1. 2.7 Density and Buoyancy

2. Archimedes – 287BC – 212BC
Greek, mathematician, physicist, engineer, and inventor
Regarded as one of the greatest mathematicians of all time
Proved area of a circle, surfaace area, volume of a sphere, area under a parabola

3. Archimedes Principle
A crown was made for King Hiero II. The king supplied the gold to the goldsmith. When the gold crown came back the king was suspicious that some silver had been mixed in with the gold.
Archimedes was commissioned to solve the problem without destroying the crown
He need to find the density, but could not find the volume of an irregular object

4. Silver was found to be mixed into the to the crown.
One day while getting into the bathtub, Archimedes notice that the water level rose. This discovering allowed him to know the volume of an irregular shape.
Excited about his discovery, he ran through the streets of Greece shouting “Eureka!” Greek for “I found it!”
Silver was found to be mixed into the to the crown.
Since the volume of the water and the object are the same, we can also assume that the mass of the water displaced is equal to the mass of the object.

5. Buoyancy
Buoyancy
The ability of a fluid to exert an upward force on an object placed in it.
Results in an apparent loss of weight in a fluid
The upward force is called the buoyant force

6. Archimedes’ Principle
Archimedes’ Principle The buoyant force of an object is equal to the weight of the fluid displaced by the object

8. Density and Buoyancy Density
Density is the ratio of an object’s mass to its volume.
Density is expressed in g/cm3
Water has a density of 1.0 g/cm3

9. Density and Buoyancy Density and Buoyancy
If an object is less dense than the fluid, it will float
If an object is more dense than the fluid, it will sink
If the fluid and the object have the same density, the object will be suspended in the fluid

10. Density and Buoyancy

11. Density and Buoyancy

12. Density and Buoyancy

13. Density and Buoyancy

14. 13.2 Assessment
Question #1
How does buoyancy affect the apparent weight of an object in a fluid?
Results in an apparent loss of weight in a fluid

15. 13.2 Assessment
Question #2
What determines if an object will float or sink in a fluid?
If an object is less dense than the fluid, it will float
If an object is more dense than the fluid, it will sink

16. 13.2 Assessment
Question #3
How does Archimedes’ principle relate the buoyant force acting on an object and the volume of fluid displaced by the object?
The buoyant force of an object is equal to the weight of the fluid displaced by the object