# Changes in energy

*These revision notes cover the section on Changes in Energy assessed as part of the AQA GCSE Physics and Combined Sciences: Trilogy qualifications.*

### Understanding Energy Changes

Energy is fundamental in physics, representing the capability to do work or cause change. It manifests in various forms, including kinetic energy, potential energy, and many others. These notes focus on how energy changes form, particularly looking at the energy associated with moving objects, stretched springs, and objects raised above ground level.

#### Kinetic Energy of a Moving Object

Kinetic energy is the energy an object possesses because of its motion. It is determined by the object’s mass and its speed. The formula to calculate kinetic energy (Ek) is:

Ek = 0.5 × mass × speed^2

- Ek is the kinetic energy in joules (J)
- mass is in kilograms (kg)
- speed is in metres per second (m/s)

**Example**: A car with a mass of 1000 kg moving at a speed of 20 m/s has a kinetic energy of:

Ek = 0.5 × 1000 × 20^2 = 200,000 J

This implies the car possesses 200,000 Joules of energy due to its motion.

#### Elastic Potential Energy in a Stretched Spring

Elastic potential energy (Ee) is the energy stored in a stretched spring. This energy depends on the spring constant (k) and the spring’s extension (e). The formula to calculate elastic potential energy is:

Ee = 0.5 × spring constant × extension^2

- Ee is the elastic potential energy in joules (J)
- spring constant in newtons per metre (N/m)
- extension in metres (m)

**Example**: A spring with a spring constant of 300 N/m stretched by 0.2 metres stores:

Ee = 0.5 × 300 × 0.2^2 = 6 J

Meaning, the spring stores 6 Joules of energy.

#### Gravitational Potential Energy of an Object Raised Above Ground

Gravitational potential energy (Ep) is energy an object has due to its position in a gravitational field. The higher an object is, the more gravitational potential energy it has. The formula for gravitational potential energy is:

Ep = mass × gravitational field strength × height

- Ep is the gravitational potential energy in joules (J)
- mass is in kilograms (kg)
- gravitational field strength is in newtons per kilogram (N/kg)
- height is in metres (m)

**Example**: A rock with a mass of 50,000 kg raised to a height of 10 metres where gravitational field strength is 9.8 N/kg has:

Ep = 50,000 × 9.8 × 10 = 4,900,000 J

This indicates the rock holds 4,900,000 Joules of energy due to its elevated position.

You could also write this as 4,900 kJ.

### Investigating Energy Transfer

Energy’s ability to transfer from one form to another is fascinating. A typical example is the transformation from gravitational potential energy to kinetic energy.

When an object is raised, it gains gravitational potential energy. If allowed to fall, this energy converts into kinetic energy as it accelerates. By the time it reaches ground level, ideally, all of its initial gravitational potential energy is transformed into kinetic energy (ignoring air resistance).

**Example**: A ball of 0.2 kg dropped from 5 metres initially has gravitational potential energy but no kinetic energy. As it falls, its potential energy converts to kinetic energy. Just before hitting the ground, all its energy is kinetic.

Initial gravitational potential energy:

Ep = 0.2 × 9.8 × 5 = 9.8 J

Assuming no air resistance, this 9.8 J of potential energy fully converts into kinetic energy by the time the ball hits the ground.

### Summary

- Kinetic energy is related to an object’s movement and is influenced by its mass and velocity.
- Elastic potential energy is stored in stretched or compressed springs, dependent on the spring constant and extension.
- Gravitational potential energy is affected by an object’s height in a gravitational field and depends on its mass and height.
- Energy can transform from one form to another, exemplifying the principle of energy conservation.

Understanding these concepts helps in grasping the principles that rule the physical world, from simple playground mechanics to the complex movements of celestial bodies.

### Video on Energy Changes

### Quiz on Energy Changes

Write out your answers on a piece of paper, then check them against the solutions below.

**Question 1**: Calculate the kinetic energy of a bicycle with a mass of 15 kg moving at a speed of 10 m/s.

A) 750 J B) 1500 J C) 75 J D) 150 J

**Question 2**: A spring with a spring constant of 400 N/m is stretched 0.25 metres. What is the elastic potential energy stored in the spring?

A) 50 J B) 12.5 J C) 25 J D) 100 J

**Question 3**: If an object with a mass of 20 kg is raised to a height of 5 metres, how much gravitational potential energy does it gain? Assume the gravitational field strength is 9.8 N/kg.

A) 49 J B) 940 J C) 1960 J D) 980 J

**Question 4**: Which equation correctly represents the calculation of kinetic energy?

A) Ek = m × g × h B) Ek = 0.5 × m × v^2 C) Ek = 0.5 × k × e^2 D) Ek = m × v

**Question 5**: True or False: The energy stored in a stretched spring decreases if the spring constant increases, assuming the extension remains the same.

A) True B) False

**Question 6**: When an object falls freely from a certain height, into which form of energy is its gravitational potential energy converted?

A) Thermal energy B) Elastic potential energy C) Kinetic energy D) Chemical energy

**Question 7**: What happens to the gravitational potential energy of an object as it is lowered towards the ground?

A) It increases B) It decreases C) It remains the same D) It first increases, then decreases

**Question 8**: A ball of mass 0.5 kg is dropped from a height of 10 metres. Calculate its kinetic energy just before it hits the ground. Assume gravitational field strength is 9.8 N/kg and ignore air resistance.

A) 49 J B) 98 J C) 450 J D) 4.9 J

**End of questions**

### Answers

**Answer 1**: A) 750 J

Explanation: Ek = 0.5 × mass × speed^2 = 0.5 × 15 × 10^2 = 750 J

**Answer 2**: B) 12.5 J

Explanation: Ee = 0.5 × k × e^2 = 0.5 × 400 × 0.25^2 = 12.5 J

**Answer 3**: D) 980 J

Explanation: Ep = mass × gravitational field strength × height = 20 × 9.8 × 5 = 490 J

**Answer 4**: B) Ek = 0.5 × m × v^2

**Answer 5**: B) False

Explanation: The energy stored in a stretched spring increases with an increase in the spring constant, assuming the extension remains the same.

**Answer 6**: C) Kinetic energy

**Answer 7**: B) It decreases

Explanation: As the object is lowered, its height decreases, leading to a decrease in gravitational potential energy.

**Answer 8**: A) 49 J

Explanation: The initial gravitational potential energy, which is fully converted into kinetic energy just before the ball hits the ground, is calculated as Ep = mass × g × height = 0.5 × 9.8 × 10 = 49 J.