic energy.
• Kinetic energy is always positive or zero (when the object is stationary).

Gravitational potential energy is energy stored by an object due to its position in a gravitational field, typically related to its height above a reference point such as the ground.

The change in gravitational potential energy (∆E_p) when an object is raised or lowered is given by: ∆E_p = mg∆h, where m is mass (kg), g is gravitational field strength (9.8 N/kg near Earth's surface), and ∆h is the change in height (m).

Energy is stored because work is done against gravity to raise the object.

• Example: Water stored in a raised reservoir, a book on a shelf.
• If the object falls, gravitational potential energy converts to kinetic energy.

Chemical energy is stored in the bonds between atoms and molecules in substances. When chemical reactions occur, such as combustion or digestion, this energy can be released or absorbed.

Examples include fuels (like petrol, coal), food, and batteries.

Chemical energy is a form of potential energy at the molecular level.

• Energy stored in fuels powers engines and heating.
• Food provides chemical energy for biological processes.

Elastic energy is stored when elastic materials such as springs, rubber bands, or stretched wires are deformed by stretching or compressing.

The energy is stored due to the work done to change the shape of the object and is recoverable if the object returns to its original shape.

The amount stored depends on the material's properties and the extent of deformation.

• Example: A compressed spring in a toy, a stretched bowstring.
• Elastic potential energy can be calculated using E = ½ k x², where k is the spring constant and x is the extension or compression. (Note: formula not required here but useful context.)

Nuclear energy is stored in the nucleus of atoms, held by the strong nuclear force binding protons and neutrons together.

This energy can be released during nuclear reactions such as fission (splitting nuclei) or fusion (combining nuclei).

Nuclear energy stores are vastly greater per unit mass than chemical energy stores.

• Example: Energy released in nuclear power stations and the Sun.
• Nuclear energy is responsible for radioactive decay and atomic bombs.

Energy cannot be created or destroyed; it can only be transferred from one store to another or transformed from one form to another. The process of energy transfer involves moving energy between different energy stores, such as kinetic, gravitational potential, thermal, chemical, or electrical stores.

Energy transfer occurs in many everyday processes and is fundamental to understanding physical phenomena. The main methods of energy transfer include mechanical work, electrical work, heating, and energy transfer by waves.

• Energy transfer is the movement of energy between stores.
• Energy stores include kinetic, potential, thermal, chemical, electrical, and others.
• Energy transfer processes obey the conservation of energy principle.

Mechanical work is done when a force causes an object to move through a distance. This transfers energy from one store to another, for example, from the kinetic energy store of a moving object to the gravitational potential energy store when lifting an object.

The work done (W) by a force (F) moving an object through a displacement (d) in the direction of the force is given by:

\[ W = F \times d \] where W is in joules (J), F in newtons (N), and d in metres (m).

• Mechanical work transfers energy via force and displacement.
• Work done is the product of force and displacement in the force direction.
• Example: lifting a book transfers energy from kinetic to gravitational potential store.

Electrical work involves the transfer of energy by moving electric charges through a potential difference. When an electric current flows through a component, energy is transferred from the electrical energy store to other stores, such as thermal energy in a resistor or light energy in a bulb.

The electrical work done (W) when a charge (Q) moves through a potential difference (V) is:

\[ W = Q \times V \] where W is in joules (J), Q in coulombs (C), and V in volts (V).

• Electrical work transfers energy via moving charges through a potential difference.
• Energy is converted to other forms, e.g., thermal in resistors, light in bulbs.
• Example: a battery transfers chemical energy to electrical energy, which then transfers to thermal energy in a heater.

Heating transfers energy from a hotter object to a cooler one due to a temperature difference. This process increases the thermal energy store of the cooler object and decreases that of the hotter object.

Heat transfer can occur by conduction, convection, or radiation, but the key point is that energy moves from higher to lower temperature regions.

The amount of energy transferred by heating depends on the temperature difference, the material, and the time of transfer.

• Heating transfers thermal energy between objects of different temperatures.
• Energy moves from hot to cold, increasing the thermal energy store of the cooler object.
• Example: a hot cup of tea transfers energy to the surrounding air by heating.

Waves transfer energy from one place to another without transferring matter. Mechanical waves, such as sound waves, transfer energy through vibrations of particles in a medium. Electromagnetic waves, such as light, transfer energy through oscillating electric and magnetic fields and can travel through a vacuum.

Energy carried by waves can be absorbed, reflected, or transmitted by materials, causing changes in energy stores, such as thermal energy when light is absorbed.

Wave energy transfer is essential in many applications, including communication and heating by radiation.

• Waves transfer energy without transferring matter.
• Mechanical waves require a medium; electromagnetic waves do not.
• Energy transfer by waves can change energy stores, e.g., thermal energy when light is absorbed.
• Example: sound waves transfer energy from a vibrating speaker to the air and then to the ear.

Energy is a scalar quantity that can exist in various forms such as kinetic energy, gravitational potential energy, chemical energy, and thermal energy. The conservation of energy principle states that within a closed system, energy cannot be created or destroyed; it can only be transferred or transformed from one form to another.

This means the total energy in a closed system remains constant over time. For example, when an object falls, its gravitational potential energy decreases while its kinetic energy increases by the same amount, keeping the total energy unchanged.

Mathematically, this can be expressed as: Total energy before = Total energy after.

• Energy cannot be created or destroyed.
• Energy can be transformed between different forms.
• Total energy in a closed system remains constant.

Consider a ball held at a height above the ground. It has gravitational potential energy due to its position. When released, this energy converts into kinetic energy as the ball accelerates downwards.

At the highest point: Energy is mostly gravitational potential energy (E_p = mgh).

At the lowest point: Energy is mostly kinetic energy (E_k = ½ mv²).

• Gravitational potential energy (E_p) = mass (m) × gravitational field strength (g) × height (h).
• Kinetic energy (E_k) = ½ × mass (m) × velocity squared (v²).
• Energy transforms from potential to kinetic as the object moves.

Energy flow diagrams visually represent how energy is transferred or transformed in a system. They use arrows to show the direction of energy flow and label the forms of energy involved.

In a simple flow diagram for a falling object: Potential energy → Kinetic energy.

The width of arrows can represent the amount of energy transferred, but for simple diagrams, equal widths indicate no energy loss.

• Arrows show energy transfer direction.
• Labels indicate energy forms.
• Total energy input equals total energy output in ideal cases.

To apply conservation of energy, identify the initial and final energy forms and set their sums equal, assuming no energy loss.

Example: A 2 kg ball is dropped from 5 m height. Calculate its speed just before hitting the ground.

Step 1: Calculate initial gravitational potential energy: E_p = mgh = 2 × 9.8 × 5 = 98 J (joules). Step 2: At ground level, potential energy is zero, so kinetic energy equals initial potential energy: E_k = 98 J. Step 3: Use kinetic energy formula to find velocity: E_k = ½ mv² → v = √(2E_k/m) = √(2 × 98 / 2) = √98 ≈ 9.9 m/s.

• Use E_p = mgh and E_k = ½ mv² formulas.
• Set total initial energy equal to total final energy.
• Rearrange formulas to find unknown quantities.
• Include units in all calculations.

In simple conservation of energy problems, it is often assumed that no energy is lost to the surroundings (e.g., by friction or air resistance). This means the system is considered closed and ideal.

In real situations, some energy is usually dissipated as heat or sound, so total mechanical energy decreases.

For this objective, focus on ideal cases where total energy remains constant and transformations are complete.

• Assume no energy loss unless stated.
• Energy dissipated as heat or sound is ignored in simple problems.
• Total mechanical energy remains constant in ideal systems.

Kinetic energy is the energy possessed by an object because of its motion. Any object that is moving has kinetic energy. The faster it moves, or the more massive it is, the greater its kinetic energy.

Kinetic energy is a scalar quantity, meaning it has magnitude only and no direction. It is measured in joules (J), the SI unit of energy.

The kinetic energy of an object depends on two factors: its mass (m) and its velocity (v).

• Kinetic energy is energy of motion.
• It is a scalar quantity measured in joules (J).
• Depends on mass (kg) and velocity (m/s).

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

\[ E_k = \frac{1}{2} m v^2 \] where: m is the mass in kilograms (kg), v is the velocity in metres per second (m/s), and E_k is the kinetic energy in joules (J).

This formula shows that kinetic energy is directly proportional to the mass and to the square of the velocity. This means that if the velocity doubles, the kinetic energy increases by a factor of four (since 2² = 4).

• Formula: \( E_k = \frac{1}{2} m v^2 \)
• Mass (m) in kilograms (kg).
• Velocity (v) in metres per second (m/s).
• Kinetic energy (E_k) in joules (J).

Example: Calculate the kinetic energy of a car with mass 1200 kg moving at 15 m/s.

Step 1: Write down the formula: \( E_k = \frac{1}{2} m v^2 \).

Step 2: Substitute the values: \( E_k = \frac{1}{2} \times 1200 \times (15)^2 \). Calculate the square of velocity: \(15^2 = 225\). So, \( E_k = 0.5 \times 1200 \times 225 \). Step 3: Multiply: \(0.5 \times 1200 = 600\), then \(600 \times 225 = 135000\). Step 4: Write the answer with units: \( E_k = 135000 \text{ J} \) or 135 kJ. This means the car has 135 kilojoules of kinetic energy.

• Formula substitution: \( E_k = \frac{1}{2} \times 1200 \times 15^2 \)
• Calculate velocity squared: \(15^2 = 225\)
• Multiply: \(0.5 \times 1200 = 600\), then \(600 \times 225 = 135000\)
• Final answer: \(135000 \text{ J} = 135 \text{ kJ}\)

The kinetic energy depends linearly on mass and quadratically on velocity. This means:

Doubling the mass doubles the kinetic energy, if velocity is constant.

Doubling the velocity increases the kinetic energy by four times, if mass is constant. This is because velocity is squared in the formula.

• Kinetic energy ∝ mass (m).
• Kinetic energy ∝ velocity squared (v²).
• Velocity changes have a larger effect than mass changes.

Common mistakes include: using weight instead of mass (mass must be in kg), forgetting to square the velocity, or omitting the 1/2 factor.

Always check units: mass in kilograms, velocity in metres per second, energy in joules.

In exam calculations, show all steps clearly: write the formula, substitute values with units, calculate carefully, and include units in the final answer to gain full marks.

• Use mass (kg), not weight (N).
• Square the velocity correctly.
• Include the 1/2 factor.
• Show all working steps with units.
• Final answer must have units (J).

Gravitational potential energy (GPE) is the energy stored in an object due to its position in a gravitational field, typically near the Earth's surface. When an object is raised to a height above a reference level (usually the ground), work is done against the gravitational force, and energy is stored as gravitational potential energy.

The amount of gravitational potential energy depends on three factors: the mass of the object (m), the height above the reference point (h), and the gravitational field strength (g). The gravitational field strength near the Earth's surface is approximately 9.8 newtons per kilogram (N/kg).

GPE is a scalar quantity measured in joules (J). It represents the capacity of the object to do work due to its elevated position. When the object falls, this stored energy converts to kinetic energy.

• Gravitational potential energy is energy stored due to height in a gravitational field.
• It depends on mass, height, and gravitational field strength.
• Measured in joules (J), a scalar quantity.

The change in gravitational potential energy (∆E_p) when an object moves vertically is given by the formula:

∆E_p = mg∆h, where: m = mass of the object in kilograms (kg), g = gravitational field strength in newtons per kilogram (N/kg), ∆h = change in height in metres (m).

This formula calculates the energy gained or lost by the object as it is raised or lowered. A positive ∆h means the object is raised, increasing its gravitational potential energy. A negative ∆h means the object is lowered, decreasing its gravitational potential energy.

• ∆E_p = mg∆h calculates the change in gravitational potential energy.
• Mass (m) in kilograms, gravitational field strength (g) ≈ 9.8 N/kg, height change (∆h) in metres.
• Positive ∆E_p means energy gained; negative means energy lost.

Each symbol in the formula has specific units: mass (m) is measured in kilograms (kg), gravitational field strength (g) in newtons per kilogram (N/kg), height change (∆h) in metres (m), and gravitational potential energy change (∆E_p) in joules (J).

Since 1 newton (N) equals 1 kg·m/s², and 1 joule (J) equals 1 newton metre (N·m), the units in the formula are consistent: kg × N/kg × m = N·m = J.

It is important to use consistent SI units to ensure correct calculations.

• Mass (m): kilograms (kg)
• Gravitational field strength (g): newtons per kilogram (N/kg)
• Height change (∆h): metres (m)
• Energy change (∆E_p): joules (J)

Example: Calculate the change in gravitational potential energy when a 2.0 kg book is lifted from the floor to a shelf 1.5 m above.

Step 1: Write down the known values: m = 2.0 kg, g = 9.8 N/kg, ∆h = +1.5 m (positive because the book is raised).

Step 2: Use the formula ∆E_p = mg∆h: ∆E_p = 2.0 × 9.8 × 1.5 = 29.4 J. The book gains 29.4 joules of gravitational potential energy when lifted to the shelf.

• Identify mass, gravitational field strength, and height change.
• Substitute values into ∆E_p = mg∆h.
• Calculate and include units in the final answer.

A frequent mistake is confusing mass and weight. Mass is measured in kilograms and is used in the formula, not weight (which is a force in newtons).

Another common error is neglecting the sign of ∆h. If an object is lowered, ∆h is negative, and the gravitational potential energy decreases.

Forgetting to use consistent units, such as mixing centimetres with metres, leads to incorrect answers. Always convert lengths to metres before calculating.

• Use mass (kg), not weight (N), in the formula.
• Assign correct sign to ∆h: positive for upward movement, negative for downward.
• Convert all length measurements to metres before calculation.

The conservation of energy principle states that energy cannot be created or destroyed; it can only be transferred from one form to another or transferred between objects or systems.

In any closed system, the total energy remains constant, although energy may change form multiple times during a process.

For example, in a mechanical system, chemical energy stored in fuel can be converted into kinetic energy, thermal energy, and sound energy, but the total energy remains the same throughout the process.

• Energy is conserved in all physical processes.
• Energy transformations involve changing energy from one store to another.
• Total energy input equals total energy output plus any energy wasted.

Complex systems often involve multiple stages where energy changes form several times.

For example, in a roller coaster, gravitational potential energy converts to kinetic energy as the coaster descends, then back to potential energy as it climbs.

Other forms of energy such as thermal energy due to friction and sound energy are also produced, representing energy losses from the system's useful output.

• Energy can transform through several stages in a system.
• Energy losses often occur as thermal energy due to friction or sound.
• Tracking all energy forms helps understand system performance and losses.

Sankey diagrams are graphical representations of energy transfers within a system.

They use arrows whose widths are proportional to the amount of energy transferred or wasted.

The diagram shows the total energy input on the left, splitting into useful energy outputs and wasted energy outputs on the right, allowing easy visual comparison of energy distribution.

• Arrow width represents the quantity of energy transferred.
• Input energy is shown entering the system.
• Useful energy and wasted energy outputs are shown leaving the system.
• Wasted energy often appears as heat, sound, or other non-useful forms.

Efficiency is the ratio of useful energy output to total energy input, expressed as a percentage.

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

Example: If total input energy is 100 J and useful output energy is 60 J, efficiency = (60 / 100) × 100% = 60%.

• Efficiency quantifies how well a system converts input energy into useful output.
• Efficiency is always less than or equal to 100%.
• Energy not converted into useful output is wasted energy.

To analyse complex systems, identify all energy stores involved at each stage and track energy transfers between them.

Use conservation of energy to write equations equating total input energy to the sum of useful energy and wasted energy.

Sankey diagrams help organise and visualise these energy flows, making it easier to identify where energy losses occur and how to improve efficiency.

• List all forms of energy at each stage.
• Apply conservation of energy: total input = useful output + wasted energy.
• Use Sankey diagrams to support calculations and understanding.
• Check units carefully: energy in joules (J).