10.15 Units of mass

Mass vs weight

Colloquially, when we use everyday words, we tend to use the word weight when what we are actually referring to is called mass.

Mass is a measurement of how much matter is in an object. Weight is a measurement of how hard the force of gravity is pulling on that object.

The mass of an object is the same wherever the object is - be that on Earth, floating around on the moon, or struggling to move on Jupiter (the biggest planet in the solar system). This is because no matter where the object is, the amount of stuff it is made of does not change.

The weight of an object, on the other hand, depends on how much the force of gravity is acting on it at a particular point in time. This means that an object would weigh less on the moon than it did on Earth, because the force of gravity is much lower there. Similarly, the object would weigh about $2.5$2.5 times more on Jupiter, due to its stronger force of gravity.

So when we talk about mass and weight, if we are talking about being on the Earth's surface then they are often used interchangeably (despite having different units). But if we want to look at the physics of a different planet or situation with different gravitational pulls, then it is important to remember the difference between mass and weight.

 

Units of mass

Mass is usually measured using one of the following units:

• milligrams (mg)
• grams (g)
• kilograms (kg)
• metric ton or tonne (t)

You will likely be familiar with most of these units through previous experiences - such as while cooking, taking medicine, or even in science experiments at school.

 

Estimating mass

Just as with lengths and areas to determine the correct unit to use, and be able to estimate the mass of an object it's useful to identify some common items that are about the mass of the units above. Such as:

• $1$1 mg is about the mass of a grain of salt
• $1$1 g is about the mass of an m&m or a thumbtack
• $1$1 kg is the mass of $1$1 litre of water
• $1$1 t is the mass of $1000$1000 litres of water (an average mid-sized car is about $1.6$1.6 tonnes)

Sometimes we need to estimate the mass of an object and when estimating it is useful to have some point of reference. Do you know your mass in kilograms? How much less would the mass of a domestic cat be? How much more would the mass of a tiger be? Considering the items above and perhaps some other common items as reference points we can estimate the mass of objects.

We can also consider the mass of a similar but differently sized object if it would be made from the same material. For example, if we know one bag of flour has a mass of around $500$500 g, we can estimate that $10$10 bags of flour would have a mass of around $5$5 kg.

 

Practice questions

Question 1

Question 2

Question 3

 

Converting units of mass

The following image shows the relationship between different units of mass.

• To move from larger mass units to smaller mass units we multiply by the conversion factor.
• To move from smaller mass units to larger mass units we divide by the conversion factor.

 

Notice that there is a nice pattern when looking at changing units of mass - between each step it is a factor of $1000$1000. That's different to the conversions we have seen in length and area, but probably easier to remember.

 

The prefixes

Notice the similarities with the naming of units here to the units we have used throughout measurement.

The prefix milli. Milli means $\frac{1}{1000}$11000​th of something. So we can see here that a milligram was $\frac{1}{1000}$11000​th of a gram, which means that $1000$1000 mg are in $1$1 gram. That is the same for a millimetre, where $1000$1000 mm are in $1$1 metre.

Also the prefix kilo. Kilo means $1000$1000 of something, so a kilogram is $1000$1000 grams and a kilometre is $1000$1000 metres.

Other common prefixes include centi for $\frac{1}{100}$1100​th of something such as centimetres and mega for a million of something such as a megalitre. A tonne could also be referred to as a megagram. There are standard prefixes for measuring very large and very small things, which can be found here.

 

Worked example

Example 1

Convert $3.25$3.25 kg into mg.

Think: Think about the steps needed to move from kg to mg. (kg $\rightarrow$→ g $\rightarrow$→ mg) we are going from large units to small units, so we need to multiply. And since there are two steps with the same conversion factor we need to multiply by $1000$1000 twice. This can be done in one calculation or in steps as below.

Do: First convert to grams:

$3.25$3.25 kg	$=$=	$3.25\times1000$3.25×1000 g
	$=$=	$3250$3250 g

Then convert to mg:

$3250$3250 g	$=$=	$3250\times1000$3250×1000 mg
	$=$=	$3250000$3250000 mg

EXAMPLE 2

Convert $148960000$148960000 mg into tonnes

Think: Think about the steps needed to move from mg to tonnes. (mg $\rightarrow$→ g $\rightarrow$→ kg $\rightarrow$→ t) and we are converting from a small unit to a larger unit, so we will need to divide by the conversion factor. The conversion factor is $1000$1000 in each case and there are three steps.

Do: First convert to grams: $148960000$148960000 mg$\div$÷​$1000$1000$=$=$148960$148960 g

Now convert to kilograms: $148960$148960 g$\div$÷​$1000$1000$=$=$148.96$148.96 kg

And then finally into tonnes: $148.96$148.96 kg$\div$÷​$1000$1000$=$=$0.14896$0.14896 t

 

 

Practice questions

QUESTION 4

QUESTION 5

QUESTION 6