Welcome to Forces and Energy!
Hello future Physicists! This chapter is super important because it connects two huge ideas you've already touched upon: Forces (pushes and pulls) and Energy (the ability to make things happen).
Don't worry if the calculations look tricky at first—we will break them down step-by-step. By the end of these notes, you'll understand exactly how forces transfer energy, how quickly they do it, and how we measure that effectiveness. Let's get started!
Key Section Overview:
- Work Done: The energy transferred when a force moves an object.
- Power: The rate at which energy is transferred.
- Efficiency: How effectively energy is converted into useful forms.
Section 1: Work Done (Energy Transfer)
In everyday life, "work" means doing chores or studying. In Physics, the definition is much stricter! Work is done whenever a force causes an object to move over a distance.
What is Work Done?
When you push a trolley, you are exerting a force. If the trolley moves, you have transferred energy to it—you have done work! If you push as hard as you can against a massive brick wall and it doesn't move, you might be tired, but in Physics, zero work has been done because the distance moved (d) is zero.
Key Definitions and Units
Work Done is measured in Joules (J).
Did You Know? 1 Joule is the same as 1 Newton-metre (1 N m). This makes sense because the calculation for work uses force (N) and distance (m)!
Calculating Work Done
The amount of work done depends on two things: how strong the force is (F) and how far the object moves (d).
The formula is:
\[
W = F \times d
\]
Where:
- \(W\) = Work Done (Joules, J)
- \(F\) = Force applied (Newtons, N)
- \(d\) = Distance moved in the direction of the force (metres, m)
Analogy: Moving a Heavy Book
Imagine you are sliding a heavy textbook across your desk.
If you use 5 N of force to slide it 2 metres:
\[
W = 5 \, \text{N} \times 2 \, \text{m} = 10 \, \text{J}
\]
You transferred 10 Joules of energy to the book (mostly into heat and sound due to friction).
🚨 Common Mistake Alert!
The distance (d) must be in the same direction as the force (F).
Example: If you carry a heavy bag horizontally across the room, you are applying an upward force (to hold it up), but the movement is sideways. Since the force (up) is perpendicular to the movement (sideways), the force you apply to hold the bag does zero work on the bag! (However, you use energy because your muscles are working, but that's a biology topic!)
- Work Done is energy transfer.
- No movement means no work done in Physics.
- Formula: \(W = Fd\).
- Units: Joules (J).
Section 2: Power (The Rate of Energy Transfer)
Work Done tells you how much energy was transferred. Power tells you how fast that energy transfer happened.
Think of two cranes lifting the exact same heavy block to the exact same height.
Crane A takes 10 seconds.
Crane B takes 60 seconds.
Both cranes do the same amount of work (W), but Crane A is much more powerful because it did the work faster!
Defining Power
Power is defined as the rate at which work is done, or the rate at which energy is transferred.
Key Definitions and Units
Power is measured in Watts (W).
Memory Aid: A Watt is defined as one Joule of energy transferred every second.
\(1 \, \text{W} = 1 \, \text{J/s}\).
Calculating Power
Since power is the rate of energy transfer, we divide the energy (or work) by the time taken.
The formulas are:
\[
P = \frac{E}{t} \quad \text{or} \quad P = \frac{W}{t}
\]
Where:
- \(P\) = Power (Watts, W)
- \(E\) or \(W\) = Energy transferred or Work Done (Joules, J)
- \(t\) = Time taken (seconds, s)
Step-by-Step Example Calculation
A small motor does 500 J of work in 2 seconds. What is its power?
Step 1: Write the formula.
\[ P = \frac{W}{t} \]
Step 2: Substitute the values (500 J and 2 s).
\[ P = \frac{500 \, \text{J}}{2 \, \text{s}} \]
Step 3: Calculate the result.
\[ P = 250 \, \text{W} \]
The motor has a power of 250 Watts.
Power measures speed. High power means a lot of energy is moved or used up very quickly. Low power means the energy transfer is slow.
Section 3: Efficiency (Using Energy Effectively)
When any device (like a lightbulb, an engine, or a human) transfers energy, we want it to transfer that energy into the form we need (the useful output). Unfortunately, no machine is perfect. Some energy is always wasted, usually as heat or sound.
The Law of Conservation of Energy (Prerequisite)
Don't worry, this is a simple concept! The Law of Conservation of Energy states that energy cannot be created or destroyed, only transferred from one store to another.
This means:
\[ \text{Total Energy Input} = \text{Useful Energy Output} + \text{Wasted Energy} \]
Defining Efficiency
Efficiency is a measure of how much of the total energy input is converted into useful energy output.
Example: When you put energy into a lightbulb, the useful output is light, but the wasted output is heat. An efficient lightbulb produces lots of light and very little heat.
Calculating Efficiency
Efficiency is usually given as a percentage (a number between 0% and 100%) or as a decimal (a number between 0 and 1).
Efficiency Formula (Percentage)
\[ \text{Efficiency} = \frac{\text{Useful Energy Output}}{\text{Total Energy Input}} \times 100\% \]
This formula can also be calculated using power, since power is just energy over time:
\[
\text{Efficiency} = \frac{\text{Useful Power Output}}{\text{Total Power Input}} \times 100\%
\]
Why We Can't Get 100% Efficiency
In any real-world energy transfer, some energy is inevitably lost to the surroundings as heat due to friction or air resistance, or as sound. Therefore, no device can ever be 100% efficient.
Step-by-Step Example Calculation
A kettle is switched on. It uses 4,000 J of electrical energy (Total Input) and converts 3,800 J into heat to warm the water (Useful Output). What is its efficiency?
Step 1: Write the formula.
\[ \text{Efficiency} = \frac{\text{Useful Output}}{\text{Total Input}} \times 100\% \]
Step 2: Substitute the values.
\[ \text{Efficiency} = \frac{3,800 \, \text{J}}{4,000 \, \text{J}} \times 100\% \]
Step 3: Calculate the decimal fraction first.
\[ \frac{3,800}{4,000} = 0.95 \]
Step 4: Convert to a percentage.
\[ 0.95 \times 100\% = 95\% \]
The kettle is 95% efficient. (The remaining 5% was likely wasted heating the kettle itself or the surrounding air.)
- Efficiency measures usefulness.
- Always divide the useful output by the total input.
- Efficiency must be between 0% and 100%.
Chapter Summary: Core Concepts Review
You have mastered the connection between forces, movement, and energy transfer! Here are the essential formulas and concepts you need for CORE Physics 9223:
The Three Pillars of Energy Transfer
1. Work Done (W)
What is it? Energy transferred by a force.
Formula:
\[ W = Fd \]
Unit: Joules (J).
2. Power (P)
What is it? The rate of energy transfer (how fast work is done).
Formula:
\[ P = \frac{E}{t} \quad \text{or} \quad P = \frac{W}{t} \]
Unit: Watts (W).
3. Efficiency
What is it? How effectively the input energy is turned into useful output.
Formula:
\[ \text{Efficiency} = \frac{\text{Useful Output}}{\text{Total Input}} \times 100\% \]
Unit: Percentage (%).
Keep practicing these formulas, and remember the definitions—they are your best tools for success!