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In this lesson, we will learn how to calculate the density of an object that is submerged in a fluid of a given density.

Q1:

Bird bones have air pockets in them to reduce their weight—this also gives them an average density significantly less than that of the bones of other animals. An ornithologist weighs an impermeable bird bone in air and in water and finds its mass is 45.0 g and its apparent mass when submerged is 3.60 g.

What mass of water is displaced?

What is the volume of the bone?

What is the average density of the bone?

Q2:

Logs sometimes float vertically in a lake because one end has become water-logged and denser than the other. What is the average density of a uniform-diameter log that floats with 2 0 % of its length above water? Use a value of 1 0 0 0 kg/m^{3} for the density of water.

Q3:

A man has a mass of 65 kg and a density of 900 kg/m^{3}, excluding the air in his lungs. A buoyant force acts on the man, directed oppositely to his weight. Use a value of 1.225 kg/m^{3} for the density of air.

What is the volume of the man?

What is the magnitude of the buoyant force that the air exerts on the man?

What is the ratio of the man’s weight to the buoyant force acting on him?

Q4:

A woman floats in fresh water of density 1 . 0 0 × 1 0 3 kg/m^{3}. 4 . 0 0 % of her volume is above the water’s surface.

What is the density of the woman?

What percent of the woman’s volume would be above water if she floated in sea water of density 1 . 0 3 × 1 0 3 kg/m^{3}?

Q5:

A person’s body has a density of 995 kg/m^{3}.

What fraction of the body will be submerged when floating gently in freshwater of density 1 . 0 0 × 1 0 3 kg/m^{3}?

What fraction of the body will be submerged when floating gently in salt water with a density of 1 0 2 7 kg/m^{3}?

Q6:

A simple compass can be made by placing a small bar magnet on a cork floating in water. Use a value of 2 . 4 × 1 0 2 kg/m^{3} as the density of cork.

What percent of an object made of cork will be submerged when floating in water?

An object made of cork has a mass of 10.0 g. A 20.0-g-mass magnet is placed on the object. What percent of the object will be submerged?

Q7:

What are the units of specific gravity?

Q8:

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. Assume that the iron has a density of 7 . 8 6 × 1 0 3 kg/m^{3}.

What mass of fluid does the iron displace?

What is the volume of the iron?

Calculate the fluid’s density.

Q9:

A rubber balloon has a mass of 1.80 g when deflated. The balloon is inflated with helium to a volume of 2.50 L. The balloon experiences a buoyant force due to the lower density of helium than air, but the weight of the balloon acts oppositely to the buoyant force on it. Use a value of 1.225 kg/m^{3} for the density of air and use a value of 0.179 kg/m^{3} for the density of helium.

What is the magnitude of the buoyant force on the balloon?

What is the magnitude of the net vertical force on the balloon? Assume the volume of the rubber in the balloon is negligible.

Q10:

A man with a mass of 70.0 kg floats in freshwater. When the man’s lungs are empty, 3 . 5 0 % of his volume is above water. When his lungs are full, 5 . 5 0 % of his volume is above water. What is the volume of air he inhales—called his lung capacity?

Q11:

Some fish have a density slightly less than that of water and must exert a force, by swimming, to stay submerged. Find the force that a fish of mass 85.0 kg must exert to stay submerged in salt water if its body density is 1 0 1 5 kg/m^{3}. Use a value 1 0 2 5 kg/m^{3} for the density of salt water.

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