Welcome to the World of Moving Energy!

In this chapter, we are going to explore two of the most important energy "stores" in Physics: Kinetic Energy and Gravitational Potential Energy. Whether it is a rollercoaster plunging down a track or a feather drifting in the wind, energy is constantly moving between these stores. Understanding this is like learning the "currency" of the universe—it tells us exactly how things move and how much "oomph" they have!

1. Gravitational Potential Energy (GPE)

Gravitational Potential Energy (GPE) is the energy an object has because of its position in a gravitational field. Think of it as "stored" energy. If you lift a book higher, you are doing work against gravity, and that energy is stored in the book as GPE.

The GPE Formula

To calculate how much GPE an object has, we use this formula:

\( GPE = m \times g \times h \)

  • \( m \) is the mass of the object (measured in kilograms, \( kg \)).
  • \( g \) is the gravitational field strength (on Earth, this is approximately \( 10 \text{ N/kg} \)).
  • \( h \) is the height the object is lifted (measured in metres, \( m \)).
  • \( GPE \) is the energy (measured in Joules, \( J \)).

Analogy: Imagine a heavy brick held above your toe. The higher you lift it, the more "potential" it has to cause a problem! That's GPE in action.

Quick Review:

If you double the mass, you double the GPE. If you double the height, you also double the GPE. They are directly proportional!


2. Kinetic Energy (KE)

Kinetic Energy (KE) is the energy of motion. Anything that is moving has kinetic energy. If an object stops moving, its kinetic energy becomes zero.

The KE Formula

This formula is a little more famous (and a bit more "maths-heavy"), so let's break it down carefully:

\( KE = \frac{1}{2} \times m \times v^2 \)

  • \( m \) is the mass (in \( kg \)).
  • \( v \) is the speed (or velocity) of the object (in \( m/s \)).
  • \( KE \) is the energy (in Joules, \( J \)).

Important Warning: In the formula, only the speed (\( v \)) is squared. Do not square the mass or the \(\frac{1}{2}\)!

Why speed is "extra" important:

Because the speed is squared, it has a massive effect on the energy. If a car doubles its speed, it doesn't just have twice the kinetic energy—it has four times the energy (\( 2^2 = 4 \))! This is why high-speed crashes are so much more dangerous than low-speed ones.


In Physics, we have a golden rule: Energy cannot be created or destroyed; it can only be transferred from one store to another. This is the Conservation of Energy.

Work Done and Energy Transfer

In a previous chapter, you learned that \( \text{Work Done} = \text{Force} \times \text{distance} \). In this context, Work Done is exactly equal to the Energy Transferred.

\( W = \Delta E \)

The Falling Object Scenario

Imagine you drop a ball from a balcony. At the very top, it has maximum GPE and zero KE (because it isn't moving yet). As it falls:

  1. The height decreases, so GPE decreases.
  2. The speed increases, so KE increases.
  3. The GPE is being transferred mechanically into KE.

If we ignore air resistance (which we often do in exam questions to keep things simple), we can say:

Loss of GPE = Gain in KE

\( m \times g \times h = \frac{1}{2} \times m \times v^2 \)

Did you know? Since mass (\( m \)) is on both sides of that equation, it actually cancels out! This means that (if there's no air resistance), a bowling ball and a feather will fall at the same rate and reach the same speed.


4. Step-by-Step: Solving a Transfer Problem

Don't worry if these calculations seem tricky. Just follow these steps:

Example Question:

An apple with a mass of \( 0.2 \text{ kg} \) falls from a branch \( 5 \text{ metres} \) high. Calculate its speed just before it hits the ground. (Assume \( g = 10 \text{ N/kg} \)).

Step 1: Calculate the GPE at the start.
\( GPE = m \times g \times h \)
\( GPE = 0.2 \times 10 \times 5 = 10 \text{ J} \)

Step 2: Use the energy link.
The energy transferred to KE is \( 10 \text{ J} \). So, \( KE = 10 \text{ J} \).

Step 3: Rearrange the KE formula to find speed (\( v \)).
\( 10 = \frac{1}{2} \times 0.2 \times v^2 \)
\( 10 = 0.1 \times v^2 \)
\( 100 = v^2 \)
\( v = \sqrt{100} = 10 \text{ m/s} \)


5. Common Mistakes to Avoid

  • Unit Traps: Always check that mass is in kg (not grams) and height is in m (not cm). If you see grams, divide by 1000!
  • Forgetting the Square: In the KE formula, students often forget to square the velocity, or they forget to take the square root at the end when finding velocity.
  • The Value of \( g \): In Edexcel IGCSE, always use \( 10 \text{ N/kg} \) for \( g \) unless the paper tells you otherwise.

Key Takeaways

1. GPE is "height energy": \( GPE = m \times g \times h \).
2. KE is "motion energy": \( KE = \frac{1}{2} \times m \times v^2 \).
3. Conservation: When an object falls, GPE is transferred into KE. When an object is thrown up, KE is transferred into GPE.
4. Work Done: Lifting an object requires work, and that work equals the GPE gained.