# Weight and mass

## Key points

• The terms and are often wrongly used to describe the same thing.

• In science, weight and mass are very different.

## Weight versus mass

The terms weight and mass are often used incorrectly. Phrases like ‘a bag of sugar weighs 1 kg’ are not scientifically correct.

Mass is a measure of the amount of an object is made out of. Mass is measured in kilograms (kg). Very small masses are sometimes measured in grams (g). There are 1000 g in one kg.

Weight is the force that acts on mass due to gravity and is therefore measured in newtons (N).

## Calculating weight and mass

The following equation can be used to calculate the weight of an object:

$$W = m \times g$$

$$Weight~(N) = mass~(kg) \times gravitational~field~strength~(N/Kg)$$

The on Earth is 10 N/kg.

This means that a 1 kg mass would be attracted to Earth by a force of 10 N.

### How to calculate weight

An apple has a mass of 0.2 kg. Calculate the weight of the apple on Earth (g = 10 N/kg).

W = ?

m = 0.2 kg

g = 10 N/kg

Use the weight equation:

$$W = m \times g$$

and substitute in the values you know:

$$W = 0.2 \times 10$$

$$W = 2~N$$

The weight of the apple on Earth is 2 N.

### How to calculate mass

A big textbook weighs 90 N. Calculate the mass of the book (g = 10 N/kg).

W = 90 N

m = ?

g = 10 N/kg

Remember to use the equation:

$$W = m \times g$$

Substitute in the values you know:

$$90 = m \times10$$

Now divide both sides by 10:

$$\frac{90}{10} = \frac{m \times 10}{10}$$

$$9 = m$$

$$m = 9~kg$$

The mass of the book is 9 kg.

Now have a go at answering this question.

A student has a mass of 45 kg. The gravitational field strength on Earth is 10 N/kg. What is the weight of the student?

The weight of the student is 450 N.

This is calculated by multiplying their mass by the gravitational field strength.

45 x 10 = 450.

## Weight and other planets

is a result of gravity interacting with . This means that an object’s weight will change depending on the strength of the acting on it.

Different objects that are in our Universe have gravitational fields of varying strengths.

The planets in order from the Sun on the left (distances not drawn to scale)

## Did you know?

The planets in our solar system have different gravitational field strengths.

For example, the gravitational field strength on Earth is 10 N/kg whereas on Jupiter it is 24.7 N/kg.

This means that a mass of 50 kg will weigh just over double on Jupiter than it would on Earth.

The table shows the different gravitational field strengths for each of the different planets.

PlanetGravitational field strength (N/kg)
Mercury4
Venus9
Earth10
Mars4
Jupiter23
Saturn9
Uranus9
Neptune11

We can also calculate how an object’s weight would be different on different planets.

For example, because the gravitational field strength on Earth is 10 N/kg, if a person has a mass of 60 kg their weight on Earth would be calculated as follows:

$$W = m \times g$$

$$W = 60 \times 10$$

$$W = 600$$ N

However on Mars, which has a gravitational field strength of 4 N/kg, the same person’s weight would be:

$$W = m \times g$$

$$W = 60 \times 4$$

$$W = 240$$ N

### More about weight and mass

Watch the video of physicist Jon Chase explaining that the mass of an object is constant but its weight depends on the gravitational force.

## Measuring weight and mass

As with most quantities in science you need to know how you can find the mass and weight of objects.

To find an object’s mass you need to use a .

It is important that you set the balance to 0 before placing any object on it so that your reading is .

Once you have used the balance to find the mass of an object you can then complete a calculation using the weight equation to calculate the weight of the object.

$$W = m \times g$$

You can also use a newton meter, sometimes called a force meter, to measure the weight of an object too.

A newton meter has a spring in it, which extends due to the weight of the object you hang from the hook at the bottom. The scale on the newton meter then indicates the amount the object weighs.