2.5 Weight, work done and calculating gravitational potential energy

Two types of calculations follow on from the 'weight and gravity' notes above.

You may encounter either of them before or after studying 'weight and gravity', but they are closely related and follow on from the notes above.

 

 Weight (N) = mass (kg) x gravitational field constant g (N/kg)

If you allow a weight to fall it can do work, because a raised weight is an energy store of gravitational potential energy (GPE).

The general formula for work done (energy transferred) is:

work done in joules = acting resultant force in newtons x distance through which the force acts in metres

Work (J) = F (N) x d (m)

 

You can then apply this equation to calculate the energy stored as GPE on raising a weight (mass x gravitational force) a given height. You therefore have also calculated the energy that can be released (ignoring friction) if the weight is allowed to fall.

The force (F) involved will be the weight of material raised or lowered

In general an object or material possesses gravitational potential energy by virtue of its higher position and can then fall or flow down to release the GPE e.g. winding up the weights on a clock, water stored behind a dam that can flow down through a turbine generator. Any object falling or material flowing downwards is converting GPE into kinetic energy and any object raised in height gains GPE.

Since gravitational energy is a form of stored energy, it does nothing until it is released and converted into another form of energy.

The amount of gravitational potential energy gained by an object raised above ground level can be calculated using the equation:

GPE = mass × gravitational field strength × height

E_gpe = m g h

gravitational potential energy, E_gpe, in joules, J

mass, m, in kilograms, kg

gravitational field strength, g, in newtons per kilogram, N/kg

height, h, in metres, m

Note: (i) In any calculation the value of the gravitational field strength (g) will be given.)

(ii) In the equation you should realise that the m x g = weight, the first two parts of the right-hand side of the equation. This is effectively the force that moves through the height the object is raised or lowered. This means the GPE equation is just a variation of the general equation for work done or energy transferred from one energy store to another.

GPE = mgh is another form of Work = Fd, so I hope you can see the connection?

Also note that when an object /material falls, the GPE is converted into kinetic energy.

The gravitational potential energy store of the material decreases and the kinetic energy store of the material/object increases.

When a object stops falling, its maximum KE equals the GPE it had with respect to the height the object falls.

To avoid repeating the same calculations see also ...

Gravitational potential energy store calculations

includes examples of using E_gpe = m g h = KE = 0.5 m v²

INDEX physics notes FORCES section 2 on mass, weight and gravity

GPE = m × g × h