# 1.1.4 Gravitational Potential Energy

### Gravitational Potential Energy

• The gravitational potential energy (Ep or GPE) of an object (also known as its gravitational store) is defined as:

The energy an object has due to its height in a gravitational field

• This means:
• If an object is lifted up it will gain Ep
• If it falls, it will lose Ep

• The Ep of an object can be calculated using the equation:

Ep = m × g × h

• Where:
• Ep = gravitational potential energy, in Joules (J)
• m = mass, in kilograms (kg)
• g = gravitational field strength in Newtons per kilogram (N/kg)
• h = height in metres (m)

#### Gravitational Field Strength

• The gravitational field strength (g) on the Earth is approximately 10 N/kg
• The gravitational field strength on the surface of the Moon is less than on the Earth
• This means it would be easier to lift a mass on the Moon than on the Earth
• The gravitational field strength on the surface of the gas giants (eg. Jupiter and Saturn) is more than on the Earth
• This means it would be harder to lift a mass on the gas giants than on the Earth

Some values for g on the different objects in the Solar System

#### Worked Example

A man of mass 70 kg climbs a flight of stairs that is 3 m higher than the floor. Gravitational field strength is approximately 10 N/kg.

Calculate the increase in his gravitational potential energy store.

Step 1: List the known quantities

• Mass of the man, m = 70 kg
• Gravitational field strength, g = 10 N/kg
• Height, h = 3 m

Step 2: Write down the equation for gravitational potential energy

Ep = mgh

Step 3: Calculate the gravitational potential energy

Ep = 70 × 10 × 3 = 2100 J

#### Exam Tip

When doing calculations involving gravitational field strength, g, don’t panic, you will always be told the value of g in your examination paper!

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