Physics
Cambridge IGCSE

TOPIC 1A: FORCES and MOTION

# 1.3 Mass and Weight

Mass and weight are terms used in science that have very specific meanings, whereas in everyday use they are often taken to describe the same thing. It can get confusing when listening to people about how much something weighs, when they are actually referring to the mass. Here are the correct meanings as used in science:

### Mass

Mass is a measure of the quantity of matter in an object. In simple terms, it relates to the number of atoms present, and how big those atoms are. The international unit for mass is the kilogram (kg).

### Weight

Figure 1. This astronaut has mass, but no weight.

Weight is a measure of the pull of gravity on an object. As it is a pull, it is also a force and is therefore measured in newtons (N). On Earth, if an object has mass, then gravity pulls on it and it has weight. However in space there is no gravity, and so nothing has any weight, only mass. Not many people have been to space, and this is why many consider weight and mass to be the same. However astronauts know from practical experience that they are very different.

Weight is caused by the effect of a gravitational field acting on a mass.

On Earth, the connection between mass and weight is quite simple as shown by this diagram:

Figure 2. The link between mass and weight.

In this diagram, the orange juice carton has a mass of 1 kg and gravity is pulling it downwards with a force of about 10 N.
It is similar for the bag of fruit - 5 kg mass experiences a force of about 50 N. The pull of gravity, or the weight, is always about 10 times higher than the mass. It is actually 9.8 times higher. We say that - on Earth - the gravitational field strength (given the letter 'g') is 9.8 newtons per kilogram, or 9.8 N/kg.

Gravitational field strength is defined as the force of gravity (weight) per unit mass.

We can put this idea together in a formula:

 gravitational field strength (N/kg )= weight (N) mass (kg)
 g = W m
Learn this formula!

Notes:

• g is actually 9.81 N/kg on Earth, but for GCSE you are OK to round this up to 9.8 N/kg - it is stated in the syllabus that you should do this.
• The units 'N/kg' are actually identical to 'm/s2', the units for acceleration. Therefore the gravitational field strength (g = 10 N/kg) can also be called the acceleration of gravity (g = 10 m/s2). This was described in section 1.2 on Motion Graphs (free fall).

### The solar system

Only a few people have ever been to the Moon. You may have seen some movie clips like the one below showing astronauts on the moon's surface. There is no air, but there is gravity - it is just much weaker than on Earth because the Moon has less mass.

YouTube video - Gene Cernan 'bunny hopping' on the Moon - Nasa 1972.

As the video shows, the gravitational field strength g is lower on the Moon - it is only 1.6 N/kg. (About 6 times lower than on the Earth).

The value of 'g' varies from planet to planet, as shown here:

Solar System Object

Gravitational Field Strength - g
(N/kg to 2 sig figs.)

Mercury 3.7
Venus 8.9
Mars 3.7
Jupiter 23
The Moon 1.6

Table 1. Variations in gravitational field strength (g).

Notice that Jupiter has a much higher field strength than the Moon. This is because the mass of Jupiter is much higher than the mass of the Moon.

It is much harder to figure out why two planets - Mars and Mercury - have similar values of 'g' even though they have different masses. Why is this?

The gravitational field strength at the surface of a planet depends on the mass of the planet, but also the distance from the surface to the centre of mass, which is the radius of the planet. Normally the mass is the key factor. However, even though Mercury has a smaller mass then Mars, it is very dense with a high concentration of metals. This means the radius is MUCH smaller than Mars, and keeps the value of 'g' relatively high.

You can use the values in table 1 to calculate the weight of objects on other planets, using the formula W = m x g.
For many of these questions, the mass of an object will remain the same (assuming it is the same object), but the weight can change as it depends on the strength of gravity acting on it.

Example:
Using data from table 1, how much would a 70 kg astronaut weigh on the Mars?

We know g = W/m, and so W = mg
m=70 kg, g=3.7 m/s2
Therefore weight = 70 x 3.7 = 259 N.

Questions:

3. If we took the 5 kg bag of fruit on a space journey, how much would it weigh in the following locations? (Use information from table 1 above).

• a). The Moon.
• b). Jupiter.
• c). Deep Space.

For all these questions, We know g = W/m, and so W = mg

• a) On the Moon, g = 1.6 N/kg (from table 1).
Therefore:
W= m x g =5 x 1.6 = 8.0 N

• b) On Jupiter, g = 23 N/kg (from table 1).
Therefore:
W= m x g =5 x 23 = 115 N

• c). In deep space, there is no gravity! g = zero.
Therefore W = 0 N (The bag is 'weightless').

4. On the Moon mission in 1972, the astronauts picked up a rock to bring back to Earth. The weight of the rock was 32 N on the Moon. Calculate:

• a). The mass of the rock.
• b). The weight of the rock when it was returned to Earth.

a). We know w = m x g. We also know that gmoon = 1.6 N/kg. Therefore:
 m = W g
So:
 m = 32 1.6

m = 20 kg.

b) If m = 20 kg, and on the Earth g = 10 N/kg,
then W = m x g
W = 20 x 10,
Therefore W = 200 N

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