Suppose you had three equally sized cubes of the following materials Suppose you had three equally sized cubes of the following materials. Which one would be the heaviest? FOAM WOOD METAL Equal Mass Set Brick and Sponge

The metal cube is heavier just as a brick is heavier than a sponge of the same size! Hair has a lot of volume: *not a great definition of mass They take up the same amount of space (volume) but the brick has more mass (more matter)!

Volume of a Rectangular Solid =_____

Volume of a Rectangular Solid =LxWxH 3cm 2cm 2cm 3cm 4cm Have students measure two objects. 3cm V= V=

Volume of a Rectangular Solid =LxWxH Volume is a measure of the physical space an object take up, 3cm 2cm 2cm 3cm 4cm 3cm 4cm x 2cm x 2cm 3cm x 3cm x 3cm V= 16cm3 V= 27cm3

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) . ρ = m/v density (g/cm3) or (kg/m3) mass (g) or (kg) Volume (cm3) or (m3) SAMPLE PROBLEM If I have a wooden block that has a mass of 20.0g and a volume of 26.0cm3, what is its density? Density Review question

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) . ρ = m/v density (g/cm3) or (kg/m3) mass (g) or (kg) Volume (cm3) or (m3) SAMPLE PROBLEM If I have a wooden block that has a mass of 20.0g and a volume of 26.0cm3. What is its density? m=20.0g v=26.0cm3 ρ =20.0g/26.0cm3=0.770g/cm3 Density Review question

Color Hardness Density How do you know which metal is which? Use physical Properties such as Aluminum Brass Copper Iron Lead Zinc Color Hardness Density Different Metals Have Different Densities

REMEMBERING DENSITY YOU DON”T WANT TO GET HIT IN THE FACE WITH DENSE OBJECTS Hair has a lot of volume: *not a great definition of mass A Pillow Fight is Fun Cinderblock fight not fun

Density Problems If 10.0cm3 of ice has a mass of 9.17g, what is the density of ice? A piece of tin has a mass of 16.52g and a volume of 2.26 cm3. What is the density of tin? 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? A cube 6cm by 5cm by 3cm has a mass of 450g. Calculate its density.

Density Problems If 10.0cm3 of ice has a mass of 9.17g, what is the density of ice? A piece of tin has a mass of 16.52g and a volume of 2.26 cm3. What is the density of tin? 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? A cube 6cm by 5cm by 3cm has a mass of 450g. Calculate its density. Density = 0.917g/cm3 Density = 7.3g/cm3 Mass = 75.7g V= 90cm3 thus p = 5g/cm3 Density Worksheet!

Density Problems Aluminum has a density of 2.69g/cm3. How much would 12cm3 of aluminum weigh? 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? A cube 6cm by 5cm by 3cm has a mass of 450g. Calculate its density.

Density Formula Manipulation Multiply both sides by v Divide both sides by p

m v p

Rank each object from the most dense to the least dense: 1kg 1kg [1] [2] [3] [4] 1kg 1kg (a) (b) (c) (d) 2kg Mathematically show increasing volume of cubes in explanation and increasing mass… 3kg 1kg 4kg [1] [2] [3] [4] (a) (b) (c) (d)

Rank each object from the most dense to the least dense: 2kg 2kg [1] [2] [3] [4] 2kg 2kg (a) (b) (c) (d) 2000g 3kg 10,000mg 3000g [1] [2] [3] [4] (a) (b) (c) (d)

Understanding the Meaning of Density Object 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 QUESTION Suppose we have 5 different cubes all with an equal volume of 1cm3. How much will each one weigh? 2.7g 1g 19.3g 0.85g 1.6g Aluminum Water Gold Wood Sugar

Density of Water: 1g/cm3 or 1000kg/m3 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 If we had two cubes of aluminum that each have a volume of 1cm3, each one should have a mass of 2.7g What happens to density if we put the two blocks together? m = 2.7g v= 1cm3 m = 2.7g v= 1cm3 #1 m = 5.4g v = 2cm3 #1 #2 #2 Density = 2.7g/cm3 p = 2.7g/cm3

WOOD BLOCK TWO WOOD BLOCKS Mass = 20g Volume 26cm3 Mass = 10g Cut in half Density ≈ 0.77g/cm3 Density ≈ 0.77g/cm3 Density ≈ 0.77g/cm3 Should be review…. WOOD BLOCK What Happens if I cut one of the small wooden blocks in half again? Mass = ??? Volume = ??? Density = ??? WOOD BLOCK

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).

HOW DO YOU DETERMINE THE VOLUME OF IRREGULARLY SHAPED OBJECTS?? VOLUME OF REGULARLY SHAPED OBJECTS IS EASY Volume of Poop? Do lab where we all poop on the table

1ml = 1cm3 Water Displacement ---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 Water Displacement Hand out graduated cylinders

If you place a large screw into a graduated cylinder with 60 If you place a large screw into a graduated cylinder with 60.0ml of water in it and the water level rises to 80.0ml, what is the volume of the screw? ---80.0ml ---60.0ml ---60.0ml

If you place a large screw into a graduated cylinder with 60 If you place a large screw into a graduated cylinder with 60.0ml of water in it and the water level rises to 80.0ml, what is the volume of the screw? ---80.0ml ---60.0ml ---60.0ml The difference is 20ml

20.0cm3 1ml = 1cm3 ---80.0ml ---60.0ml ---60.0ml 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? 20.0cm3 1ml = 1cm3 ---80.0ml ---60.0ml ---60.0ml The difference is 20.0ml

If you place a large screw into a graduated cylinder with 57 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? ---78.6ml ---57.4ml ---47.5ml

Final – initial position 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? Get the difference! Final – initial position 81.6ml – 57.4ml = 24.2ml ---81.6ml ---57.4ml ---57.4ml

Final – initial position 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? Get the difference! Final – initial position 81.6ml – 57.4ml = 24.2ml ---81.6ml ---57.4ml ---57.4ml 24.2cm3 1ml = 1cm3

Two-Step Density Problems 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?

-------- 49.10ml -------- 45.50ml 49.1-ml – 45.5ml = 3.6ml ml and cm3 are interchangeable. So mass = 28.5g and volume = 3.6cm3 p =m/v 28.5g / 3.6cm3 = 7.9g/cm3 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? -------- 49.10ml -------- 45.50ml

What if an object is too big to fit in a graduated cylinder? You might consider using a beaker instead but in general a graduated cylinder is far more accurate at measuring volume than a beaker. So we can use something called an overflow can.

Overflow Can. Fill the can above the drain line with water. Let the excess drip out until the water is level with the drain. Now any object placed in it will cause the water to overflow through the drain.

Overflow Can. Fill the can above the drain line with water. Let the excess drip out until the water is level with the drain. Now any object placed in it will cause the water to overflow through the drain. Catch the water in a graduated cylinder or other device and measure its volume in ml. This is the volume of the object in cm3

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.

Will a penny sink or float in liquid mercury? 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?

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 Water 1g = 1ml = 1cm3 Density of Water = 1g/cm3 Objects denser than water tend to sink whereas object less dense than water tend to float. Density does not depend on the amount of a substance you have. A small block of aluminum has the same density as a big block of aluminum. Shape has in impact on density.

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 Objects generally sink or float based upon density. More dense = sinks Less dense - floats You must use 3 solids! Hand in a labeled picture in COLOR! Bring it in for extra credit!

How much of an Object will Float above Water? 0.92g/cm3 7.13g/cm3 ICE CUBE Zinc 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? About 8% visible If 92% is under water then the other 8% is visible!

Just the Tip of the Iceberg!!! Photo via: Adventure-Journal 90% of this ice berg is below water (salt water)

Artistic Rendition of an iceberg. Most of an Iceberg is below water! Think about this and ships traveling in the ocean. The TITANIC Wiki commons

Flotation Problems (Handout) Knock on Wood Floating Basketball 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? A basketball has a mass of 624g and a volume of 7512cm3. What percentage of a basketball will be visible above water? 70% under 30% above D = m/v = 624g/ 7512.1cm3 = 0.831g/cm3 Dball / Dwater = 0.831g/cm3 / 1g/cm3 x 100 = 8.3% 91.7% of a basketball will float above water

Rank each object from the most dense to the least dense: [1] [2] [3] [4] [5] [6] Least Dense F E

Buoyancy: How can a ship made of iron that weighs about 200 million pounds float? FOIL SHAPE PREDICTION OBSERVATION EXPLANATION Boat Sink or Float Ball Block

Aluminum Foil Boats Objective: To design/build two different aluminum foil boats that will hold as many pennies as possible without sinking. Procedure Obtain two 20cmx20cm pieces of aluminum foil. Build your boats. Test them by adding pennies until they sink. Dry the pennies off and return them. Which boat in the class won? Why?

Shape and density determine if something will float.

Buoyant Force: When an object displaces water the water pushes back on it. Hold a basketball in water, let it shoot up…..Have students feel the pressure, this is buoyant force… What happens to the weight of an object when placed in water?

Phet Physics: Forces Go to the Phet Simulation and click on the Net Force tab. Make sure the boxes that say “sum of forces” and “values” are check-marked. Set it up so that 150N of force is pulling left and 50N is pulling right. What is the net force? Set it up so that there is 300N of force pulling to the right and 150N of force pulling to the left. What is the net force? How is net force calculated?

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. Tug of war with students https://phet.colorado.edu/en/simulation/forces-and-motion-basics

These four cubes are resting on a table These four cubes are resting on a table. Each cube is made of a different material. Rank these cubes in terms of mass, weight and volume from largest to smallest. (a) (b) (c) (d) Mass Highest to Lowest [1] [2] [3] [4] or Not enough information Weight Highest to Lowest [1] [2] [3] [4] or Not enough information Volume Highest to Lowest [1] [2] [3] [4] or Not enough information

These four cubes are resting on a frictionless surface These four cubes are resting on a frictionless surface. Each cube is pushed and pulled by different forces. Rank each object from the highest to lowest net force Force arrows show direction only, they are not drawn to scale. 70N 100N 50N 100N 35N 65N 80N 90N 10kg 10kg 10kg 10kg (a) (b) (c) (d) Explain: [1] [2] [3] [4] Highest Lowest

10kg 10kg 10kg 10kg Explain: (a) (b) (c) (d) 80N 590N 40N 70N 70N 35N

These four cubes are resting on a frictionless surface These four cubes are resting on a frictionless surface. Each cube is pushed and pulled by different forces. Rank each object from the highest to lowest net force Force arrows show direction only, they are not drawn to scale. 30N 40N 75N 65N 60N 85N 90N 10kg 10kg 10kg 10kg 10N 10N (a) (b) (c) (d) Explain: [1] [2] [3] [4] Highest Lowest

Buoyant Force (upward push of water) If Weight is greater than Buoyant Force an object sinks. If Buoyant Force is greater than weight the object rises and then floats. When Buoyant Force equals weight the object floats or suspends. Weight Force (heaviness of object)

Which is greater: the Weight or Buoyant Force? Trick question, the object is floating and at rest so they are equal…reference the tug of war demo earlier…

Floating: Buoyant Force = Weight 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 = 100N F = 150N F = 100N F = 150N

Buoyant Force (upward push of water) 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! Weight Force (heaviness of object)

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. 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. When floating the buoyant force on ball equals its weight. Buoyant Force > Weight

100ml What happens to the height of the water when you put in the basketball? Lazily these numbers are fake…

150ml 100ml The water level rises by 50 ml.

150ml 100ml The buoyant force according to Archimedes' principle is equal to the weight of the water displaced (50ml)

Buoyant force = the weight of 300ml of water now! If you push the whole ball under there is much more water displacement and therefore much more buoyant force! So the bigger the boat the more water it displaces

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).