# Energy Calculations

## Energy Calculations Revision

**Energy Calculations**

The amount of energy stored **kinetic**, **gravitational **and **elastic potential** energy stores can be calculated using different equations. Energy is measured on **Joules (J)**.

**Kinetic Energy**

Whenever an object is **moving**, it has energy in its **kinetic energy store**. The amount of kinetic energy depends on the **mass** and** velocity** of the object.

You can calculate the amount of energy in an object’s kinetic energy store (\bold{E_k}) using the following formula:

E_k = \dfrac{1}{2} m v^2

- m= the mass of the object in kilograms \text{(kg)}
- v= the velocity of the object in metres per second \text{(m/s)}.

**Gravitational Potential Energy**

When an object is lifted in a **gravitational field**, it gains energy in its **gravitational potential energy store**. The amount of gravitational potential energy depends on the **mass** of the object,** how high **it has been lifted and the **strength** of the** gravitational field**. On Earth, the gravitational field strength is approximately 9.8\text{ m/s}^2.

The amount of energy in the gravitational potential energy store (\bold{E_p}) can be calculated using the following formula:

E_p = mgh

- m= the mass of the object in kilograms \text{(kg)}
- g= the gravitational field strength in newtons per kilogram \text{(N/kg)}
- h= the change in the height of the object in metres \text{(m)}.

You may have to calculate the height the object has been lifted by subtracting the **starting height** from the **final height**.

**Elastic Potential Energy**

When an object is **stretched** or **squashed**, it gains energy in its **elastic potential store**. The amount of elastic potential energy depends on the **extension** (distance the object is stretched or squashed) and the **spring constant **of an object. The spring constant is individual to each object and is measured in Newtons per metre (\text{N/m}).

The amount of elastic potential energy (\bold{E_e}) stored in an object can be calculated using the following formula:

E_e = \dfrac{1}{2} k x^2

- k= the spring constant of the object measured in newtons per metre \text{(N/m)}
- x = the extension (or compression) of the object in metres \text{(m)}. This is shown on the diagram on the right.

You may have to calculate the extension of the object by subtracting the **final length** from the **starting length**.

**Example: Calculating Elastic Potential Energy**

A 10\text{ cm} long wire with a spring constant of 5\text{ N/m} is stretched until it measures 12\text{ cm}. Calculate the potential energy stored by the stretched wire.

**Step 1:** Calculate the extension of the wire:

**Step 2:** Calculate the elastic potential energy stored by the wire:

## Energy Calculations Example Questions

**Question 1:** A rubber ball is at rest on the floor. State one way you could increase the energy of the ball and state which store of energy increases.

**[2 marks]**

**Push the ball** so that it rolls along the floor. This increases the **kinetic energy**.

*or*

**Lift the ball** above the ground. This increases the **gravitational potential energy**.

*or *

**Squash the ball**. This increases the **elastic potential energy**.

Accept suitable alternatives.

**Question 2:** A model airplane has mass 3\text{ kg} and is travelling at 2\text{ m/s}. Calculate the kinetic energy the model airplane is storing.

**[2 marks]**

E_k= \dfrac{1}{2}\times3\times2^2 = \bold{6\text{ J}}

**Question 3: **An athlete competing in the high jump jumps 3\text{ m}. Calculate the gravitational potential energy gained by the athlete as they jump to this height. The mass of the athlete is 85\text{ kg}. Give your answer to 2 significant figures.

**[2 marks]**

**Question 4: **When stretched, a spring with a spring constant of 10\text{ N/m} increases from 4\text{ cm} long to 5\text{ cm} long. Calculate the energy stored in the spring.

**[3 marks]**