DENSITY
OR, WHY DO SOME THINGS
FLOAT WHILE OTHERS SINK.
What Is Density?
• Density is how heavy something is for its
size.
• Density is mass divided by volume or
D=m/v
Where D equals density, m equals mass and
v equals volume
Another Way of Looking at It.
• You will often hear density referred to as
“mass per unit volume.”
• Let’s break this down:
• Mass is how much matter the object has.
• Per simply means divided by
• Unit volume is a measure of how much
space it takes up
So…
• When you hear mass per unit volume, you
should think…
• Take the mass and divide by its volume!
What Are the Units of Density?
• Mass units would include
– Grams for very small objects or
– Kilograms for larger objects
• Volume units would include
–
–
–
–
Cubic centimeters for small objects or
Cubic meters for large objects
Milliliters for small amounts of liquids
Liters for larger amounts of liquid
• Lets stick to grams and cubic centimeters for now.
How to State Density Units
• You have grams for mass
• You have cubic centimeters for volume
• These are not the same units, they don’t
cancel so you have to include both units in
your answer
How to State Density Units
• The units of density are:
• Grams/Cubic Centimeter or
g/cm3
Why Cubic Centimeters
• Remember that volume is
length multiplied by width multiplied by
height or
l XwXh
• In each case, the distance is in cm and since
you are multiplying it three times, you get
cubic centimeters.
• Easy huh!
Now, How About an Example?
Mass= 100 grams
l=10 cm
h=5 cm
w=2 cm
Use the information provided to calculate the density of the
object
What Did You Get?
• If you got 1g/cm3, you are correct!
• Lets see how this works:
V=l x w x h
V=10 cm X 5 cm X 2 cm
V=100cm3
Mass = 100 g (given)
D=m/v
D=100 g/100cm3=1g/cm3
A Few Words About the Mass/volume
Relationship of Liquids and Solids.
When working with a sample of any liquid or
solid - wood, steel, or peanut butter,
• If you decrease the mass, you also decrease
the volume
• If you decrease the volume, you also
decrease the mass
A Few Words About the Mass/volume
Relationship of Liquids and Solids.
When working with a sample of any liquid or
solid - wood, steel, or peanut butter,
• If you increase the volume, you also
increase the mass
• If you increase the mass, you also increase
the volume
Let’s Think About It for a
Second.
• If you add more peanut butter to the pile
(more mass) it is going to take up more
space (more volume)
• If you remove peanut butter from the pile
(less mass) it is going to take up less space
(less volume)
What About Volume?
The same holds true for volume.
• If you start with the volume of peanut butter in the
jar (lets say 16 oz) and you have to move it into
another container (say 2 oz). You definitely have
less peanut butter in the 2 oz jar than in the 16 oz
jar therefore the mass of the 16 oz of peanut butter
would be more than the mass of the 2 oz of peanut
butter. Remember, we’re not massing the jars but
the contents of the jars.
Does the Density of a Liquid or Solid Change
When Mass and Volume Change?
What do you think?
Does the Density Change When
Mass and Volume Change?
• The answer is NO and here is why:
• Density is a proportional relationship
meaning as long as mass and volume are in
proportion to each other, the density of a
liquid or solid remains the same. This is
how we know that certain objects have a
predictable density regardless of the sample
size.
Let Me Prove It to You.
l=10 cm
h=5 cm
Mass= 100 grams
w=2 cm
!!"#$%&%#'(#&)*#+&#+"&
!"#$%&'()!*'+',)$-.!/0'
!"#$%
&!"#$%%&'($'&'("&)"*+,'-&
!"#$%&'$()*+ !
!"#$%&'()*%"#++,-%$'%.$/%*,-/.$0%.1%&,%2($%.$%.-%"#)13
l=5 cm
h=5 cm
l=5 cm
h=5 cm
50 grams
w=2 cm
50 grams
w=2 cm
Let Me Prove It to You.
l=5 cm
h=5 cm
l=5 cm
h=5 cm
50 grams
50 grams
w=2 cm
• The new volume of either half is:
5 cm x 5 cm x 2 cm = 50 cm3
• The new mass of either half is:
100g ÷ 2 = 50g
• So, the new density of either is:
50g/50cm3 or still 1.0 g/cm3
w=2 cm
What About Gases?
• By definition, gases have no specific volume and
no specific shape
• They expand or contract to entirely fill the vessel
containing them
• So, gases can have different densities, depending
on their conditions
• In fact, that is what distinguishes them from
liquids
• For this class, you will be given the density of a
gas, as opposed to having to calculate it
A Word About Irregularly
Shaped Objects.
• If you are given an irregularly shaped object
and told to find the density, you might have
a problem.
• If the length, width, and height of the object
are not uniform (the same), you cannot use l
X w X h to determine volume.
A Word About Irregularly
Shaped Objects.
• To determine the volume of an irregularly shaped
object, start with a graduated cylinder of water
filled about half full
• Record the volume of water in the cylinder
• Drop in the irregularly shaped object
• Record the volume of water in the cylinder with
the object in it
• Subtract the original volume from the second
volume to determine the volume of the object
A Word About Irregularly
Shaped Objects.
• You are measuring the amount of water
displaced by the object which is equal to the
volume of that object
• This is called:
volume by displacement
• Cool!!
Liquids
• So far we have been talking mostly about
solids. Solids have densities that can be
easily expressed in g/cm3
• Liquids tend to be measured in milliliters or
liters. This is not a problem because you
can convert milliliters or liters into grams
per cubic centimeter using a metric
conversion factor
Liquids
• You can also weigh a liquid to determine its mass.
Now we are going to use the word massing for
weighing to avoid confusion
• To do this, measure your cylinder in grams and
record its empty mass
• Add your liquid
• Now mass the cylinder again
• Subtract the mass of just the cylinder and you
have the mass of your liquid
Liquids
• To determine the volume, simply look at
where the liquid measures in your cylinder
and record the amount
• In order to convert your volume reading
(milliliters or liters) you would use a
conversion factor to change milliliters or
liters to cubic centimeters.
Liquids
• For this class, you will be given liquid
densities already converted to g/cm3
• Whew!
Lets Look at Some Specific
Densities.
Substance
Density (g/cm3)
Air
0.0013
Gasoline
0.7
Wood (oak)
0.85
Water (ice)
0.92
Water (liquid)
1.0
Aluminum
2.7
Lead
11.3
Mercury
13.5
Gold
19.3
Ever Notice…
• When you fill a glass with water, there isn’t
a large bubble of air at the bottom of your
cup.
• When you put ice in your water it floats to
the top.
That’s Because
• Air is less dense than water and will
naturally be displaced by the water and the
air will be at the top.
• Ice is also less dense than water by just a
little bit. That is why your ice floats to the
top of your water.
• Now you know!!!
Some General Comments About
Density
• In order to compare the density of two
objects, they must first be in the same units
(g/cm3)
• The material with the lower density will
always float to the top of the material with
the higher density (think ice and water), as
long as the materials don’t react with each
other and mix
Sink or Float?
• Solids can float or sink in a liquid.
Can you guess what kind of
solid would sink in water?
Answer:
• Any solid will sink in water if it has a
density greater than the density of water.
• Water has a density of 1g/cm3. Any solid
with a density greater than 1g/cm3 will sink
in water!
Sink or Float?
• Comparing densities to determine if
something will float, only makes sense if at
least one of the materials is a liquid
• A piece of steel (high density) can sit on top
of a piece of wood (low density) because
the wood cannot float through the steel!