Density
Density
We know that matter is anything
that occupies a space and has
mass.
Mass = the amount of matter in an object
Volume = the space an object occupies
Density is the amount of
matter there is in a given
space.
Examples
Metal vs. Wood
Water vs. Oil
Metal
Water
Wood
Oil
The amount of particles there are in the metal
and water that occupies the space provided is a
lot more than the amount of particles present in
the oil and wood in the same amount of space.
Water and metal are more dense.
What do we use density for?
Density is one of the basic
ways to measure and
compare the physical
properties of different
matter
Which one is more dense?
People in a square (popular place vs. not
popular place)
How about this: Which square is more
dense?
•Do they occupy the
same volume?
•Do the have the same
amount of particles?
A
B
Which one is more dense?
Now which one is more dense?
•Do they occupy the
same volume?
•Do the have the same
amount of particles?
B
A
A is more dense because for the small
volume it holds, it has more matter.
Even though they have the same amount
of particles, if A was the same size as B, A
would have 4 times as much particles.
B
A
A
A
A
A
What is density?
To find density, the amount of mass (a
measurement if the particles present)
is divided by the volume of the
substance.
Density = mass OR
volume
mass ÷ volume.
Mass is measured in grams and kilograms.
Volume is measured in cubic centimeters
or cubic milliliters.
Mass
ALWAYS
REMEMBER
Grams is represented as a g
UNITS!
Kilograms is represented as a kg
Volume
3
Cubic centimeters = cm,
solid
Cubic milliliters = mL,3
liquid
1mL3 = 1cm3
So if Density = mass , Density = g or g
volume
cm3 mL3
SI Units: International System of Units
Modern metric system, measurements
Mass
 Grams = g
 Kilograms = kg
Length
 Meter = m
 Millimeter = mm
Liquid
 Liters = L
 Milliliter = mL
ALWAYS
REMEMBER
UNITS!
Time
 Seconds = s
 Milliseconds = ms
Conversions
Milli = m __
centi= c __
Kilo = k __
Let’s try a density problem together
 Frank has a paper clip. It has a mass of 9g and a
volume of 3cm3. What is its density?
Given:
D= ?
m= 9g
V = 3cm3
Formula:
m
D
V
ALWAYS
REMEMBER
UNITS!
Solve:
D= m/V =9g/3cm3
= 3g/cm3
Answer:
3g/cm3
 Frank also has an eraser. It has a mass of 4g,
and a volume of 2cm3. What is its density?
Given:
D=?
m =4 g
Solve:
ALWAYS
REMEMBER
=4g/2cm3 UNITS!
D= m/v
= 2g/cm3
V =2cm3
Formula
m
D
V
Answer:
2g/cm3
Work on these problems with your neighbor.
Jack has a rock. The rock has a mass of
6g and a volume of 3cm3. What is the
density of the rock?
Jill has a gel pen. The gel pen has a mass
of 8g with a volume of 4cm3. What is the
density of the rock?
Now, try these on your own.
Alicia has a watch. It has a mass of 4g and
a volume of 2cm3. What is the density of
the watch?
Mia has a wallet. It has a mass of 15g and
a volume of 5cm3. What is the density of
the wallet?
•To actually calculate density we need measuring
instruments.
•To measure the mass, we need to use a balance.
•If we use a scale, we measure the weight of the object.
The weight is the force due to gravity pulling down.
•You weigh less on the moon because gravity is less.
But the amount of particles you are made of doesn’t
change.
•Only mass is measured
by the balance because
the object’s mass
counteract with the
weights on the balance.
Measuring the volume of an object can be very
tricky as well. Most objects are not regular
shapes that we have formulas for to calculate the
volume.
V  l  wh
V    r2  h
r
Cube or
Cubic
rectangle
l
h
Cylinder
w
h
 Frank measured another eraser. He used a
balance to measure the mass at 4g. However
Frank is having trouble finding the volume. Can
you help him?
h = 2 cm
l = 5cm
V  l  wh
w = 1cm
Given:
L = 5 cm
w = 1 cm
h = 2 cm
ALWAYS
REMEMBER
UNITS!
Solve:
V = 5cm x 1cm x 2cm
= 10 cm3
Formula
V  l  wh
Answer:
10 cm3
 Frank has a cup for soda. He wants to know how
much soda the cup could hold so he measures the
volume of the cup. What is the volume?
V  r h
2
d
h = 10 cm
d = 4 cm
Before we attempt
this problem here are
some clarification:
ALWAYS
REMEMBER
UNITS!
 π has a numerical value of 3.14.
 The Formula can be written V = 3.14 x r 2 x h
d = 4 cm
h = 10 cm
What’s the area of a
circle?
 A=πxr2
= πxrxr
 The volume is just the
area of the base
times the height.
V=πxr2xh
d
 d is twice the radius
so: d = 2 x r
 r = d/2
 Frank has a cup for soda. He wants to know how
much soda the cup could hold so he measures the
volume of the cup. What is the volume?
V  r h
2
d
h = 10 cm
d = 2 x r, r = d/2
r2 =r x r
d = 4 cm
Given:
V= ?
r = ? Cm
d = 4 cm
h = 10 cm
Formulas:
V = 3.14 x r 2 x h
r = d/2
= 3.14 x r 2 x h
Solve:
ALWAYS
REMEMBER
UNITS!
r = 4 cm/2
= 2 cm
V = 3.14 x (2cm)2x 10 cm
= 3.14x (2cm) x (2cm) x 10 cm
= 3.14 x 40 cm3
= 125.6637 cm3 = 125.66 cm3
Answer:
125.66 cm3
In real life, most objects only resemble these
shapes.
Most objects are odd shaped.
It is almost impossible to accurately calculate
the volume of most objects.
That’s where volume by
displacement comes into
play.
When you think of
displacement, what do you
think of?
In volume by displacement, the displacement of
water or any other liquid is involved.
In a graduated cylinder, we measure the initial
volume of water. V1
Then we drop our object in.
The object takes a certain
amount of space.
The water particles rises to a
new final volume. VF
The difference in the water
levels from before and after
will give you the volume of
the object.
The equation for volume of displacement
Volume of the object = Volume of water after –
Volume of water before
Vo = Vf-Vi
What is the volume of
this object?
Vo= ?
Vf = 9 mL
Vi = 7 mL
Vo = 9mL – 7mL
2mL
Measuring Accuracy
 There many type of errors
Instrumental: The balance is not calibrated right
Human Error: mathematical, looking at the ticks on the
instruments, eyes play trick on you.
 When measuring Volume of liquids:
Meniscus: Bottom arch water of used for measuring
volume.
Liquid Layers
If you pour together liquids that don’t mix
and have different densities, they will form
liquid layers.
When liquids don’t mix that means they’re
_____________
insoluble
The liquid with the highest density will be
on the bottom.
The liquid with the lowest density will be
on the top.
Liquid Layers
 Which layer has the highest
density?
 Which layer has the lowest
density?
 Imagine that the liquids on the
left have the following densities:
10g/cm3.
6g/cm3.
3g/cm3.
5g/cm3.
 Which density would go with
which layer?
Liquid Layers – Try with your neighbor
 Which liquid has the
highest density?
 Which liquid has the
lowest density?
 Which liquid has the
middle density?
Liquid Layers – Try on your own!
 Imagine that the
liquids on the right
have the following
densities:
15g/cm3
3g/cm3
7g/cm3
10g/cm3
9g/cm3
12g/cm3
 Match the colors to
the correct densities.
3g/cm3
7g/cm3
9g/cm3
10g/cm3
12g/cm3
15g/cm3
Review
What is the formula for density?
What two methods can be used to
measure volume?
What is a meniscus?
What happens if you pour together liquids
that have different densities?
Will the liquid on the top have the highest
or lowest density?
Will the liquid on the bottom have the
highest or lowest density?
Super Scientist Question of the Day
Jake has a book, a ruler, and a balance.
How can Jake find the density of the
book with the tools he has?
Practice Volume by displacement and
density at:
http://www.sciencejoywagon.com/explrsci/media/density.htm
Website is on the Homework page under Friday 6th.