Energy stores and transfers

Welcome to the World of Energy!

Hello there! Today, we are diving into one of the most important chapters in your H1 Physics journey: Energy Stores and Transfers. Think of energy as the "currency" of the universe. Just like you need money to buy snacks or a bus ride, the universe needs energy to make things happen—whether it’s a car zooming down the PIE or your phone screen lighting up. By the end of these notes, you’ll understand how energy is saved, spent, and moved around. Don’t worry if some of the formulas look scary at first—we will break them down step-by-step!

1. Energy Stores and Transfers

In the past, you might have heard of "types" of energy. In A-Level Physics, we prefer to think of energy being kept in stores and moved via transfers.

What is an Energy Store?

Imagine energy as water. A "store" is like a bucket holding that water. It’s energy that is just sitting there, waiting to be used. Common stores include:

• Kinetic Energy Store: Anything that is moving (a running cat, a flying plane).
• Gravitational Potential Store: Anything that could fall (a book on a high shelf).
• Elastic Potential Store: Anything stretched or squashed (a rubber band).
• Electric Potential Store: Energy due to the position of charges in an electric field.

What is an Energy Transfer?

This is the process of moving energy from one bucket to another. One of the most important transfers is Work Done. When you push a box across the floor, you are transferring energy from your body’s chemical store into the box’s kinetic store via mechanical work.

Did you know? Even when you are sleeping, your body is busy transferring energy from your chemical store (food) to your thermal store to keep you warm!

Key Takeaway: Energy is stored in systems and moved between them through various transfer pathways, like work or heat.

2. The Law of Conservation of Energy

This is the "Golden Rule" of Physics: Energy cannot be created or destroyed; it can only be transferred from one store to another.

The total energy in an isolated system always stays the same. If a ball loses 10 Joules of potential energy as it falls, it must gain 10 Joules of kinetic energy (assuming no air resistance).

Quick Review: If you start with 100J of energy, you must end with 100J in total, even if it's spread across different stores.

3. Work Done: The Mechanical Transfer

In Physics, "Work" has a very specific meaning. You only do Work if you use a force to move something.

The Formula

Work Done (\(W\)) is defined as the product of the force and the displacement in the direction of the force.

\(W = F \times s\)

Where:
• \(W\) is Work Done in Joules (J)
• \(F\) is the Force in Newtons (N)
• \(s\) is the displacement in metres (m)

Common Mistake to Avoid: If you carry a heavy box and walk horizontally at a constant speed, you are technically doing zero work on the box in the direction of motion. Why? Because your lifting force is UP, but the movement is SIDEWAYS. For work to be done, the force and the movement must be in the same direction!

Key Takeaway: Work is the mechanical way of transferring energy. No movement in the direction of the force = No work done!

4. Kinetic Energy (\(E_k\))

Kinetic Energy is the energy a body possesses due to its motion.

The Equation

\(E_k = \frac{1}{2}mv^2\)

Where:
• \(m\) is mass (kg)
• \(v\) is velocity (m s\(^{-1}\))

How did we get this? (The Derivation)
Don't panic! It's just a mix of what you already know:
1. We know Work Done \(W = Fs\).
2. From Newton's Second Law, \(F = ma\). So, \(W = mas\).
3. From kinematics, \(v^2 = u^2 + 2as\). If we start from rest (\(u=0\)), then \(as = \frac{v^2}{2}\).
4. Substitute \(as\) back into the work equation: \(W = m(\frac{v^2}{2})\).
5. Therefore, the work done to accelerate an object is stored as \(E_k = \frac{1}{2}mv^2\).

Key Takeaway: If you double the speed of a car, its kinetic energy increases by four times (because of the \(v^2\))! This is why speeding is so dangerous.

5. Potential Energy: The Energy of Position

Potential energy is energy stored due to the position or state of an object.

A. Gravitational Potential Energy (GPE)

When you lift an object in a uniform gravitational field (like near Earth's surface), you do work against gravity.

\(\Delta E_p = mg\Delta h\)

• \(g\) is the gravitational field strength (approx. 9.81 m s\(^{-2}\) on Earth).
• \(\Delta h\) is the change in height.

B. Elastic Potential Energy

When you stretch a spring, you are storing energy in it. If the spring obeys Hooke’s Law (\(F = kx\)), the energy stored is the area under the force-extension graph.

The Formula: \(E_p = \frac{1}{2}Fx\) or \(E_p = \frac{1}{2}kx^2\)

C. Electric Potential Energy

Similar to gravity, if you move a charge in an electric field, you change its Electric Potential Energy. We define the force on a charge in a field as \(F = qE\).

Key Takeaway: Potential energy is "hidden" energy that has the potential to do work later.

6. The Concept of a Field

A field is just a region of space where an object experiences a force. Think of it like an "invisible influence."

• Gravitational Field Strength (\(g\)): The gravitational force per unit mass (\(g = \frac{F}{m}\)).
• Electric Field Strength (\(E\)): The electric force per unit positive charge (\(E = \frac{F}{q}\)).

Important Concept: Field lines show the direction of the force. For a mass in a gravitational field, the work done by the field is equal to the negative change in potential energy. If the field does work (pulling a ball down), the potential energy decreases.

7. Power and Efficiency

Sometimes it’s not just about how much energy you transfer, but how fast you do it.

Power (\(P\))

Power is the rate of energy transfer (or rate of work done).

\(P = \frac{W}{t}\)

Unit: Watt (W), which is 1 Joule per second.

For a moving object being pushed by a constant force: Mechanical Power \(P = Fv\).

Efficiency

In the real world, machines are never perfect. Some energy is always "lost" to the surroundings (usually as heat due to friction).
Efficiency is the ratio of useful energy output to total energy input.

\(Efficiency = \frac{Useful\,Energy\,Output}{Total\,Energy\,Input} \times 100\%\)

Example: If an LED bulb uses 10J of electric energy but only gives off 9J of light, its efficiency is 90%. The remaining 1J is "wasted" as heat.

Quick Review Box:
1. Work Done: \(W = Fs\)
2. Kinetic Energy: \(E_k = \frac{1}{2}mv^2\)
3. Potential Energy: \(E_p = mgh\)
4. Power: \(P = \frac{W}{t} = Fv\)
5. Efficiency: \(\frac{Useful}{Total}\)

Final Encouragement

You’ve made it through the core concepts of Energy! Remember, Physics is less about memorizing and more about understanding the story of what's happening. When you see a problem, ask yourself: "Where was the energy at the start, and where did it go at the end?" Keep practicing those calculations, and you'll be an energy expert in no time!