14.4 Archimedes’ Principle and Buoyancy

More force is required to pull the plug in a full bathtub than when it is empty. Does this contradict Pascal’s principle? Explain your answer.

Will the same ship float higher in salt water than in freshwater? Explain your answer.

If a person’s body has a density of $995 \text{kg}/\text{m}^{3}$, what fraction of the body will be submerged when floating gently in (a) freshwater? (b) In salt water with a density of $1027 \text{kg}/\text{m}^{3}$?

Archimedes’ principle can be used to calculate the density of a fluid as well as that of a solid. Suppose a chunk of iron with a mass of 390.0 g in air is found to have an apparent mass of 350.5 g when completely submerged in an unknown liquid. (a) What mass of fluid does the iron displace? (b) What is the volume of iron, using its density as given in the reference? (c) Calculate the fluid’s densi…

What is the density of a woman who floats in fresh water with $4.00 \%$ of her volume above the surface? (This could be measured by placing her in a tank with marks on the side to measure how much water she displaces when floating and when held under water.) (b) What percent of her volume is above the surface when she floats in seawater?

A simple compass can be made by placing a small bar magnet on a cork floating in water. (a) What fraction of a plain cork will be submerged when floating in water? (b) If the cork has a mass of 10.0 g and a 20.0-g magnet is placed on it, what fraction of the cork will be submerged? (c) Will the bar magnet and cork float in ethyl alcohol?

Referring to the figure, prove that the buoyant force on the cylinder is equal to the weight of the fluid displaced (Archimedes’ principle). You may assume that the buoyant force is $F_{2} - F_{1}$ and that the ends of the cylinder have equal areas$A$. Note that the volume of the cylinder (and that of the fluid it displaces) equals $\left(h_{2} - h_{1}\right) A$.