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

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.
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. 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.
Density
mass
volume
Density =
mass
volume

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

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 = ml
ΔV = 75.0mL – 50.0mL
= ml
Vi = ml

19. Now to connect to density problems:
mass
volume
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 !!