Gravitational Field Strength (DP IB Physics): Revision Note

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Katie M

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Gravitational Field Strength

  • There is a universal force of attraction between all matter with mass

    • 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 defined as:

A region of space where a test mass experiences a force due to the gravitational attraction of another mass

  • The direction of the gravitational field always acts toward the centre of the mass which produces the field

    • This is because gravitational forces are always attractive

  • Gravity has an infinite range, meaning it affects all objects in the universe

    • There is a greater gravitational force around objects with a large mass (such as planets)

    • There is a smaller gravitational force around objects with a small mass (almost negligible for atoms)

Gravitational Attractive Force, downloadable AS & A Level Physics revision notes

The Earth's gravitational field produces an attractive force. The force of gravity is always attractive

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

The force per unit mass experienced by a test mass at that point

  • This can be written in equation form as:

g space equals space F over m

  • Where:

    • g = gravitational field strength (N kg−1)

    • F = force due to gravity, or weight (N)

    • m = mass of test mass in the field (kg)

  • This equation shows that:

    • 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

  • An object's mass remains the same at all points in space

    • However, on planets such as Jupiter, the weight of an object will be greater than on a less massive planet, such as Earth

    • This means the gravitational force would be so high that humans, for example, would not be able to fully stand up

gravitational field strength, downloadable AS & A Level Physics revision notes

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

  • Factors that affect the gravitational field strength at the surface of a planet are:

    • the radius r (or diameter) of the planet

    • the mass M (or density) of the planet

  • This can be shown by equating the equation F = mg with Newton's law of gravitation:

F space equals space fraction numerator G M m over denominator r squared end fraction

  • Substituting the force F with the gravitational force mg leads to:

m g space equals space fraction numerator G M m over denominator r squared end fraction

  • Cancelling the mass of the test mass m leads to the equation:

g space equals space fraction numerator G M over denominator r squared end fraction

  • Where:

    • G = Newton's Gravitational Constant

    • M = mass of the body causing the field (kg)

    • r = distance from the mass where you are calculating the field strength (m)

  • This equation shows that: 

    • The gravitational field strength g depends only on the mass of the body M which produces the field

  • Hence, objects with any mass m in that field will experience the same gravitational field strength

    • The gravitational field strength g is inversely proportional to the square of the radial distance, r2

Worked Example

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

Answer:

Worked Example

The mean density of the Moon is 3 over 5 times the mean density of the Earth. The gravitational field strength on the Moon is 1 over 6 the gravitational field strength on Earth.

Determine the ratio of the Moon's radius r subscript M to the Earth's radius r subscript E.

Answer:

Step 1: Write down the known quantities

  • g subscript M = gravitational field strength on the Moon, rho subscript M = mean density of the Moon

  • g subscript E = gravitational field strength on the Earth, rho subscript E = mean density of the Earth

rho subscript M space equals space 3 over 5 rho subscript E

g subscript M space equals space 1 over 6 g subscript E

Step 2: Write down the equations for the gravitational field strength, volume and density

Gravitational field strength:  g space equals space fraction numerator G M over denominator r squared end fraction

Volume of a sphere:  V space equals space 4 over 3 straight pi r cubed space space space space space rightwards double arrow space space space space space space V space proportional to space r cubed

Density:  rho space equals space M over V space space space space space rightwards double arrow space space space space space M space equals space rho V space equals space 4 over 3 straight pi rho r cubed space space space space space rightwards double arrow space space space space space M space proportional to space rho r cubed

Step 3: Substitute the relationship between M and r into the equation for g

g space proportional to space rho fraction numerator open parentheses r cubed close parentheses over denominator r squared end fraction space space space space space rightwards double arrow space space space space space space g space proportional to space rho r

Step 4: Find the ratio of the gravitational field strength

g subscript M space proportional to space rho subscript M r subscript M

g subscript E space proportional to space rho subscript E r subscript E

g subscript M space equals space 1 over 6 g subscript E space space space space space rightwards double arrow space space space space space rho subscript M r subscript M space equals space 1 over 6 rho subscript E r subscript E

Step 5: Substitute the ratio of the densities into the equation

open parentheses 3 over 5 rho subscript E close parentheses space r subscript M space equals space 1 over 6 rho subscript E r subscript E

3 over 5 r subscript M space equals space 1 over 6 r subscript E

Step 6: Calculate the ratio of the radii

r subscript M over r subscript E space equals space 1 over 6 divided by 3 over 5 space equals space 5 over 18 space equals space 0.28

Examiner Tips and Tricks

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!

Remember the equation density space equals space fraction numerator space mass over denominator volume end fractionwhich may come in handy with some calculations. The equation for the volume of common shapes is in your data booklet.

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Katie M

Author: Katie M

Expertise: Physics Content Creator

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.