Changes in energy Revision Notes for AQA GCSE Physics

Changes in energy

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

What is kinetic energy?

Kinetic energy is the energy that moving objects have. The faster something moves, the more kinetic energy it has. This type of energy is directly related to motion - when an object stops moving, its kinetic energy becomes zero.

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

Where:

$E_k$ = kinetic energy (in joules, J)
$m$ = mass (in kg)
$v$ = speed (in m/s)

chatImportant

Always remember to square the speed value when calculating kinetic energy. This is the most common mistake students make in kinetic energy calculations.

Key relationships for kinetic energy

Understanding how kinetic energy changes with mass and speed is crucial for solving problems effectively.

Mass relationship: If you double the mass, you double the kinetic energy
Speed relationship: If you double the speed, the kinetic energy increases by four times (because speed is squared)

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The speed relationship is particularly important - small changes in speed create large changes in kinetic energy because of the squared relationship.

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Worked Example: Calculating Kinetic Energy

A ball with mass 0.8 kg moves at 14 m/s. Calculate its kinetic energy.

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

Step 2: Substitute the values $E_k = \frac{1}{2} \times 0.8 \times 14^2$

Step 3: Calculate step by step $E_k = \frac{1}{2} \times 0.8 \times 196 = 78.4 \text{ J}$

What is gravitational potential energy?

Gravitational potential energy is the energy an object gains when it's lifted above the ground. The higher you lift it, the more energy it stores. This energy comes from doing work against gravity and can be converted back to kinetic energy when the object falls.

Formula: $E_p = mgh$

Where:

$E_p$ = gravitational potential energy (in joules, J)
$m$ = mass (in kg)
$g$ = gravitational field strength (10 N/kg on Earth)
$h$ = height above ground (in metres, m)

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On Earth, we use $g = 10 \text{ N/kg}$ as a standard value for gravitational field strength. This makes calculations simpler while maintaining good accuracy.

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Worked Example: Calculating Gravitational Potential Energy

A 73 kg person climbs 26 m high. Calculate the gravitational potential energy gained.

Step 1: Write down the formula $E_p = mgh$

Step 2: Substitute the values $E_p = 73 \times 10 \times 26$

Step 3: Calculate $E_p = 18,980 \text{ J}$

What is elastic potential energy?

Elastic potential energy is the energy stored in stretched or compressed springs. The more you stretch a spring, the more energy it stores. This energy is released when the spring returns to its original shape.

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

Where:

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

chatImportant

When measuring extension in centimetres, convert to metres by dividing by 100. Forgetting to convert units is a common source of errors in elastic potential energy calculations.

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Worked Example: Calculating Elastic Potential Energy

A spring with spring constant 48 N/m is stretched by 0.25 m. Calculate the elastic potential energy stored.

Step 1: Write down the formula $E_e = \frac{1}{2}ke^2$

Step 2: Substitute the values $E_e = \frac{1}{2} \times 48 \times 0.25^2$

Step 3: Calculate step by step $E_e = \frac{1}{2} \times 48 \times 0.0625 = 1.5 \text{ J}$

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Key Points to Remember:

Kinetic energy depends on mass and speed squared: $E_k = \frac{1}{2}mv^2$
Gravitational potential energy depends on mass, gravity, and height: $E_p = mgh$
Elastic potential energy depends on spring constant and extension squared: $E_e = \frac{1}{2}ke^2$
Always square the values for speed and extension in your calculations
Energy is always measured in joules (J)
Remember to check your units - convert centimetres to metres when needed

Changes in energy (AQA GCSE Physics): Revision Notes