FOAM WOOD METAL Suppose you had three equally sized cubes of the following materials. Which one would be the heaviest?

FOAM WOOD METAL

Suppose you had three equally sized cubes of the following materials. Which

one would be the heaviest?

The metal cube is heavier just as a brick is heavier than a sponge of the same size!

They take up the same amount of space (volume) but the brick has more mass (heaviness of an object*)!

Volume of a Rectangular Solid =_____

Volume of a Rectangular Solid =LxWxH

4cm

2cm

2cm

3cm

3cm

3cm

V= V=

Volume of a Rectangular Solid =LxWxH

4cm

2cm

2cm

3cm

3cm

3cm

V= 16cm3 V= 27cm3

4cm x 2cm x 2cm 3cm x 3cm x 3cm

Volume is a measure of the physical space an object take up,

6

Density (ρ) is a measure of how compact the atoms or molecules in a

substance are. It is a ratio of an object’s mass (m) to its volume (v) .

SAMPLE PROBLEM• If I have a wooden block

that has a mass of 20g and a volume of 26cm3, what is its density?

•ρ = m/v• density (g/cm3) or (kg/m3)

• mass (g) or (kg)• Volume (cm3) or (m3)

Density (ρ) is a measure of how compact the atoms or molecules in a

substance are. It is a ratio of an object’s mass (m) to its volume (v) .

SAMPLE PROBLEM• If I have a wooden block

that has a mass of 20g and a volume of 26cm3. What is its density?

• m=20g v=26cm3

• ρ = 20g/26cm3=0.77g/cm3

•ρ = m/v• density (g/cm3) or (kg/m3)

• mass (g) or (kg)• Volume (cm3) or (m3)

Rank each object from the most dense to the least dense:

[1][2][3][4]3kg2kg 4kg1kg

(a) (b) (c) (d)

1kg1kg 1kg1kg(a) (b) (c) (d)

[1][2][3][4]


[1][2][3][4]

3kg2000g 3000g10,000mg

(a) (b) (c) (d)

2kg2kg 2kg2kg(a) (b) (c) (d)

[1][2][3][4]

Density Formula Manipulation

Multiply both sides by v

Divide both sides by p

Density Problems1. If 10.0cm3 of ice has a mass of

9.17g, what is the density of ice?

2. A piece of tin has a mass of 16.52g and a volume of 2.26 cm3. What is the density of tin?

3. A piece of metal has a density of 11.3 g/cm3 and a volume of 6.7 cm3. What is the mass of this piece of metal?

4. A cube 6cm by 5cm by 3cm has a mass of 450g. Calculate its density.

Density Problems1. If 10.0cm3 of ice has a mass of

9.17g, what is the density of ice?

2. A piece of tin has a mass of 16.52g and a volume of 2.26 cm3. What is the density of tin?

3. A piece of metal has a density of 11.3 g/cm3 and a volume of 6.7 cm3. What is the mass of this piece of metal?

4. A cube 6cm by 5cm by 3cm has a mass of 450g. Calculate its density.

1. Density = 0.917g/cm3

2. Density = 7.3g/cm3

3. Mass = 75.7g

4. V= 90cm3 thus p = 5g/cm3

Density Worksheet!

Fill in the table and Create Scale Model Cubes Object Density (g/cm3) Density (kg/m3) Mass (g) Volume (cm3) Length (cm)

Aluminum 2.7 g/cm3 2700kg/m3 21.6g

Water 1 g/cm3 1000kg/m3 27g

Gold 19.3 g/cm3 19,300kg/m3 1235.2g

Wood 0.85g/cm3 850kg/m3 6.8g

Sugar 1.6g/cm3 1600kg/m3 1.6g

Color the Cubes an appropriate color, tape/glue them to a piece of computer paper and list each one’s mass, volume

and density underneath it.

First One: Aluminum• mass = 21.6g• Density = 2.7g/cm3

• Volume = mass / density• V = 21.6g / 2.7g/cm3 = 8cm3

• The cube must have side lengths of 2cm each because 2cm x 2cm x 2cm = 8cm3

Fill in the table and Create Scale Model Cubes Object Density (g/cm3) Density (kg/m3) Mass (g) Volume (cm3) Length (cm)

Aluminum 2.7 g/cm3 2700kg/m3 21.6.2g 8cm3 2cm

Water 1 g/cm3 1000kg/m3 27g 27cm3 3cm

Gold 19.3 g/cm3 19,300kg/m3 1235.2g 64cm3 4cm

Wood 0.85g/cm3 850kg/m3 6.8g 8cm3 2cm

Sugar 1.6g/cm3 1600kg/m3 1.6g 1cm3 1cm

Color the Cubes an appropriate color, tape/glue them to a piece of computer paper and list each one’s mass, volume

and density underneath it.

First One: Aluminum• mass = 21.6g• Density = 2.7g/cm3

• Volume = mass / density• V = 21.6g / 2.7g/cm3 = 8cm3

• The cube must have side lengths of 2cm each because 2cm x 2cm x 2cm = 8cm3

Aluminum Water Gold Wood

Understanding the Meaning of DensityObject Density (g/cm3) Density (kg/m3)

Aluminum 2.7 g/cm3 2700kg/m3

Water 1 g/cm3 1000kg/m3

Gold 19.3 g/cm3 19,300kg/m3

Wood 0.85g/cm3 850kg/m3

Sugar 1.6g/cm3 1600kg/m3

Sugar

Suppose we have 5 different cubes all with

an equal volume of 1cm3. How much will

each one weigh?

QUESTION

Aluminum Water Gold Wood

Understanding the Meaning of DensityObject Density (g/cm3) Density (kg/m3)

Aluminum 2.7 g/cm3 2700kg/m3

Water 1 g/cm3 1000kg/m3

Gold 19.3 g/cm3 19,300kg/m3

Wood 0.85g/cm3 850kg/m3

Sugar 1.6g/cm3 1600kg/m3

Sugar

Suppose we have 5 different cubes all with

an equal volume of 1cm3. How much will

each one weigh?

QUESTION

2.7g 1g 1.6g19.3g 0.85g

Density of Water: 1g/cm3 or 1000kg/m3

Water1m3

Assuming 1kg = 2.2lbs, how much would 1m3 of water weigh? Could you lift it?

Show me how big that is using meter sticks.

Which has a higher density?

Aluminum

Aluminum

The Density is the same: 2.7g/cm3

#1 #2

If we had two cubes of aluminum that each have a volume of 1cm3, each one should have a mass of 2.7g

m = 2.7gv= 1cm3

m = 2.7gv= 1cm3

Density = 2.7g/cm3

What happens to density if we put the two blocks together?

#2

#1m = 5.4gv = 2cm3

p = 2.7g/cm3

20

WOODBLOCK

WOOD BLOCK

Mass = 20gVolume 26cm3

Density ≈ 0.77g/cm3

WOODBLOCK

TWO WOOD BLOCKS

WOODBLOCK



Cut in half

Density ≈ 0.77g/cm3 Density ≈ 0.77g/cm3

What Happens if I cut one of the small wooden blocks in half again?WOODBLOCK

WOODBLOCK

Mass = ???Volume = ???Density = ???

DENSITY KEY CONCEPT

• Density does NOT depend on the amount of the substance you have.

• Regardless of whether you have a small piece of gold or a giant truck full of it, the density of that gold will be 19.3g/cm3.

• Likewise, a drop of water has the same density as a swimming pool full of water (1g/cm3).

Volume: the amount of space something takes up!

BATHTUB

BATHTUB

What happens to the level of the water when you step in a bathtub?

What happens to the level of the water when you step in a bathtub?

BATHTUB

Volume or Water Displacement

• Water is generally incompressible.• An object will displace a volume of

water equal to the volume of the object itself when submerged.

• Both cm3 and ml measure volume or the amount of space an object takes up.

• 1ml is = 1cm3

• Water displacement is useful for determining the volume of irregularly shaped objects.

TOILET WATER

DETENTION!

---60ml

If you place a large screw into a graduated cylinder with 60ml of water in it and the water level rises to 80ml, what is the volume of the screw?

1ml = 1cm3

---60ml ---60ml

---80ml


---60ml ---60ml

---80ml


The difference is 20ml

---60ml ---60ml

---80ml


20cm3

1ml = 1cm3

The difference is 20ml

---57.4ml ---57.4ml

---81.6ml

If you place a large screw into a graduated cylinder with 57.4ml of water in it and the water level rises to 81.6ml, what is the volume of the screw?

---57.4ml ---57.4ml

---81.6ml


Get the difference!Final – initial position

81.6ml – 57.4ml = 24.2ml

---57.4ml ---57.4ml

---81.6ml


Get the difference!Final – initial position

81.6ml – 57.4ml = 24.2ml

24.2cm3

1ml = 1cm3

• A 28.5 g of iron shot is added to a graduated cylinder containing 45.50 mL of water. The water level rises to the 49.10 mL mark, from this information, calculate the density of iron.

• An irregularly shaped stone was lowered into a graduated cylinder holding a volume of water equal to 12 ml. The height of the water rose to 17 ml. If the mass of the stone was 25 g, what was its density?

• A 28.5 g of iron shot is added to a graduated cylinder containing 45.50 mL of water. The water level rises to the 49.10 mL mark, from this information, calculate the density of iron.

• An irregularly shaped stone was lowered into a graduated cylinder holding a volume of water equal to 12 ml. The height of the water rose to 17 ml. If the mass of the stone was 25 g, what was its density?

-------- 45.50ml

-------- 49.10ml

49..1-ml – 45.5ml = 3.6mlml and cm3 are interchangeable.So mass = 28.5g and volume = 3.6cm3

p =m/v 28.5g / 3.6cm3 = 7.9g/cm3

YOUR TASK

Measure the volume of a large screw ________ Measure the volume of a 10g mass________

What is the screw’s density?________

A paper clip is too small to accurately measure its volume. Come up with a method that can be

used to determine the volume of one paper clip. Write it down in your notebook.

What is the volume of a single paper clip______

Read at the base of the meniscus!Keep it flat, read at eye level!

What if an object is too big to fit in a

graduated cylinder?

1) You might consider using a beaker instead but in general a graduated cylinder is far more accurate at measuring volume than a beaker.

2) So we can use something called an overflow can.

Overflow Can.

1) Fill the can above the drain line with water.

2) Let the excess drip out until the water is level with the drain.

3) Now any object placed in it will cause the water to overflow through the drain.

Overflow Can.

1) Fill the can above the drain line with water.

2) Let the excess drip out until the water is level with the drain.

3) Now any object placed in it will cause the water to overflow through the drain.

4) Catch the water in a graduated cylinder or other device and measure its volume in ml.

5) This is the volume of the object in cm3

CLASS ACTIVITY

Determine the density • a rock:• a 200g mass• a 500g mass

•What metal is the mass made of? (use the internet to look up your density value).

DENSITY

CLASS ACTIVITY •Determine the mass in grams of the following volumes of water:

VOLUME (ml) MASS (g)

5

20

32

40

46

50

Pattern?

Key Points•Water displacement is used to determine the volume of irregularly shaped objects.

•Milliliters (ml) and centimeters cubed (cm3) are interchangeable.

1ml = 1cm3

•For H2O 1g = 1ml = 1cm3

Density and Flotation

• Task: Given 3 eggs, salt, water, and 3 beakers, make it so that one egg sinks, one egg floats and one egg stays suspended in the middle of the water.

• Objects sink or float based upon density.

• If an object is less dense that water (p < 1g/cm3) it will float.

• If an object is more dense than water (p < 1g/cm3) it will sink.

Object Density (g/cm3) Sink or Float

Aluminum 2.7 g/cm3

Penny 7.2 g/cm3

Gold 19.3 g/cm3

Wood 0.85g/cm3

Sugar 1.6g/cm3

Ice 0.917g/cm3

Baby Oil 0.83g/cm3

Mercury 13.94g/cm3

Will a penny sink or float in liquid mercury?

Mercury Video

QUIZ: make an 8 item density column.

7 Layer Density Column

Object Density g/cm3

Honey 1.42

Light Corn Syrup 1.33

Dawn Dish Soap 1.06

Water 1.00

Vegetable Oil .92

Baby Oil .83

Rubbing Alcohol 0.79

You must use 3 solids!Hand in a labeled picture in COLOR! Bring it in for extra credit!

Objects generally sink or float based upon density. • More dense = sinks• Less dense - floats

How much of an Object will Float above Water?

Zinc

0.92g/cm3 7.13g/cm3

The zinc will sink as its denser than water

The ice floats as its less dense than water

But how much is underneath the water?

If 92% is under water then the other 8% is visible!

ICE CUBE

About 8% visible

Just the Tip of the Iceberg!!!

Photo via: Adventure-Journal

90% of this ice berg is below water (salt water)

Most of an Iceberg is below water!

Think about this and ships traveling in the

ocean.

The TITANIC

Artistic Rendition of an iceberg.

Wiki commons

Flotation Problems (Handout)

Knock on Wood

• A branch snaps and falls into a river. It has a density of 0.7g/cm3, will it sink or float and if it floats how much of it will be visible?

Floating Basketball

• A basketball has a mass of 624g and a volume of 7512cm3. What percentage of a basketball will be visible above water?


AB

CD

E

F

Most Dense

[1][2][3][4][5][6]

Least Dense

Buoyancy: How can a ship made of iron that weighs about 200 million pounds float?

FOIL SHAPE PREDICTION OBSERVATION EXPLANATION

Boat Sink or Float Sink or Float

Ball Sink or Float Sink or Float

Block Sink or Float Sink or Float

Aluminum Foil Boats

• Objective: To design/build two different aluminum foil boats that will hold as many pennies as possible without sinking.

• Procedure1. Obtain two 20cmx20cm pieces of aluminum foil. 2. Build your boats.3. Test them by adding pennies until they sink.4. Dry the pennies off and return them.5. Which boat in the class won? Why?

Shape and density determine if something will float.

55

Buoyant Force: When an object displaces water the water pushes back on it.

What happens to the weight of an object when placed in water?

Intro to Forces: PHET Sim

• Force: a push or a pull (unit: Newtons)

• If Forces are balanced an object will not move or change its motion!

• Unbalanced forces lead to changes in motion.

https://phet.colorado.edu/en/simulation/forces-and-motion-basics


Buoyant Force (upward push of water)

Weight Force (heaviness of object)

1. If Weight is greater than Buoyant Force an object sinks.

2. If Buoyant Force is greater than weight the object rises and then floats.

3. When Buoyant Force equals weight the object floats or suspends.

58

Which is greater: the Weight or Buoyant Force?

Floating: Buoyant Force = Weight

F = 100N

F = 100N

If a 100N boat is floating the water must be pushing on it

with a force of 100N

If we add weight (50N) to the boat it will sink down deeper and the

buoyant force will increase.

F = 150N

F = 150N

Buoyant Force (upward push of water)

Weight Force (heaviness of object)

Archimedes Principle: Buoyant force is equal to the weight of the fluid displaced.

The more water an object displaces the more buoyant force pushing on it.

This is why a block of aluminum sinks but an aluminum foil boat floats.

Shape is important!

If you were to hold a basketball under water it will push back very

hard and would fly upwards if your were to release it.

Buoyant Force > Weight

If you were to hold a basketball under water it will push back very

hard and would fly upwards if your were to release it.

Buoyant Force > Weight

When floating the buoyant force on ball

equals its weight.

Why is it easier to lift a person in water?

50N

50N

Weight (force)

Lift (force)

Why is it easier to lift a person in water?

50N

50N

Weight (force)

Lift (force)

Weight (force)

Lift (force)Buoyant (force)

The water helps you!

Concrete Boats

• Heavy iron ships can float because they are shaped to displace a large amount of water and being hollow and filled with air reduces their overall density.

• Its easier to pick someone up in water because the water helps you (buoyant force).


FOAM WOOD METAL Suppose you had three equally sized cubes of the following materials. Which one would be the heaviest?

Documents

volume v

objects mass

density of ice

density of tin

ones mass

3gcm3 mass

mass heaviness

mass densityv