Density 1. Mass and Volume 2. What is density? 3. d = m/V 4. Solving Density Problems 5. Archimedes...

Density1. Mass and Volume2. What is density?3. d = m/V4. Solving Density Problems5. Archimedes6. Buoyancy7. Applications8. 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!

MassMass

–A physical property that represents the amount of matter an object contains

–Measured in:–Grams (g)–Kilograms (kg)

VolumeVolume

–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: GivensU: UnknownE: EquationS: SubstituteS: SolveS: Statement

ExampleWhat 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/vS: 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