14.4 Archimedes’ principle and buoyancy  (Page 4/6)

Marbles dropped into a partially filled bathtub sink to the bottom. Part of their weight is supported by buoyant force, yet the downward force on the bottom of the tub increases by exactly the weight of the marbles. Explain why.

What fraction of ice is submerged when it floats in freshwater, given the density of water at $0\text{°C}$ is very close to $1000{\text{kg/m}}^3$ ?

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

A rock with a mass of 540 g in air is found to have an apparent mass of 342 g when submerged in water. (a) What mass of water is displaced? (b) What is the volume of the rock? (c) What is its average density? Is this consistent with the value for granite?

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 [link] ? (c) Calculate the fluid’s density and identify it.

Calculate the buoyant force on a 2.00-L helium balloon. (b) Given the mass of the rubber in the balloon is 1.50 g, what is the net vertical force on the balloon if it is let go? Neglect the volume of the rubber.

What is the density of a woman who floats in fresh water with $4.00\text{\%}$ 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 man has a mass of 80 kg and a density of $955{\text{kg/m}}^3$ (excluding the air in his lungs). (a) Calculate his volume. (b) Find the buoyant force air exerts on him. (c) What is the ratio of the buoyant force to his weight?

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?

What percentage of an iron anchor’s weight will be supported by buoyant force when submerged in salt water?

Referring to [link] , 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 $(h_2-h_1)A$ .

A 75.0-kg man floats in freshwater with 3.00% of his volume above water when his lungs are empty, and 5.00% of his volume above water when his lungs are full. Calculate the volume of air he inhales—called his lung capacity—in liters. (b) Does this lung volume seem reasonable?