National 5PhysicsSQARevision NotesDynamicsEnergyGravitational Potential Energy

Gravitational Potential Energy (SQA National 5 Physics): Revision Note

Exam code: X857 75

Katie M

Written by: Katie M

Reviewed by: Caroline Carroll

Updated on

Gravitational potential energy

  • Gravitational potential energy is defined as:

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

  • To lift an object through a gravitational field, work must be done against gravity, or the weight of the object

  • Whenever work is done, energy is transferred, which means:

    • If an object is lifted, energy is transferred to it as gravitational potential energy 

    • If an object is lowered, its gravitational potential energy is transformed into a different type of energy

Gravitational potential energy of an object lifted through a gravitational field

Person lifting a mass labelled "m" to a height "h" with the equation for gravitational potential energy shown: ΔEp = mgΔh.
When a mass is lifted up through a gravitational field, work is done. This work is transferred to the object as gravitational potential energy

Calculating gravitational potential energy

  • The gravitational potential energy gained or lost by an object can be calculated using the relationship:

E subscript p space equals space m g h

  • Where:

    • E subscript p = gravitational potential energy, measured in joules (J)

    • m = mass, measured in kilograms (kg)

    • g = gravitational field strength, measured in newtons per kilogram (N kg-1)

    • h = change in height, measured in metres (m)

  • This relationship is found from:

Change in potential energy = work done

E subscript p space equals space E subscript w

E subscript p space equals space F d

  • Where:

    • the applied force F is the weight, m g

    • the distance d moved is the height, h

E subscript p space equals space m g cross times d space equals space m g h

Worked Example

A man climbs a flight of stairs that is, in total, 3.0 m higher than the floor. The man has a mass of 72 kg, and the gravitational field strength on Earth is approximately 9.8 N kg-1.

Calculate the energy transferred to the man as gravitational potential energy.

Answer:

Step 1: List the known quantities

  • Mass of the man, m space equals space 72 space kg

  • Gravitational field strength, g space equals space 9.8 space straight N space kg to the power of negative 1 end exponent

  • Change in height, h space equals space 3.0 space straight m 

Step 2: Write down the relationship between potential energy, mass, gravitational field strength, and height

E subscript p space equals space m g h

Step 3: Calculate the gain in potential energy

E subscript p space equals space 72 space cross times space 9.8 space cross times space 3.0

E subscript p space equals space 2116.8 space straight J

Step 4: Round to an appropriate number of significant figures

  • The input values are to 2 s.f., therefore, the output value must be to 2 s.f.

E subscript p space equals space 2100 space straight J space open parentheses 2 space straight s. straight f. close parentheses

Examiner Tips and Tricks

In the exam, you will generally be expected to round your answers to an appropriate number of significant figures.

Your answer can only be as accurate as your least accurate input value. Therefore, your final answer should round to the lowest number of significant figures of all your input values.

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    Author
    Reviewer
    Katie M

    Author: Katie M

    Expertise: Physics Content Creator

    Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.

    Caroline Carroll

    Reviewer: Caroline Carroll

    Expertise: Physics & Chemistry Subject Lead

    Caroline graduated from the University of Nottingham with a degree in Chemistry and Molecular Physics. She spent several years working as an Industrial Chemist in the automotive industry before retraining to teach. Caroline has over 12 years of experience teaching GCSE and A-level chemistry and physics. She is passionate about creating high-quality resources to help students achieve their full potential.