Kinetic & Gravitational Potential Energy

Kinetic Energy

Kinetic energy is the energy an object has due to its motion (or velocity)
- The faster an object is moving, the greater its kinetic energy
When an object is falling, it is gaining kinetic energy since it is gaining speed
- This energy is transferred from the gravitational potential energy it is losing

Kinetic energy can be calculated using the following equation:

$E_{k} = \frac{1}{2} m v^{2}$

Where:
- E_k = kinetic energy (J)
- m = mass (kg)
- v = velocity (m s^–1)

Kinetic energy diagram, downloadable AS & A Level Physics revision notes

Kinetic energy: The energy an object has when it is moving

Worked example

A body travelling with a speed of 12 m s^-1 has kinetic energy 1650 J .The speed of the body is increased to 45 m s^-1.

Determine the body's new kinetic energy.

WE - kinetic energy answer image, downloadable AS & A Level Physics revision notes

Examiner Tip

When using the kinetic energy equation, note that only the speed is squared, not the mass or the ½.

If a question asks about the ‘loss of kinetic energy’, remember not to include a negative sign since energy is a scalar quantity.

Gravitational Potential Energy

Gravitational potential energy is energy stored in a mass due to its position in a gravitational field
- If a mass is lifted up, it will gain gravitational potential energy
- If a mass falls, it will lose gravitational potential energy
The equation for gravitational potential energy for energy changes in a uniform gravitational field is:

$∆ E_{p} = m g ∆ h$

Where:
- ΔE_p = gravitational potential energy (J)
- m = mass (kg)
- g = gravitational field strength (9.81 N kg^–1)
- Δh = change in height (m)

GPE diagram, downloadable AS & A Level Physics revision notes

Gravitational potential energy: The energy an object has when lifted up

The potential energy on the Earth’s surface at ground level is usually taken to be equal to zero
- However, any position can be taken as zero if you are calculating the change in gravitational potential energy
This equation is only relevant for energy changes in a uniform gravitational field (such as near the Earth’s surface)

Gravitational Potential Energy v Height Graphs

The two graphs below show how the gravitational potential energy changes with height for a ball being thrown up in the air and then falling down (ignoring air resistance)

GPE graphs, downloadable AS & A Level Physics revision notes

Graphs showing the linear relationship between gravitational potential energy and height

Since the graphs are straight lines, gravitational potential energy and height are said to have a linear relationship
These graphs would be identical for gravitational potential energy against time instead of height

Worked example

To get to his apartment, a man has to climb five flights of stairs.

The height of each flight is 3.7 m and the man has a mass of 74 kg.

What is the approximate change in the man's gravitational potential energy during the climb?

A. 13 000 J B. 2700 J C. 1500 J D. 12 500 J

WE - GPE answer image, downloadable AS & A Level Physics revision notes

Examiner Tip

This equation only works for objects close to the Earth’s surface, where we can consider the gravitational field to be uniform.

At A level, you might have to consider examples where the gravitational field is not uniform, such as in space, where this equation will not be relevant.

Gravitational potential energy is often shortened to GPE for ease. In your equations, you should stick to the correct symbol, which is $∆ E_{p}$

Kinetic & Gravitational Potential Energy (AQA AS Physics)

Revision Note