Buoyancy and Archimedes' Principle

Flashcards covering buoyancy definitions, Archimedes' Principle, upthrust calculations, and practical examples like submarines and wetsuits.

What is buoyancy?

The ability of an object to sink or float in a fluid.

What is the difference between positive, negative, and neutral buoyancy?

Positive buoyancy occurs when an object is lighter than the fluid and floats; negative buoyancy occurs when an object is denser and sinks; neutral buoyancy occurs when an object's weight is equal to the fluid it is submerged in, meaning it neither floats nor sinks.

How do fish and divers control their buoyancy?

Fish control buoyancy through their swim bladder, while divers use their breath to aid in buoyancy.

Who was Archimedes?

Archimedes ($287-212\,BC$) was a pre-eminent Greek mathematician and inventor credited with discovering buoyancy.

What is Archimedes' Principle?

When an object is totally or partially immersed in a fluid, it experiences an upthrust equal to the weight of the fluid displaced.

What is the difference between mass and weight?

Mass is the constant amount of matter in an object, while weight is the force of gravity on that object which varies depending on gravitational pull.

What is upthrust (or buoyant force)?

The upward force exerted on an object floating in a substance, which is equal to the mass of the water displaced and reduces the actual weight of the object in water.

What are the densities of fresh water and salt water?

The density of fresh water is $1\,kg/L$ and the density of salt water is $1.03\,kg/L$.

How is upthrust (mass of water displaced) calculated?

$$\text{Mass of water displaced (upthrust)} = \text{object volume} \times \text{density of water}$$

How is an object's apparent mass calculated?

$$\text{Apparent mass} = \text{weight of object on land} - \text{upthrust}$$

Under what condition of upthrust will an object float?

An object will float if the upthrust is greater than the mass of the object.

Under what condition of upthrust will an object sink?

An object will sink if the upthrust is less than the mass of the object.

If an object has a volume of $75\,L$ and a mass of $150\,kg$ on land, what is its apparent mass in fresh water and will it sink?

The upthrust is $75\,kg$ ($75\,L \times 1\,kg/L$), and the apparent mass is $75\,kg$ ($150\,kg - 75\,kg$). The object will sink.

A diver has a mass of $57\,kg$ on land and a volume of $60\,L$. What is their apparent mass in fresh water, and how do they reach neutral buoyancy?

The upthrust is $60\,kg$ ($60\,L \times 1\,kg/L$), and the apparent mass is $-3\,kg$. To reach neutral buoyancy, the diver must add $3\,kg$ of weights.

According to the principles of buoyant force and flotation, when does an object move up or down?

An object moves up if the buoyant force is greater than the weight ($\text{Buoyant force} > \text{weight}$) and moves down if the buoyant force is less than the weight ($\text{Buoyant force} < \text{weight}$).

Why does a ship immerse deeper in warm fresh water than in cold sea water?

Fresh water and warm water are less dense than cold sea water, requiring more water to be displaced to keep the upthrust force equal to the weight of the boat.

Why does plasticine float when shaped as a hull but sink when shaped as a ball?

The hull has a larger surface area and displaces a larger weight of water, resulting in a greater upthrust that can hold it up, whereas the ball displaces less water and has a smaller upthrust.

How do ballast tanks affect the buoyancy of a submarine?

When ballast tanks are empty, upthrust is greater than weight and the submarine rises; when tanks are full, upthrust is less than weight and the submarine sinks.

Why do wetsuits made of neoprene provide positive buoyancy?

Neoprene is less dense than water because it is made of gas bubbles enclosed within the material, causing the wetsuit to displace more water than it weighs.