Changes in energy Revision Notes for AQA GCSE Physics Combined Science

Changes in energy

Energy changes can be calculated for moving objects, stretched springs and objects raised above the ground. There are three main types of energy you need to know about: kinetic energy, gravitational potential energy, and elastic potential energy.

Kinetic energy

Kinetic energy is the energy stored in moving objects. Any object that moves has kinetic energy.

How to calculate kinetic energy

The formula for kinetic energy is:

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

Where:

$E_k$ = kinetic energy in joules (J)
$m$ = mass in kilogrammes (kg)
$v$ = speed in metres per second (m/s)

chatImportant

Remember to square the speed value $(v \times v)$ when using this formula.

Key facts about kinetic energy

Understanding the relationships in kinetic energy is crucial for problem-solving:

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Kinetic energy is directly proportional to mass. If you double the mass, you double the kinetic energy.
Kinetic energy is directly proportional to the square of speed. If you double the speed, the kinetic energy increases by four times.
The faster something moves, the more kinetic energy it has.

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Worked Example: Calculating Kinetic Energy

A mass of 800g is moving at 14m/s. Calculate its kinetic energy.

Step 1: Convert units 800g = 0.8kg

Step 2: Apply the formula $E_k = \frac{1}{2}mv^2$

Step 3: Substitute values $E_k = \frac{1}{2} \times 0.8 \times 14^2 = \frac{1}{2} \times 0.8 \times 196 = 78.4J$

Gravitational potential energy

Gravitational potential energy is the energy gained when an object is raised above the ground. The higher up an object is, the more gravitational potential energy it has.

How to calculate gravitational potential energy

The formula is:

$E_p = mgh$

Where:

$E_p$ = gravitational potential energy in joules (J)
$m$ = mass in kilogrammes (kg)
$g$ = gravitational field strength in newtons per kilogramme (N/kg) - usually 10N/kg on Earth
$h$ = height in metres (m)

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Worked Example: Calculating Gravitational Potential Energy

A body of mass 73kg is lifted through a vertical height of 26m. Calculate the gravitational potential energy gained.

Step 1: Apply the formula $E_p = mgh$

Step 2: Substitute values $E_p = 73kg \times 10N/kg \times 26m = 18,980J$

Elastic potential energy

Elastic potential energy is the energy stored in a stretched spring or elastic material. When you stretch or compress a spring, it stores energy.

How to calculate elastic potential energy

The formula is:

$E_e = \frac{1}{2}ke^2$

Where:

$E_e$ = elastic potential energy in joules (J)
$k$ = spring constant in newtons per metre (N/m)
$e$ = extension in metres (m)

chatImportant

Remember to square the extension and convert centimetres to metres by dividing by 100.

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Worked Example: Calculating Elastic Potential Energy

A spring is distorted elastically. It increases its length by 25cm when a total weight of 12N is added. The spring constant is 48N/m.

Step 1: Convert units 25cm = 0.25m

Step 2: Apply the principle Energy stored = work done

Step 3: Apply the formula $E_e = \frac{1}{2}ke^2$

Step 4: Substitute values $E_e = \frac{1}{2} \times 48N/m \times (0.25m)^2 = 1.5J$

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Key Points to Remember:

Kinetic energy = $\frac{1}{2}mv^2$ - energy of moving objects
Gravitational potential energy = $mgh$ - energy of objects raised up high
Elastic potential energy = $\frac{1}{2}ke^2$ - energy stored in stretched springs
Always use the correct units: mass in kg, speed in m/s, height in m, extension in m
Remember to square the speed and extension in the formulas
All energy is measured in joules (J)

Changes in energy (AQA GCSE Physics Combined Science): Revision Notes