# Applying Density

In this worksheet, students apply the ideas of density to work out the density of irregular objects. They will also learn how to manipulate equations in physics to solve problems.

### QUESTION 1 of 10

Have you ever picked up something that looks really heavy only to find out that it is really light? This obviously makes you looked like a fool in front of your friends but try to style it out into a fancy dance move (it totally worked BTW). Well, this is the concept of density in action – and (amazingly) the topic of this activity. You will be defining density and explaining how to measure it experimentally by the end of this activity – like a boss!

So – density a measurement of the mass of each particle AND how many of those particles there are in that object. If you have a lot of heavy particles in 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 solid, liquid and gas particle models.

In a solid, the particles are close together in a regular lattice. They are vibrating all over the place, but they ten d 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 in the same space. This means that the density is slightly less than a solid – this is why water is so heavy, because it has a high density.

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

So that is an overview of density – now how about we look at how to measure density in a lab. This is a common question, so you need to remember this method of measuring density. Let’s start off by thinking about how you would measure density. Well we know it is the mass of the particles and how many there are in an area. This means that we need to use a divide – what do you think it should be?

This is the equation:

The sign 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 always measured in kg/m3. Did you spot it? The unit of measurement for density is just the unit of measurement of mass / the unit of measurement of volume. That is because the slash mean divided by, so all we are saying is that the unit is kg divided by meters cubed.

EDPLACE TOP TIP TIME!

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 you know the equation you need is m divided by s. Cheat method 1 done!

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?

IMAGE OF ALL EQUIPMENT HERE

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 it on the balance and hay presto – there is you 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 – what he had realised was that he had an amount of water out of the bath that was the same as his volume – so all we need to do is make a fancy bath that will collect the water as it falls out.

This is an Archimedes can – and it measures the water displaced by an irregular object. In this case, we would put the rock in and measure the amount in millilitres (ml) that come 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! Be aware though - this only works for objects that sink.

The measurement of mass needs to be taken before the measurement of volume when calculating the density of an irregular object. Explain why. (2 marks)

Describe the steps in measuring the density of a regular object. Talk about the equipment as well as how you would use it. (3 marks)

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 aprticels in an object

The amount of space an object takes up

Describe and explain which state of matter has the highest density (2 marks)

Match the symbol to the unit for the density equation.

## Column B

Density (ρ)
meters cubed (m3)
Volume (V)
kilogrammes per meter cubed (kg/m3)
Mass (m)
kilogrammes (kg)

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.

Describe what happens to the density of an object as you heat it (2 marks).

Calculate the mass of the air in a room that measured 2 m, 5, m, 3 m.

Density of air = 1.2 kg/m3

Describe how to find the density of an irregular object. (3 marks)

Some object float in water. Explain why it would not be suitable to use an Archimedes can to measure the volume of these objects. (1 mark)

• 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 marks)

EDDIE SAYS
This one is all about the water. So, your rock is chilling on the beach, nice a dry, being baked by the midday sun and getting a tan (or whatever rocks do). Here's a little known fact about rocks, they are obsessed with their weight (that's why they erode so easily) is it gives itself a measurement and it is 15.8 g. 'Perfect,' thinks the rock 'that'll do nicely, 0.1 g less than yesterday.' Suddenly, a wave hits the rock and he gets drenched! Oh no, poor rock. The rock sulks for a bit and then decides to measure its mass again. 'What?!' Exclaims the rock '16.4g? How?' Well, rock, it is because water has a mass and if you are covered in it then it will add to your mass. See how this applies to our situation? If you submerge the rock to start off with then you will get a false reading for the mass. Measure the mass first time, every time!
• Question 2

Describe the steps in measuring the density of a regular object. Talk about the equipment as well as how you would use it. (3 marks)

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 a volume. Done. Next is use the balance to get the mass. NOT a scale to get the weight, we are working with mass and not weight. We use balance and not scales in science! Picky picky terminology! Finally, divide the mass by the volume and hey presto!
• 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 (it's like learning a new language!). These are important, because in science when we say things we are very specific about what we mean. So if a question asks you about density, then it is asking you about this and only this.
• Question 4

Describe and explain which state of matter has the highest density (2 marks)

EDDIE SAYS
So, solid right? 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 symbol to the unit for the density equation.

## Column B

Density (ρ)
kilogrammes per meter cubed (kg/m...
Volume (V)
meters cubed (m3)
Mass (m)
kilogrammes (kg)
EDDIE SAYS
You don't really need to remember the symbols (especially Rho (ρ)) but you do 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 making it easier to answer the exam question. Everyone likes tricks that make answering the question easier, right?!
• 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.

1.5
EDDIE SAYS
This one has 2 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 A - find the numbers and write them down: ρ = ? m = 2 kg V = 0.8 m3 B - put them into the equation: ρ = 2/0.8 C - do the maths ρ = 2.5 kg/m3 Step 2 - Now take this new value for density away from the original value of density. 2.5 - 1 = 1.5 kg/m3 DONE! Amazing :)
• Question 7

Describe what happens to the density of an object as you heat it (2 marks).

EDDIE SAYS
Think about what heat is - how much particles are vibrating. If you heat up an object then 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 has an effect on the density - now 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 measured 2 m, 5, m, 3 m.

Density of air = 1.2 kg/m3

36
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 = 30m3 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 marks)

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 object float in water. Explain why it would not be suitable to use an Archimedes can to measure the volume of these objects. (1 mark)

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! You could say it\'s pointless! (get it, because I said point a little bit ago? We\'re so funny here at edplace)