Examples

Question

Find the weight of a person on Earth if they have a mass of 65 kg (g = 10 N/kg)

W = mg

m = 65 kg

g = gravitational field strength g = 10 N/kg

W = 65 kg x 10 N/kg

W = 650 N

The weight of the person is 650 N.

Gravitational pull on the Moon

The Moon has a smaller mass than the Earth and so the pull of gravity by the moon on an object is smaller than on the earth.

The moon has a smaller gravitational field strength.

On the Moon, g = 1.6 N/kg.

In other words, a 1 kg mass has a weight on the Moon of 1.6 N.

Question

What is the weight of a 45 kg girl on:

  1. the Earth, where g = 10 N/kg
  2. the Moon, where g = 1.6 N/kg

1. The Earth

W = mg

m = 45 kg

g = gravitational field strength g = 10 N/kg

W = 45 kg x 10 N/kg

W = 450 N

The weight of the girl on the Earth is 450 N

2. The Moon

W = mg

m = 45 kg

g = gravitational field strength g = 1.6 N/kg

W = 45 kg x 1.6 N/kg

W = 72 N

The weight of the girl on the Moon is 72 N.

The mass of the girl is the same on the Earth and the Moon because the amount of matter in the girl is the same in both places.

However, the weight of the girl on the Earth is much greater than the weight of the girl on the Moon because the Earth’s pull of gravity is much greater than the Moon’s.

Question
  • What is the mass of a person who weighs 120 N on the Moon? (g = 1.6 N/kg)?
  • What would the mass and weight of the same person be back on Earth where g = 10 N/kg?

1. The Moon

  • m = \frac{\text{W}}{\text{g}}
  • W = 120 N
  • g = gravitational field strength g = 1.6 N/kg
  • m = 120 N ÷ 1.6 N/kg
  • m = 75 kg
  • The mass of the person on the Moon is 75 kg

2. The Earth

  1. The mass of the person back on the Earth will also be 75 kg as mass does not change from place to place.
  2. W = mg
  3. m = 75 kg
  4. g = gravitational field strength g = 10 N/kg
  5. W = 75 kg x 10 N/kg
  6. W = 750 N
  7. The weight of the person on the Earth is 750 N.

Summary

MassWeight
Scalar quantityVector quantity
Measured in kilogrammes kgMeasured in newtons N
A measure of the amount of matterThe force of gravity acting on the object
Never changesVaries from place to place