Gravitational Fields (Cambridge International A-Level Physics)

Defining Gravitational Field

• There is a force of attraction between all masses

  • This force is known as the ‘force due to gravity’ or the weight

• The Earth’s gravitational field is responsible for the weight of all objects on Earth

• A gravitational field is an example of a field of force and is defined as:

A region of space where a mass experiences a force

• The direction of the gravitational field is always towards the centre of the mass

  • Gravitational forces are always attractive, and never repulsive

Gravitational field strength

• The gravitational field strength at a point is defined as:

The force per unit mass acting on a small mass at that point

• The strength of a gravitational field at a point can be calculated using:

$g=\frac{F_{g}}{m}$

• Where:

  • g = gravitational field strength (N kg^-1)
  • F_g = force due to gravity, or weight (N)
  • m = mass (kg)

• This equation tells us:

  • On planets with a large value of g, the gravitational force per unit mass is greater than on planets with a smaller value of g
  • This means objects will have a larger weight with a larger value of g

Weight of a person on Earth and Jupiter

A person’s weight on Jupiter would be so large a human would be unable to fully stand up

Worked Example Calculate the mass of an object with a weight of 10 N on Earth.

Answer:

Step 1: State the gravitational field strength equation

$g=\frac{F_{g}}{m}$

Step 2: Rearrange to make mass the subject

$m=\frac{F_{g}}{g}$

Step 3: Substitute in the known values to calculate

$m=\frac{10}{9.81}=1.0\mathrm{kg}$

Exam Hint There is a big difference between g and G (sometimes referred to as ‘little g’ and ‘big G’ respectively), g is the gravitational field strength and G is Newton’s gravitational constant. Make sure not to use these interchangeably!

Representing Gravitational Fields

• The direction and magnitude of a gravitational field is represented by gravitational field lines

  • Gravitational fields can be uniform or non-uniform

• Radial fields are non-uniform fields

  • The gravitational field strength g decreases with distance from the centre of the object
  • The gravitational field lines around a point mass are directed radially inwards

• Parallel field lines represent a uniform field

  • The gravitational field strength g is the same throughout the field
  • The gravitational field lines of a uniform field, where the field strength is the same at all points, is represented by equally spaced parallel lines
  • The Earth's gravitational field near the surface is almost uniform; therefore, it can be approximated as uniform

Gravitational field lines for a point mass and for a uniform gravitational field

Gravitational field lines for a point mass are radial and, for a uniform gravitational field, are parallel

Exam Hint Always add the arrows on the field lines! Gravitational forces are attractive only. Remember:

• For a radial field: it is towards the centre of the sphere or point charge
• For a uniform field: towards the surface of the object e.g. Earth