Density
1.
2.
3.
4.
5.
6.
7.
8.
Mass and Volume
What is density?
d = m/V
Solving Density Problems
Archimedes
Buoyancy
Applications
Practice Problems
Which is heavier?
1 kilogram of feathers
Or
1 kilogram of lead?
They are both 1 kg so they weight the same!
Both of these substances have the same
mass, but would have different volumes
This means that lead and feathers have
different densities!
Mass
Mass
– A physical property that
represents the amount of matter
an object contains
– Measured in:
–Grams (g)
–Kilograms (kg)
Volume
Volume
– A physical property that
represents how much space an
object occupies
– Measured in:
–Millilitres (mL)
–Litres (L)
–Centimetres cubed (cm3)
What is density?
Density is a quantitative property
It is a measure of how close the
particles in a substance are.
It is a measure of how much mass there is
in a specific amount of space.
Density
• If you have two objects (say iron and wood) of the
same size, which will feel heavier? Why?
• The iron because it has more stuff squeezed
into the same volume (amount of space).
– Both objects have the same volume but the particles inside
the iron are much closer together. Therefore, iron will have
a higher mass
– Higher mass with the same volume = higher density
wood
iron
Formula!!
• FORMULA: d = m/V
• Where, d=density m=mass V=volume
Components
Solving Density Problems
• When solving density problems use the
GUESSS method
G: Givens
U: Unknown
E: Equation
S: Substitute
S: Solve
S: Statement
Example
What is the density of 5 g cube with one side having
a length of 2 cm?
G: m=5g, v= 2x2x2 = 8 cm3
U: d=?
E: d=m/v
S: d= 5g/ 8 cm3
S: d= 0.625g/cm3
S: Therefore, the density of the cube is
0.63g/cm3
*Volume Formulas*
These will be provided
V = l x w x h
V = pr2h (cylinder)
V = 4/3 pr3h (Sphere)
Irregular shaped objects: Use the
method of displacing water
The Genius of Archimedes
287-212 BC
Archimedes
• Famous Greek
mathematician.
• Much of Archimedes
fame comes from his
relationship with Hiero,
the king of Syracuse, as
he performed a number
of favors using his
intellect
• The most famous of these favors for
the king was that of the gold crown
• Watch the following video
Crown of Syracuse
Gold or Silver??
•
•
•
•
Recall formulas and figures:
Density of gold = 19.34 g/cm3
Density of silver = 10.5 g/cm3
Density = mass
volume
• Eg. Aristotle is given a 730 g crown…
what should he do to determine if it is
authentic?
• PUT IT IN WATER!!!!!!!!
• After sinking it in water he observes that
it displaces 45 cm3 of water…. Is it
authentic???
• Density = mass
volume
• Density = 730g
45cm3
= 16.22 g/cm3
• The crown is not authentic as it is not
dense enough to be gold (Density of
gold = 19.34g/cm3).
End of Day 1
• Density Calculations Worksheet and
Answers
Coke vs. Diet Coke
Terms
• Negatively Buoyant – Will Sink
• Positively Buoyant – Will Float
• Neutral Buoyant – Will neither sink or
float, it will hang out in the middle (like
a fish)
Buoyancy
• When an object is placed into a fluid it
takes up room (displaces)
• The greater the volume of the object,
the more fluid it will displace
Buoyant Force
• The displaced fluid places an upward force
on the object
• This fluid has mass, if the mass of this
displaced fluid is greater than the mass
of the object, the object will float
Buoyant Force
• That is why you weigh less in water
because there is an upward force which
decrease the downward force caused by
gravity
• Since the downward force (gravity) is
decreased by the upward force
(buoyant) of water, you can push heavy
objects like a boat easily in water.
Eureka! Buoyancy Video
Put Another Way
• Submerged objects always
displace fluid upwards (the level
of water in the bathtub rose
when Archimedes got in).
• Thus, he reasoned that the
buoyant force on an object
must be equal to the mass of
fluid that object displaces.
Put Another Way
• If the mass of an object is
greater than the mass of
displaced fluid, it will sink, if the
mass of the object is less
than the mass of displaced
fluid, it will rise.
– Which object has a mass
greater than the mass of the
displaced fluid?
• The volume of displaced
fluid is precisely equal to the
volume of the submerged
part of the object
• If the force of gravity (mass of
object x gravity) is greater than
the buoyant force, the object
will sink
Example
• If you place an object that weighs 63 lbs into
fresh water, the object is displacing 62.4 lbs of
water, but weighs 63 lbs. This object will be
negatively buoyant - it will sink. It is however
being buoyed up with a force of 62.4 lbs
• If we put the same object into salt water, it would
still weigh 63 lbs, but would be buoyed up by a
force of 64 lbs, and it would float (more on
salt water soon!)
Buoyancy Simplified
• Buoyancy is the tendency of an object
to float in a fluid (gases are considered
fluid in this case).
• If an object is less dense than the fluid it
will float.
Buoyancy Simplified
• This explains why wood and Styrofoam float on
water, whereas concrete and steel sink. It also
explains why it is possible to make boats out of
steel or even concrete.
– As long as there are portions of the boat
below the surface of the water that are hollow
(i.e. contain air), the overall density of the
boat can be less than that of water
If…..
• If however, the boat takes on water than the part of
the boat once filled with air (not very dense) now
becomes filled with water (much denser).
• It no longer has a strong buoyant force and sinks
Why do things sink or float Video
Water
• Water is the most common fluid but what
is the density of water?
• 1.0 g/mL or 1.0 g/cm3
• Anything that has a density less than
1.0g/mL will float!
Applications
• Life jackets keep you afloat
because they are full of air which
decreases your density below
that of water
• Scuba divers can increase and
decrease the amount of air in
their suits to go up or down
Floating
• When you hold your breath you are
effectively decreasing your density by
filling your lungs with air. If you breath
out you will sink
Fat Floats
• If you add oil to water,
the oil will float to the
top
• People who are obese
can also float without
holding their breath
because all the fat makes
them less dense than the
water
Oil Spills
• An oil spill can have
devastating consequences
because oil doesn’t dissolve in
water and is less dense.
• As a result, it floats on the
surface. Ultimately a great
deal of the oil spreads out
on the water until it reaches
the shore
The Dead Sea
• On average, sea water is 3% denser than
fresh water
• This is why floating is easier in salt
water than in fresh.
The Dead Sea
• Near Jordan
• 8.6 times more salty than the ocean
• People can float without holding their breath
Problems
• Recall: Density of gold = 19.34 g/cm3
1. Which one of the following is gold?
– A 1000 g crown that displaces 40 cm3 of water
– A 300g crown that displaces 11 cm3 water
– A 567g crown that displaces 24 cm3 water
2. Is a 2200 g crown that displaces 113 cm3 a gold
crown?
3. Is 1300 g crown that displaces 124 cm3 a silver
crown?
4. A 400 g silver crown should displace how much
water?
5. How much should a gold crown weigh if it
displaces 40 cm3 of water?
The End
• Density Problems Worksheet 2