Examples
Question
Find the weightThe force acting on an object due to the pull of gravity from a massive object like a planet. The force acts towards the centre of the planet and is measured in newtons (N). of a person on Earth if they have a massThe amount of matter an object contains. Mass is measured in kilograms (kg) or grams (g). 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:
- the Earth, where g = 10 N/kg
- 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
- The mass of the person back on the Earth will also be 75 kg as mass does not change from place to place.
- W = mg
- m = 75 kg
- g = gravitational field strength g = 10 N/kg
- W = 75 kg x 10 N/kg
- W = 750 N
- The weight of the person on the Earth is 750 N.
Summary
| Mass | Weight |
| Scalar quantity | Vector quantity |
| Measured in kilogrammes kg | Measured in newtons N |
| A measure of the amount of matter | The force of gravity acting on the object |
| Never changes | Varies from place to place |
| Mass | Scalar quantity |
|---|---|
| Weight | Vector quantity |
| Mass | Measured in kilogrammes kg |
|---|---|
| Weight | Measured in newtons N |
| Mass | A measure of the amount of matter |
|---|---|
| Weight | The force of gravity acting on the object |
| Mass | Never changes |
|---|---|
| Weight | Varies from place to place |