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 **W = 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.