Spark image

Gravitational Potential energy

The gravitational potential energy of a mass m is the energy required to bring the mass m from infinity to a point on the field. The zero point for the field strength, and therefore for the gravitational energy, being taken as being at infinity.

For this reason gravitational potential energy described in this way is taken as negative. Energy must be put into an object to raise it away from the surface of the Earth - making its gravitational potential energy less negative. If this seems strange remember that the input of energy when you lift something is positive - the change in the gravitational energy of the object is positive. It can be calculated by simply multiplying the gravitational potential (VG = g) at the point by the mass m and the vertical distance moved (h) or by using the formula given below based on gravitation theory.

Gravitational potential energy = mgh

where g is the intensity of the gravitational field (assumed uniform here) and h is the vertical distance moved in the field.

It is important to understand that gravitational energy (= Force x distance) is a scalar.

The energy is converted to other forms when the gravitational potential energy changes due to a movement within the field. (Figure 2) If the distance moved parallel to the gravitational field is Δh then the change in potential energy is:

Gravitational potential energy change = mgΔh

It is important not to confuse gravitational energy with gravitational potential, the gravitational potential energy refers to a mass m and so the gravitational energy at a point in the field distance r from the centre of the mass producing the field is:



Gravitational potential energy = -GMm/r


Example problems
1. A crane lifts a load of 300 kg through a distance of 2.5 m onto a truck. Calculate the gain in gravitational potential energy. Gravitational field intensity = 9.8 Nkg-1.

Gravitational potential energy gained = mgΔh = 300x9.8x2.5 = 7350 J

2. A mass of 25 kg is moved a distance of 35 m at an angle of 20o to a gravitational field of intensity 9.8 Nkg-1. Calculate the change in gravitational energy.

Change in gravitational potential energy = 25x9.8x35cos 20 = 8057 J


Example problems
When a body is moved from the Earth's surface to a height we can write the change in gravitational potential energy as Δ(p.e.) = + GmMh/[R(R+ h)]

So for a mass of 2 kg moved through 100 m we have:
Δ(p.e.) = [62x107x2x100]/6400x103= 1969 J which is very close to the value obtained using mgh.


See also: Gravitational potential energy
 

A VERSION IN WORD IS AVAILABLE ON THE SCHOOLPHYSICS USB
 
 
 
 
© Keith Gibbs 2020