# Apply Density

In this worksheet, students will calculate the density of irregular objects. Students will also learn how to manipulate equations in physics to solve problems.

Key stage:  KS 4

Difficulty level:

### QUESTION 1 of 10

In this activity, we will be defining density and explaining how to measure it. Density is a measurement of the mass of each particle within a certain space.  If you have a lot of heavy particles in a space of 1 cm3 then you will have a high density, but if you have only a few light particles in 1 cm3 then you will have a low density.

The easiest way of picturing this is by looking at the models for solid, liquid and gas particles.

In a solid, the particles are close together in a regular lattice. They are vibrating all over the place but they tend to stay in their one specific spot. This makes solids denser because there are a lot of particles in a small area. What do you think about liquids and gases then?

In liquids, the particles are all touching still but they are free to flow over each other. This can lead to small gaps forming in their shapes and that means that you can’t fit as many particles into the same space. This means that the density is slightly less than that of a solid.

In a gas, the particles are free to go wherever they want - they tend to move quickly and have large gaps between them. This means that they have a low density because the particles are far apart.

So that's density – but how can we measure it?   Fortunately, there is a very important equation to help us out here:

density = mass ÷ volume

ρ = m ÷ V

The sign ρ is the Greek letter rho – in this case it stands for density (because d was already used…), m is obviously mass and V is volume (as in how much space it takes up, not how loud it is…).

Mass is measured in kg, volume is measured in m3  and density is measured in kg/m3. The unit of measurement for density is just the unit of measurement for mass divided by the unit of measurement for volume. That is because the slash means divided by, so all we are saying is that the unit is kg divided by metres cubed.

If you know the unit of measurement of the thing you are trying to find, you can normally work out what needs to go into the equation to find the answer. For example, if you are asked to work out a speed in m/s, then you know that the equation you need is m divided by s.

Now let’s look at how to find the density of an irregular object.

Let’s say you have a rock – how will you work out the density of that object using this equipment?

[insert Royalty-free stock vector ID: 1362981782]

What do we need to know in order to calculate the density? It’s the mass and volume, right? So mass is nice and easy, you just put the rock on the balance and hey presto – there is your mass. For volume, it would be easy if it was a regularly shaped object, but it’s not. This is a problem that was solved by Archimedes back in the Ancient Greek times. He sat in the bath and saw the water spill out over the side – what he realised was that the amount of water that came out of the bath was the same as his volume – so all we need to do is make a fancy bath that will collect the water as it spills out.

This is an Archimedes or eureka can – and it measures the water displaced by an irregular object. In this case, we put the rock in and measure the amount of water in millilitres (ml) that comes out. 1 ml = 1 cm3.

All you need to do then is take your measurements and divide the mass by the volume and you’ve got your density!

One important point though - this only works for objects that sink!

Are you ready to tackle some questions now?

The measurement of mass needs to be taken before the measurement of volume when calculating the density of an irregular object.

Explain why.

[2]

Describe the steps that need to be taken in measuring the density of a regular object.

Talk about the equipment as well as how you would use it.

[3]

Select the correct definition for density from the list given below.

The amount of mass per unit area

The number of particles in a given space

The mass of all of the particles in an object

The amount of space an object takes up

Describe and explain which state of matter has the highest density.

[2}

Match the symbols to their units for the density equation.

## Column B

Density (ρ)
Kilograms (kg)
Volume (V)
Kilograms per metre cubed (kg/m3)
Mass (m)
Metres cubed (m3)

An object has an original density of 1 kg/m3 and is then heated. Its new volume after heating is 0.8 m3.

Calculate the change in density of the object.

Object mass = 2 kg.

## Column B

Density (ρ)
Kilograms (kg)
Volume (V)
Kilograms per metre cubed (kg/m3)
Mass (m)
Metres cubed (m3)

Describe what happens to the density of an object as you heat it.

[2]

Calculate the mass of the air in a room that measures 2 m by  5 m by 3 m.

Density of air = 1.2 kg/m3

Describe how to find the density of an irregular object.

[3]

Some objects float in water.

Explain why it would not be suitable to use an Archimedes can to measure the volume of these objects.

[1]

• Question 1

The measurement of mass needs to be taken before the measurement of volume when calculating the density of an irregular object.

Explain why.

[2]

EDDIE SAYS
Did you struggle with this one? It does seem tricky at first but when you think about it, it is actually obvious! Remember how to measure the volume of an irregular shaped object? You have to put it into the special Archimedes can and measure how much water is displaced. Once you've done this, the object is going to be wet! The addition of water to the object will make a slight change (however small) to its mass and will therefore give a false reading. Therefore, it is important that you measure the mass before getting the object wet. It makes sense really.
• Question 2

Describe the steps that need to be taken in measuring the density of a regular object.

Talk about the equipment as well as how you would use it.

[3]

EDDIE SAYS
This is for a regular object, so all you need to do is use a ruler to measure the size of it and then convert this into the volume. Next, use a balance to find the mass - not a scale to get the weight, we are working with mass and not weight. We use a balance and not scales in science! Picky terminology but important! Finally, divide the mass by the volume and you should have found the density!
• Question 3

Select the correct definition for density from the list given below.

The amount of mass per unit area
EDDIE SAYS
This is one of those definitions that you need to remember - you'll find there are a lot of these in science. These are important because, in science, when we say things we need to be very specific about what we mean. If you weren't totally sure about this one, then spend some time learning it so that it is really secure in your head.
• Question 4

Describe and explain which state of matter has the highest density.

[2}

EDDIE SAYS
Did you get the answer solid? The particles are all packed together in a regular lattice. Did you get that word? Regular lattice? You know what a regular lattice is, it's just a repeating pattern of particles (normally layers of particles over each other). If the density is a measurement of how many particles there are in an area, then a solid will have loads because of this regular lattice pattern they form.
• Question 5

Match the symbols to their units for the density equation.

## Column B

Density (ρ)
Kilograms per metre cubed (kg/m
Volume (V)
Metres cubed (m3)
Mass (m)
Kilograms (kg)
EDDIE SAYS
You need to be able to match the words to their symbols. This will make it easier for you to find the information needed in an exam question and everyone likes tricks that make answering the question easier, don't they?
• Question 6

An object has an original density of 1 kg/m3 and is then heated. Its new volume after heating is 0.8 m3.

Calculate the change in density of the object.

Object mass = 2 kg.

EDDIE SAYS
This one has two parts to it. The first part is the simple 'work out the density' part, but then it turns into a 'work out the difference between these two parts' question. Let's have a look at how we would tackle this type of question. Part 1 Work out the density: Find the numbers and write them down: ρ = ? m = 2 kg V = 0.8 m3 Put them into the equation: ρ = 2 ÷ 0.8 Do the maths: ρ = 2.5 kg/m3 Step 2 Now take this new value for density away from the original value: 2.5 - 1 = 1.5 kg/m3 And there you have it!
• Question 7

Describe what happens to the density of an object as you heat it.

[2]

EDDIE SAYS
Think about what heat is - it is simply how much particles are vibrating. If you heat up an object, you are making the particles move around more, and this makes stuff happen to the object. The object will grow (thermal expansion) because each particle is taking up more space. This means that the volume has increased. If there is a higher volume but the mass is unchanged, then the density is going to go down.
• Question 8

Calculate the mass of the air in a room that measures 2 m by  5 m by 3 m.

Density of air = 1.2 kg/m3

EDDIE SAYS
Okay, so quite a complex question with a few parts to it. Let's go through them step by step and break down the question into manageable chunks. Part 1 Work out the volume of the room. You should be able to do this: 2 x 5 x 3 = 30 m3 Part 2 Rearrange the density equation: ρ = m ÷ V m = ρ x V Part 3 Put in the numbers: m = 1.2 x 30 m = 36 kg
• Question 9

Describe how to find the density of an irregular object.

[3]

EDDIE SAYS
This is the kind of question that will be followed up by asking you about accuracy or other experimental skills. For more information on this, take a look in our skills section! Basically, this question is testing you to see if you know how to use an Archimedes (or eureka) can to measure the volume. If you see the term 'irregular object', you should always think Archimedes (or eureka) can.
• Question 10

Some objects float in water.

Explain why it would not be suitable to use an Archimedes can to measure the volume of these objects.

[1]

EDDIE SAYS
In order for this can to work, you need to have an object submerged. If the object is not submerged, then it will not be displacing the water. This means that you will not be measuring the volume of the object from that point! How do you feel about this topic now, having completed ten questions on it? If you're still finding it a bit challenging, why not reread the Introduction and maybe have another go at some of the questions you found tricky.