There are three fundamental units of measurement:
Mass is measured in kilograms (kg) or in grams (g)
(This means that the UNIT of mass is the kilogram)
NOTE: 1000g = 1 kg
1kg • 2 pounds
Mass is measured with a top-pan balance
Some typical masses:
Mass of an apple = 150g
Mass of 12 year old boy = 40kg
Distance (or length) is measured in metres (m), centimetres (cm) or in millimetres (mm)
(this means that the UNIT of distance is the metre)
NOTE: 10mm = 1cm
100cm = 1m
1000mm = 1m
30cm = 1 foot
The UNIT of volume is the cubic metre (m3) or cubic centimetre (cm3)
The volume of a liquid is often measured in millilitres (ml) or litres (l)
1 cubic centimetre = 1 millilitre
1000ml = 1litre
1 gallon • 4.5 litres
1 litre • 1.5 pints
How to find the volume of a block of wood:
Measure the HEIGHT, LENGTH and WIDTH and multiply them together.
Volume of block = a x b x c cm3
Lower the stone into a measuring cylinder containing some water and measure the volume of the displaced water.
2. Using a displacement can: Lower the object into a displacement can full of water and measure the volume of the displaced water.
1. Fill displacement can with water.
2. Place empty beaker under spout.
3. Carefully lower the object being measured into the water in the displacement can.
4. Catch the water that overflows into the beaker.
5. Pour the water in the beaker into the measuring cylinder to find its volume
The unit of time is the SECOND (s)
The speed of an object is a measure of how far it travels in a given time.
The SI unit of speed is metres per second (m/s) which tells how many meters an object moves in one second.
Example: A toy car takes 4 seconds to travel a distance of 10 meters
What is the average speed of the car?
Answer: Speed = distance / time
Speed = 10 / 4 = 2.5 m/s
(Remember, always show your working and dont forget the units)
Temperature is measured in degrees Celcius (ºC) using a themometer.
The density of a substance is the mass (in grams) of one cubic centimetre of it.
Mass = density x volume
Volume = mass ÷ density
If blocks of several different substances all have the same volume then the one with the largest mass is the most dense.
|These cubes all have a volume of 1cm3.||
The one with the greatest mass has the highest density.
If blocks of several substances all have the same mass then the one with the highest density will have the least volume
These cubes all have a mass of 10g.
|The block with the largest volume will have the lowest density.|
Finding the density of a solid with a regular shape eg a rectangular block
1. Place the block on a balance to find its mass.
2. Measure the height, width, and length and multiply them together to find he volume.
3. Divide the mass by the volume
These are the results: Mass = 120g,
Volume = height x width x length = 3cm x 4cm x 5cm
ˆ Volume = 60cm3
Density = mass/volume ˆ Density = 120 / 60 ˆ Density = 2g/cm3
Finding the density of a liquid.
1. Pour some liquid into a beaker and find the mass of the beaker and the liquid..
2. Pour the liquid into a measuring cylinder to find its volume.
3. Find the mass of the liquid by weighing the empty beaker and subtracting this from the mass of the beaker and the liquid.
(Mass of liquid = mass of liquid + container – mass of container)
4. Divide the mass of the liquid by its volume to find the density.
|Finding the density of a solid with an irregular shape eg a stone|
1. Find the mass of the stone using a balance.
(volume of stone = final volume – original volume)
3. Divide the mass of the stone by its volume .
Finding the density of a gas eg carbon dioxide
Mass of boiling tube before heating = 193.5g
mass of boiling tube after heating = 193.2g
ˆ loss in mass = 0.2g
Volume of gas released into syringe = 78cm3
Density = mass ÷volume
ˆdensity = 0.2÷78 = 0.0025 g/cm3
1. Find the mass of a boiling tube that contains some calcium carbonate*.
2. Set the syringe at zero and warm the boiling tube gently until the syringe is filled with gas.
3. Let the apparatus cool and then record the volume of gas released.
4. Re-weigh the boiling tube and subtract this from the original mass. The loss in mass of the calcium carbonate tells us the mass of carbon dioxide produced.
5. To find the density of carbon dioxide then divide the mass of carbon dioxide by its volume.
(*The boiling tube can contain any chemical that produces carbon dioxide when heated.
eg To find the density of oxygen the calcium carbonate could be replaced by potassium permanganate.)
Finding the density of air
1. Set up a 1 litre flask with a stopper and tap and weigh the flask
2. Suck all of the air out of the flask and weigh it again..
3. Subtract reading 2 from reading 1. This gives you the mass of the air.
4. Find the exact volume of air removed by filling the flask with water and then pouring this water into a measuring cylinder.
4. Divide the mass of the air in the flask by its volume.
Floating and sinking
If the density of an object is MORE than the density of water (or whatever the liquid is) it will sink.
If its density is less than water it will float.
the density of some oil is 0.8 g/cm3. The density of water is 1g/cm3. This means that oil will float on water.
Some plastic is found to have a density of 0.9 g/cm3. This means some plastic will sink in the oil but float on the water.
To see a simulation about density and buoyancy click the image below ↓
DENSITY: Some worked examples A glass stopper has a mass of 55g and a volume of 11cm3 .
a) What is the density of glass?Hover here for answer
b) Explain how you might find the volume of the glass in the stopperHover here for answer
2. A bar of steel measures 5cm x 5cm x 1m. If steel has a density of 8g/cm3 what would be the mass of the bar?
Answer: To solve this problem you need to do two things:
First calculate the volume of the bar (i) and then find the mass (ii).
i) Volume of bar = 5 x 5 x 100 (Remember to convert the 1m to 100cm. You must not mix the units)
= 2500 cm3
ii) Mass of bar = density x volume
= 8 x 2500
= 20 000 grams (= 20kg)
Two liquids are poured into a beaker.
Liquid A is seen to float on to of liquid B.
A golf ball is carefully dropped into the beaker and comes to rest between the two liquids as shown in the diagram.
A 10p coin sinks to the bottom of the beaker.
a) Explain why liquid B is below liquid A
b) which has a higher density
i) the golf ball or the 10p?
Ii) The golf ball or liquid A?
Which would take up more space, 1kg of golf balls or 1kg of 10p coins? Explain.