Archimedes' principle and buoyant force

State Archimedes' principle in your own words: what upthrust is, in what direction and sense it acts, and what its magnitude is equal to.

When you get into a swimming pool you feel lighter, as if the water were supporting you. What force appears when you submerge yourself? What exerts it and in which direction does it push?

A cube fully submerged in water displaces a volume of $0,002\ \text{m}^3$ (about $2\ \text{L}$), as shown in the figure.

Calculate the upthrust it receives using $E = d\cdot V\cdot g$. Data: $d_{agua} = 1\,000\ \text{kg/m}^3$; take $g = 10\ \text{m/s}^2$.

On the table you have a cork stopper ($d = 240\ \text{kg/m}^3$) and an iron nut ($d = 7\,870\ \text{kg/m}^3$). Without carrying out calculations, predict which one will float and which will sink in water ($d = 1\,000\ \text{kg/m}^3$) and explain the criterion you used.

Ice cubes float in a glass of water. Knowing that the density of ice is about $900\ \text{kg/m}^3$, explain why they float and state the condition that the density of a body must meet to float in a liquid.

A block of $3\ \text{kg}$ has a volume of $0,004\ \text{m}^3$ and is fully submerged in water ($d = 1\,000\ \text{kg/m}^3$), as shown in the figure. Take $g = 10\ \text{m/s}^2$.

1. a) Calculate its weight.
2. b) Calculate the upthrust it receives.
3. c) Does it float or sink? State what net force acts on it and in which direction.

A stone of $5\ \text{kg}$ and a volume of $0,001\ \text{m}^3$ hangs from a force meter and is fully submerged in water, as shown in the figure. Data: $d_{agua} = 1\,000\ \text{kg/m}^3$; take $g = 9,8\ \text{m/s}^2$.

1. a) Calculate its true weight.
2. b) Calculate the upthrust from the water.
3. c) What reading does the force meter show with the stone submerged? Explain why this "apparent weight" is smaller.

A metal part of $2\ \text{kg}$ has a volume of $0,0005\ \text{m}^3$ ($0,5\ \text{L}$). Data: $d_{agua} = 1\,000\ \text{kg/m}^3$; take $g = 10\ \text{m/s}^2$.

1. a) Calculate its weight.
2. b) Calculate the upthrust it receives if fully submerged in water.
3. c) Does it float or sink? Also calculate its density and compare it with that of water to confirm your answer.

A steel ship weighing thousands of tonnes floats, but a small steel ball sinks to the bottom. If both are made of the same material, explain what enables the ship to float (think about its hollow shape and average density).

A hot-air balloon rises when the burner heats the air inside it. Explain what happens to the density of the air when heated and why the upthrust from the cool outside air ends up lifting the balloon.

A log of $0,01\ \text{m}^3$ is fully submerged, first in a lake and then in the sea. Take $g = 10\ \text{m/s}^2$.

1. a) Calculate the upthrust it receives in the lake ($d = 1\,000\ \text{kg/m}^3$).
2. b) Calculate the upthrust it receives in the sea ($d = 1\,025\ \text{kg/m}^3$).
3. c) Using these results, explain why swimmers float "higher" in the sea than in a swimming pool.