Energy, work and power - Physics (0625) - Cambridge IGCSE

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IGCSE Physics (0625): Comprehensive Study Notes

Chapter 1.7: Energy, Work, and Power

Welcome to the exciting world of Energy, Work, and Power! This chapter is the backbone of Physics—it explains why things move, how we use fuel, and how we pay our electricity bills. Don't worry if the formulas look intimidating; we’ll break down these concepts step-by-step using clear language and everyday examples.

By the end of these notes, you will understand how energy changes form, how forces do work, and how quickly we can use that energy (power!).

1. Energy Stores and Transfers (1.7.1)

What is Energy?

In simple terms, Energy is the ability to do work or cause a change. You can't create it, and you can't destroy it—it simply moves around or changes form. The standard unit for energy is the Joule (J).

The Eight Main Energy Stores (Core Content)

Energy is always stored somewhere. Here are the main stores you need to know:

Kinetic Energy ($E_k$): Energy stored in anything that is moving. (e.g., A running car, a dropped ball.)
Gravitational Potential Energy ($E_p$): Energy stored in an object due to its position in a gravitational field (its height). (e.g., Water held behind a dam, a book sitting on a high shelf.)
Chemical Energy: Energy stored in the bonds of atoms and molecules. Released during chemical reactions. (e.g., Food, fuels like petrol and wood, batteries.)
Elastic (Strain) Energy: Energy stored in objects that are stretched, squashed, or compressed. (e.g., A stretched rubber band, a coiled spring.)
Nuclear Energy: Energy stored within the nucleus of an atom. Released during fission or fusion. (e.g., Nuclear power plants, the Sun.)
Electrostatic Energy: Energy stored due to the force between two electric charges. (e.g., A charged capacitor, lightning.)
Internal (Thermal) Energy: Energy stored by the random movement (kinetic) and potential energy of the particles (atoms/molecules) inside a substance. Often called Heat Energy. (e.g., Hot coffee, a burning radiator.)
Magnetic Energy: Energy stored due to the force between magnetic poles. (e.g., Two magnets pushing apart.) (Note: While not explicitly listed as one of the eight in the summary, it is often grouped with Electrostatic and Nuclear as a specific field-related store.)

How is Energy Transferred? (Core Content)

When energy moves between stores, it is called an Energy Transfer. The syllabus requires you to know these four main methods:

By Forces (Mechanical Work Done): Energy transferred when a force moves an object.
By Electrical Currents (Electrical Work Done): Energy transferred by moving charges (electricity). (e.g., A fan motor turning, current flowing through a wire.)
By Heating: Energy transferred due to a temperature difference (conduction, convection, radiation). (e.g., Heat radiating from a stove.)
By Waves: Energy transferred by sound, light, or electromagnetic waves. (e.g., Solar radiation warming the Earth, sound waves making your eardrum vibrate.)

The Conservation of Energy (Core & Supplement)

This is arguably the most important principle in Physics:

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

Analogy: Think of a roller coaster. At the top of the hill, it has maximum Gravitational Potential Energy ($E_p$). As it falls, this $E_p$ is converted into Kinetic Energy ($E_k$). At the bottom, $E_k$ is maximum. Throughout the ride, some energy is lost to the surroundings as unwanted Internal/Thermal Energy (due to friction) and Sound Energy.

Sankey Diagrams (Supplement)

Sankey diagrams are visual tools used to show how energy is converted in a system. They look like flow charts where the width of the arrow represents the amount of energy (or power).

The total input energy is the width of the main input arrow.
The useful output energy is shown by a straight arrow.
The wasted energy (usually thermal/heat) is shown by arrows branching off, often downwards.

Calculating Kinetic and Potential Energy (Supplement)

1. Kinetic Energy ($E_k$): The energy of movement depends on mass ($m$) and speed ($v$).

$$E_k = \frac{1}{2}mv^2$$

$E_k$ is Kinetic Energy (in J)
$m$ is mass (in kg)
$v$ is speed (in m/s)

Don't worry if this seems tricky at first! Notice that speed ($v$) is squared. This means doubling the speed quadruples the kinetic energy!

2. Gravitational Potential Energy Change ($\Delta E_p$): The change in energy stored by lifting an object depends on its mass ($m$), the gravitational field strength ($g$), and the change in height ($\Delta h$).

$$\Delta E_p = mg\Delta h$$

$\Delta E_p$ is the change in GPE (in J)
$m$ is mass (in kg)
$g$ is gravitational field strength (approximately $9.8 \, \text{N/kg}$ on Earth)
$\Delta h$ is the change in vertical height (in m)

Quick Review: Energy Stores

Energy is conserved. It moves between stores (like KE and GPE) and transfers (like Work and Heat). Focus on the definitions and the difference between the two main mechanical stores: Kinetic (moving) and Gravitational Potential (height).

2. Work Done (1.7.2)

In physics, "work" means something very specific. You might feel exhausted pushing a wall, but if the wall doesn't move, you haven't done any physical work!

Defining Mechanical Work Done (Core Content)

Work Done ($W$) is defined as the energy transferred when a force moves an object in the direction of the force.

We also need to understand that Work Done is Equal to the Energy Transferred ($\Delta E$). Whether you're lifting a mass (doing mechanical work) or switching on a light (doing electrical work), you are simply transferring energy.

The Formula for Work Done

We recall and use the equation for mechanical work done:

$$W = Fd = \Delta E$$

$W$ is Work Done (in J)
$F$ is the Force applied (in N)
$d$ is the distance moved in the direction of the force (in m)

Example: If you push a trolley with a force of 50 N over a distance of 10 m, the work done is $W = 50 \, \text{N} \times 10 \, \text{m} = 500 \, \text{J}$.

Common Mistake to Avoid: Work is only done by the component of the force that acts in the direction of motion. If you carry a heavy box horizontally, you are applying an upward force (to hold it up), but since the motion is horizontal, the work done *by your upward force* is zero.

Key Takeaway: Work

Work is Force × Distance. If you apply a force but the object doesn't move, $d=0$ and therefore $W=0$.

3. Power (1.7.4)

Power tells us how fast energy is being transferred or how quickly work is being done.

Defining Power (Core Content)

Power ($P$) is defined as the work done per unit time, or the energy transferred per unit time.

The Formula for Power

Since power measures the rate of transfer, time ($t$) is involved:

$$P = \frac{W}{t}$$ $$P = \frac{\Delta E}{t}$$

$P$ is Power (measured in Watts (W))
$W$ is Work Done (in J)
$\Delta E$ is Energy Transferred (in J)
$t$ is time taken (in s)

One Watt is equal to one Joule per second ($1 \, \text{W} = 1 \, \text{J/s}$).

Analogy: Imagine two cranes lifting the same heavy beam to the top of a building. Both cranes do the exact same amount of work (they transfer the same amount of GPE). However, the crane that does it faster has a higher power output.

Quick Review: Power

Power is all about speed. It is the rate of energy transfer. High power means energy is transferred quickly.

4. Efficiency (1.7.3)

In the real world, no machine is perfect! Some input energy is always wasted, usually as heat or sound. Efficiency measures how good a device is at converting input energy into the desired useful output energy.

Understanding Efficiency (Core & Supplement)

Efficiency is the ratio of useful energy (or power) output to the total energy (or power) input. It is usually expressed as a percentage.

Calculating Efficiency (Supplement)

You can calculate efficiency using either energy or power:

Using Energy: $$\text{(\%)} \text{ efficiency} = \frac{\text{useful energy output}}{\text{total energy input}} \times 100\%$$

Using Power: $$\text{(\%)} \text{ efficiency} = \frac{\text{useful power output}}{\text{total power input}} \times 100\%$$

Example: A light bulb uses 100 J of electrical energy per second (Input). If it only produces 10 J of light energy per second (Useful Output) and 90 J of heat energy (Wasted Output), its efficiency is:

$$\text{Efficiency} = \frac{10 \, \text{J}}{100 \, \text{J}} \times 100\% = 10\%$$

A perfect machine would have 100% efficiency. In reality, most devices are far less efficient.

5. Energy Resources (1.7.3)

We rely on different sources to provide the energy we need. The syllabus requires you to understand the main resources and evaluate them based on renewability, availability, reliability, scale, and environmental impact.

Did You Know? Radiation from the Sun is the main source of energy for almost all resources, except for Geothermal, Nuclear, and Tidal energy.

Non-Renewable Resources (Finite)

These resources exist in limited amounts and cannot be replaced within a human lifetime.

Fossil Fuels (Coal, Oil, Natural Gas): Chemical energy stored from ancient life.
- Advantage: High availability, high reliability, high energy density.
- Disadvantage: Non-renewable, releases greenhouse gases ($\text{CO}_2$) causing global warming, causes acid rain (sulphur dioxide).
Nuclear Fuel (e.g., Uranium): Energy released by nuclear fission.
- Advantage: Very high energy output, no greenhouse gases, high reliability.
- Disadvantage: Produces dangerous radioactive waste that is hard to dispose of, high initial cost, risk of catastrophic accidents.

Renewable Resources (Sustainable)

These resources are replenished naturally and will not run out.

Water (Hydroelectric Dams, Waves, Tides): Uses the gravitational potential energy of water held high (dams) or kinetic energy of moving water (waves/tides).
- Hydro Advantages: Very reliable, quickly dispatchable, clean energy.
- Hydro Disadvantages: Requires flooding large areas (habitat loss), high construction cost.
- Tidal/Wave: High reliability (tides), but often low availability (waves).
Geothermal: Uses internal (thermal) energy from hot rocks deep underground.
- Advantage: Renewable, reliable in specific locations (volcanic areas).
- Disadvantage: Restricted to certain geographical regions, may release some toxic gases.
Solar (Solar Cells/Panels): Converts light (solar cells) or infrared radiation (solar panels for heating water) into useful energy.
- Advantage: Renewable, widely available, no pollution during operation.
- Disadvantage: Unreliable (only works in daylight/sunshine), low energy output per area, high cost of manufacturing.
Wind: Uses the kinetic energy of air movement to turn turbines.
- Advantage: Renewable, clean, low running costs.
- Disadvantage: Unreliable (needs wind), noisy, visually disruptive, large land use.
Biofuels (e.g., Ethanol, Biogas): Chemical energy from recently living plants or animal waste.
- Advantage: Renewable (can be grown), considered 'carbon neutral' (though this is debatable).
- Disadvantage: Low energy density, uses land that could be used for food crops, releases $\text{CO}_2$ when burned.

Nuclear Fusion Research (Supplement)

The energy source of the Sun is nuclear fusion—joining light nuclei (like hydrogen) to form heavier ones (like helium), releasing vast amounts of energy. Scientists are investigating fusion as a future energy source on Earth because:

The fuel (hydrogen isotopes) is plentiful.
It produces very little radioactive waste compared to fission.

However, achieving and sustaining the high temperatures and pressures required remains a huge technological challenge.

Final Summary of 1.7

Energy defines existence (conserved). Work Done is the mechanical transfer of energy ($W=Fd$). Power is how fast you transfer it ($P=\Delta E/t$). Efficiency tells you how much of the energy input is useful output.