Example Lesson: Buoyancy Why some objects float gravity buoyancy

Preliminary Concepts Density = mass / volume -or- ρ = m / V For example a rock has more mass and thus weighs more than a dinner roll of equal size. h h w w Which object do you think would be most likely to float in water, the stone or the dinner roll? This is because the dinner roll is less dense.

Archimedes According to legend… King Hiero II gave a goldsmith an amount of pure gold to construct a crown. After the crown was delivered the king became suspicious that the craftsman had stolen some of the gold and mixed the rest with silver. He asked Archimedes to determine if this was true without melting the crown.

Archimedes While taking a bath, Archimedes noticed that the level of the water in the tub rose as he got in, and realized that this effect could be used to determine the volume of the crown. The submerged crown would displace an amount of water equal to its own volume. By dividing the mass of the crown by the volume of water displaced, the density of the crown could be obtained. This density would be lower than that of gold if cheaper and less dense metals had been added.

Archimedes Archimedes then took to the streets naked, so excited by his discovery that he had forgotten to dress, crying "Eureka!" (meaning "I have found it!"). The test was conducted successfully, proving that silver had indeed been mixed in.

= Archimedes Principle A body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces Downward force equal to the weight of the object = Upward force equal to the weight of the displaced fluid

Buoyancy Positively Buoyant Neutrally Buoyant Negatively Buoyant An object that is less dense than water will float Neutrally Buoyant An object that is just as dense as water will float Negatively Buoyant An object that is less dense than water will float

Buoyancy and ROVs Typically ROVs used by companies and universities are made to be slightly positively buoyant Why might this be? This is so the ROV will float to the surface if it is damaged or communication is broken

Buoyancy and Your ROV Should you make your own ROV positively, negatively, or neutrally buoyant? What are the advantages and disadvantages of each? In this setting it is typically best to make an ROV neutrally buoyant

- Ballast How to Change Buoyancy + Floats To increase buoyancy add something that is very positively buoyant like foam - Ballast To decrease buoyancy add something that is very negatively buoyant like metal

Why Might You Want Both?

How to Actively Change Buoyancy Rises Sinks Adding air to a balloon on the ROV makes it rise Adding water to a tank on the ROV makes it sink

Buoyancy Activity How could we determine the mass of an object without using a scale? Hints: The density of water is 1g / mL This will not work if the object sinks in water (Archimedes Principle applies to floating objects)

Buoyancy Activity See how much water the object displaces Use the density equation to solve for mass ρ = m / V (remember ρ stands for density) (1g / mL) = (mass) / ( volume measured in mL) (1 g / mL) * ( # mL) = the object’s mass Check your answer using a scale