Welcome to the World of Energy!
Hi there! This chapter is all about Energy—the fundamental ingredient needed for literally everything to happen, from the Sun shining to you walking up a flight of stairs.
Don't worry if the formulas look scary at first! We will break them down step-by-step using simple analogies and clear examples. By the end of these notes, you’ll be a pro at tracking, calculating, and understanding how energy moves around the universe. Let's get started!
Section 1: Forms of Energy and Conservation
1.1 What is Energy?
In simple terms, Energy is defined as the capacity to do work or the ability to cause change. The unit we use to measure energy (and work done) is the Joule (\(J\)).
The Eight Main Forms of Energy
Energy doesn't just exist in one way; it takes on many forms. Remember these eight key types, as they are crucial for describing energy transfers:
- Kinetic Energy (KE): Energy due to movement. (A moving car)
- Gravitational Potential Energy (GPE): Stored energy due to height/position in a gravitational field. (A book on a high shelf)
- Elastic Potential Energy (EPE): Stored energy due to stretching or compressing. (A stretched rubber band or spring)
- Thermal Energy (Heat): Energy related to the temperature of an object. (A warm radiator)
- Chemical Energy: Stored energy in the bonds of atoms and molecules. (Food, fuel, or batteries)
- Light Energy (Radiant): Energy transferred by electromagnetic waves. (Light bulbs, the Sun)
- Sound Energy: Energy transferred by vibrations. (A ringing bell)
- Electrical Energy: Energy transferred by moving electric charges. (Current flowing through wires)
🧠 Memory Trick: You can remember some of these key forms using a simple acronym, like C-K-GELTS (Chemical, Kinetic, GPE, Elastic, Light, Thermal, Sound).
1.2 The Law of Conservation of Energy
This is the single most important rule in physics regarding energy.
The Law of Conservation of Energy states: Energy cannot be created or destroyed, it can only be transferred from one object to another or transformed from one form into another.
Analogy: Think of energy like money in a bank account. The total amount of money in the world stays the same. It just gets moved between people (transfer) or changed from cash into an investment (transformation).
Energy Transformation and Dissipation
When we use a device, we are forcing an energy transformation.
Example: When a lamp is switched on, Electrical Energy is transformed into Light Energy (useful output).
However, no device is 100% perfect. Some energy always ends up in a form we didn't want. This is usually Thermal Energy (heat) and sometimes Sound Energy.
- Dissipation (Wasted Energy): Energy that spreads out, usually into the surroundings as Thermal Energy, making it less useful. This often happens due to friction or air resistance.
Quick Review: The Big Idea
Total Energy Input = Useful Energy Output + Wasted Energy Output
Section 2: Work Done and Power
2.1 Work Done
In physics, Work Done (\(W\)) has a very specific meaning: it is the amount of energy transferred when a force moves an object through a distance.
If you push against a wall all day, you might feel tired, but you haven't done any physics work because the wall didn't move!
Calculating Work Done
Work Done is calculated using the formula:
\[ W = F \times d \]
- \(W\) = Work Done (Joules, \(J\))
- \(F\) = Force applied (Newtons, \(N\))
- \(d\) = Distance moved in the direction of the force (metres, \(m\))
Common Mistake Alert! Always make sure the distance (\(d\)) is in metres and the force (\(F\)) is in Newtons. If you move an object \(10\) metres using a force of \(5\) Newtons, the work done is \(5 \times 10 = 50\, J\).
Did you know? Because work done is a measure of transferred energy, the unit for work done is also the Joule (\(J\)). If you do 1 Joule of work, you have transferred 1 Joule of energy.
2.2 Power
Power tells us how fast energy is being transferred or how quickly work is being done. A powerful engine can do the same amount of work as a weak engine, but it does it in less time.
Power (\(P\)) is defined as the rate of energy transfer.
The unit for power is the Watt (\(W\)). One Watt means one Joule of energy is transferred every second (\(1\, W = 1\, J/s\)).
Calculating Power
Power can be calculated using this formula:
\[ P = \frac{E}{t} \quad \text{or} \quad P = \frac{W}{t} \]
- \(P\) = Power (Watts, \(W\))
- \(E\) = Energy transferred (or \(W\) = Work Done) (Joules, \(J\))
- \(t\) = Time taken (seconds, \(s\))
Analogy: Imagine two people climbing the same set of stairs (doing the same amount of work). The person who reaches the top fastest has the greater power.
Section 3: Calculating Stored and Moving Energy
Now we look at the specific formulas for two of the most important energy stores: Gravitational Potential Energy (GPE) and Kinetic Energy (KE).
3.1 Gravitational Potential Energy (GPE)
GPE (\(E_p\)) is the energy stored in an object due to its position above the ground. The higher or heavier the object is, the more GPE it stores.
The GPE Formula
\[ E_p = m \times g \times h \]
- \(E_p\) = Gravitational Potential Energy (Joules, \(J\))
- \(m\) = Mass of the object (kilograms, \(kg\))
- \(g\) = Gravitational field strength (Newtons per kilogram, \(N/kg\)). You will usually use \(g = 9.8\, N/kg\) or \(g = 10\, N/kg\) for simple calculations, depending on the question.
- \(h\) = Height above the ground (metres, \(m\))
Remember this! When an object falls, GPE is transformed into KE. The total energy stays the same (Conservation Law).
3.2 Kinetic Energy (KE)
Kinetic Energy (\(E_k\)) is the energy an object possesses because it is moving. KE depends on two things: the object's mass and its speed (velocity).
The KE Formula
\[ E_k = \frac{1}{2} m v^2 \]
(Also written as \(E_k = 0.5 \times m \times v^2\))
- \(E_k\) = Kinetic Energy (Joules, \(J\))
- \(m\) = Mass of the object (kilograms, \(kg\))
- \(v\) = Speed (velocity) of the object (metres per second, \(m/s\))
A key point: Notice that velocity (\(v\)) is squared. This means that doubling the speed of an object quadruples its kinetic energy! That’s why speeding just a little bit in a car is so dangerous.
Encouraging Note: Don't worry if you mix up the formulas initially! Write them down on a flashcard and practice identifying the units. Once you practice substitution, the calculations become routine.
Section 4: Efficiency
Efficiency measures how good a device is at transferring the energy input into the useful energy output we want, rather than wasting it.
Efficiency is always a value between 0 (terrible) and 1 (perfect, 100%).
4.1 Calculating Efficiency
Efficiency can be calculated using either energy values or power values, as long as you use the same units for the top and bottom of the fraction.
The Efficiency Formula (as a fraction):
\[ \text{Efficiency} = \frac{\text{Useful Energy Output}}{\text{Total Energy Input}} \]
The Efficiency Formula (as a percentage):
\[ \text{Percentage Efficiency} = \frac{\text{Useful Energy Output}}{\text{Total Energy Input}} \times 100\% \]
Example: A light bulb is given 100 J of electrical energy. It converts 20 J into light and 80 J into heat.
Useful Energy Output = 20 J (Light)
Total Energy Input = 100 J
Efficiency = \(\frac{20}{100} \times 100\% = 20\%\)
4.2 Energy Transfer Diagrams (Sankey Diagrams)
While you might not have to draw them, you need to understand what an Energy Transfer Diagram (sometimes called a Sankey Diagram) shows.
- The arrow starts wide, representing the Total Energy Input.
- The main arrow flowing straight represents the Useful Energy Output.
- Arrows branching off downwards or sideways represent the Wasted Energy Output (usually thermal energy).
- The total width of all output arrows (useful + wasted) must equal the width of the input arrow (Conservation of Energy!).
Key Takeaway: Because energy is always dissipated (wasted) in the form of heat or sound due to friction, air resistance, or electrical resistance, no real machine can ever be 100% efficient.
Chapter Summary - Quick Checklist
- Energy Unit: Joule (\(J\)). Power Unit: Watt (\(W\)).
- Conservation: Energy is never created or destroyed.
- Work Done: \(W = F \times d\). Force times distance.
- Power: \(P = E / t\). Energy transferred per second.
- GPE: \(E_p = m \times g \times h\). Depends on height.
- KE: \(E_k = 0.5 \times m \times v^2\). Depends heavily on speed.
- Efficiency: Useful output divided by total input. Never 100%.
Great job completing the Energy chapter notes! Keep practicing those formulas, and you will master this fundamental topic. Good luck with your studies!