Which do you think would have the greater volume and mass? Why?

1. 1 kg of feathers 1 kg of rock Which do you think would have the greater volume and mass?Why?

2. DENSITY Density is defined as mass per unit volume. It is a measure of how tightly packed and how heavy the molecules are in an object. Density is the amount of matter within a certain volume.

3. Proof that water and ice have different densities

4. To find the density 1- Find the mass of the object 2- Find the volume of the object 3- Divide Density = Mass Volume

5. Units for density g/cm3 or g/ml Formula: M = mass V= volume D = density V= L x W x H (length x width x height) M = D x V V = M / D D = M / V

6. To find density: • Find the mass of the object • Find the volume of the object • Divide : Density = Mass - Volume Ex. If the mass of an object is 35 grams and it takes up 7mL of space, calculate the density.

7. To find density: • Find the mass of the object • Find the volume of the object • Divide : Density = Mass - Volume Ex. If the mass of an object is 35 grams and it takes up 7 mL of space, calculate the density. Set up your density problems like this: Given: Mass = 35 grams Unknown: Density (g/ mL) Volume = 7 mL Formula: D = M / V Solution: D = 35g/7 mL D = 5 g/mL

8. To find the density of an irregular object: • Find the mass of the object • Find the volume of the object • Divide : Density = Mass - Volume Ex. If the mass of an object is 35 grams and it takes up 7 cm3 of space, calculate the density. Set up your density problems like this: Given: Mass = 35 grams Unknown: Density (g/ cm3) Volume = 7 cm3 Formula: D = M / V Solution: D = 35g/7 cm3 D = 5 g/cm3

9. Density of an Irregular Solid Object Water Displacement

10. mass mass Density = volume Density volume Let’s Review • We already know how to calculate the density of any system. • We simply use the density equation or refer to the density pyramid.

11. To Practice: A solid object has a mass of 180 grams and a volume of 45 mL. What is the density of this object? Mass = 180 grams Volume = 45mL

12. mass mass Density = volume Density volume Using the “Pyramid”: 180 grams = 45 mL = 4.0 grams/mL

13. But what if the object does not have a nice geometric shape? ? height width length How do you find the volume of a solid object that does not have convenient length, width, and height ?? Easy to calculate the volume here !!

14. The answer is: Water Displacement !!! Fact of Life: A solid object will displace (means pushes out of the way) a volume of water exactly equal to the volume of the object itself. (This will be true for any liquid – not just water…) • Mass of the object has nothing to do with this. • Shape of the object has nothing to do with this. • Only the volume of the object determines how much water is displaced. This is why the water rises when you get into the bath tub…

15. How does this work? We fill a graduated cylinder half full of water. This original volume of the water is called the initial volume = Vi Remember that we read the bottom of the “meniscus” in a graduated cylinder to know the volume of the liquid.

16. Next: We add the solid object to the graduated cylinder. As expected, the water level rises. The volume of the water after the object has been added is called the final volume = Vf Remember – this first volume was the initial volume.

17. Now to calculate: The difference between the initial volume and the final volume is called “delta V”. You can easily determine its value by subtraction. Vf Δ V We write “delta V” like this: Vi

18. So… If an irregular solid object is placed into a graduated cylinder that contains 50.0 ml of water and the water level rises to a final reading of 75.0 ml, we can calculate the Δ V is 75.0 – 50.0 = 25.0 ml. Vf = 75.0 ml ΔV = 75.0mL – 50.0mL = 25.0 ml Vi = 50.0 ml

19. mass Density volume Now to connect to density problems: Remember that density is still equal to mass divided by volume. That equation does not care how you get the volume of the object – it will work for both regular and irregular solid objects. Δ V is the volume of the object !!