Sink Our Ship

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Sink Our Ship. A STEM Unit by Kyle Berry 8 th Grade Mathematics. What is buoyancy?. Buoyancy is the ability of an object to float on a liquid or gas. How does buoyancy work?. Buoyancy depends on balancing forces. How does buoyancy work?. Buoyancy depends on balancing forces. Gravity.

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Sink Our Ship

A STEM Unit by Kyle Berry

What is buoyancy?
• Buoyancy is the ability of an object to float on a liquid or gas.
How does buoyancy work?
• Buoyancy depends on balancing forces.
How does buoyancy work?
• Buoyancy depends on balancing forces.

Gravity

Mass

Pressure

• Archimedes (287-212 BC) was one of the greatest mathematicians of his time. He lived in the Greek colony of Syracuse, but studied in Alexandria, Egypt.
• Source: AIMS Historical Connections in Mathematics, Vol. I
• Archimedes was often called on by King Hieron to solve problems. Once, the king gave a goldsmith a certain amount of gold to make a sold-gold crown. Once the crown was finished the king was suspicious of the goldsmith, thinking that he had kept some of the gold for himself and replaced it with cheaper metals.
• Source: AIMS Historical Connections in Mathematics, Vol. I
• The problem was brought to Archimedes. He decided to take a bath and consider the problem. As he sat in the bath he noticed that the weight of his body displaced the water in the bath. He suddenly realized the answer!
• Source: AIMS Historical Connections in Mathematics, Vol. I
The Greek Streak…
• Archimedes leapt from the bath, and ran down the street shouting “Eureka!” (I have found it!).
• Source: AIMS Historical Connections in Mathematics, Vol. I
Density!
• A crown made of solid gold would have a certain weight and volume due to its density. A crown made of anything else would have either a different volume or weight due to having a different density. Archimedes was able to show that the goldsmith had stolen from the king…you can probably guess what happened to the goldsmith…
• Source: AIMS Historical Connections in Mathematics, Vol. I

Density!
• Comparing densities can also help us understand how buoyancy works!
Density!
• The average density (specific gravity) of water is one gram per cubic centimeter (1g/cm3)

1g/cm31g/cm3 1g/cm3 1g/cm3 1g/cm3 1g/cm3 1g/cm3 1g/cm3 1g/cm3 1g/cm3

Density!
• If the average density of the boat is less than 1gm/cm3, the object will float.

d < 1gm/cm3

1g/cm31g/cm3 1g/cm3 1g/cm3 1g/cm3 1g/cm3 1g/cm3 1g/cm3 1g/cm3 1g/cm3

Density!
• If the average density of the boat is greater than than 1gm/cm3, the object will sink.

1g/cm31g/cm3 1g/cm3 1g/cm3 1g/cm3 1g/cm3 1g/cm3 1g/cm3 1g/cm3 1g/cm3

d < 1gm/cm3