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In this lesson, we will learn how to calculate the density of materials and how to find the pressure at a given depth in a liquid of a given density.

Q1:

A trash compactor can compress its contents to 0.350 times their original volume. Neglecting the mass of air expelled, by what factor is the density of the rubbish increased?

Q2:

A cylindrical coffee cup holds 375 g of coffee when filled to a depth of 7.50 cm. Find the radius of the cup. Use a value of 1.00 g/cm^{3} for the density of coffee.

Q3:

Find the mass of the air inhaled during a deep breath. Use a value of 2.00 L for the volume of the air and use a value of 1.29 kg/m^{3} for the density of air.

Q4:

The density of water at a temperature of 0 . 0 0 ∘ C is 999.84 kg/m^{3}, whereas the density of ice at 0 . 0 0 ∘ C is 917 kg/m^{3}. What pressure would need to be applied to water in a container by the container walls to prevent the water from expanding as it froze? Use a value of 2.20 GPa for the bulk modulus of water. Neglect the temperature changes that would result from this pressure.

Q5:

Find the length of a side of a cube having a mass of 1.0 kg and the density of nuclear matter, 2 . 3 × 1 0 1 7 kg/m^{3}.

Q6:

What is the density of 18.0-karat gold that is a mixture of 18 parts gold, 5 parts silver, and 1 part copper? (These values are parts by mass, not volume.) Assume that this is a simple mixture having an average density equal to the weighted densities of its constituents.

Density of gold is 19.3 g/cm^{3}.

Density of silver is 10.5 g/cm^{3}.

Density of copper is 8.92 g/cm^{3}.

Q7:

A person hits a tennis ball with a mass of 0.058 kg against a wall. The average component of the ball’s velocity perpendicular to the wall is 11 m/s, and the ball hits the wall every 2.1 s on average, rebounding with the opposite perpendicular velocity component.

What is the average force exerted on the wall?

If the part of the wall the person hits has an area of 3.0 m^{2}, what is the average pressure on that area?

Q8:

How tall must a water-filled manometer be to measure blood pressure as high as 300 mmHg?

Use a value of 1 . 3 6 × 1 0 4 kg/m^{3} for the density of mercury.

Q9:

A dam is used to hold back a river. The dam has a height of 12.0 m and a width of 10.0 m. Determine the net force on the dam. Use a value of 1 . 0 × 1 0 3 kg/m^{3} for the density of water.

Q10:

Normal forces are applied uniformly over the surface of a spherical volume of water whose radius is 20.00 cm. If the pressure on the surface is increased by 2 . 0 × 1 0 8 Pa, by how much does the radius of the sphere decrease?

Q11:

A glass tube contains mercury. How high would a column of mercury in the tube need to be to produce a pressure of 1.00 atm? Use a value of 1 = 1 . 0 1 × 1 0 a t m P a 5 for atmospheric pressure and a value of 1 . 3 6 × 1 0 4 kg/m^{3} for the density of mercury.

Q12:

Calculate the mass of air in a classroom. Assume a classroom of side lengths 8.00 m, 7.00 m, and 3.00 m, containing air with a density of 1.225 kg/m^{3}.

Q13:

Calculate the depth to which Avogadro’s number of table tennis balls would cover Earth. Each ball has a diameter of 3.75 cm. Assume the space between balls increases their volume by 2 5 . 0 % and assume they are not crushed by their own weight. Use 6 3 7 1 km as the value of the Earth’s radius.

Q14:

Find the height of Earth’s atmosphere. Use a value of 1 0 1 9 kg for the mass of the atmosphere, a value of 1 kg/m^{3} for the atmosphere’s density, and a value of 6 3 7 1 km for Earth’s radius.

Q15:

Under normal conditions, the density of iron is 7.86 g/cm^{3}. Find the density of iron under normal conditions in kilograms per cubic meter.

Q16:

A liquid with a density 5.3 times the density of water is used in a manometer. A pressure difference of 2 7 6 0 0 Pa corresponds to what head of this liquid?

Q17:

A liquid with a density 8.0 times the density of water is used in a manometer. A pressure difference of 1 7 2 0 Pa corresponds to what head of this liquid?

Q18:

A centrifugal pump is used to lift water at a rate of 5.0 gallons per minute against a head of 50 feet of water. The efficiency of the pump is 7 0 % . What power input is required by the pump?

Q19:

A centrifugal pump is used to lift water at a rate of 18.9 L per minute against a head of 75 feet of water. The efficiency of the pump is 6 5 % . What power input is required by the pump?

Q20:

A centrifugal pump is used to lift water at a rate of 284 L per minute against a head of 175 feet of water. The efficiency of the pump is 7 5 . 0 % . What power input is required by the pump?

Q21:

A pump with a power input of 8.5 kW pumps water at a rate of 1 7 0 3 L per minute against a pressure of 2.189 atm. What is the operating efficiency of the pump?

Q22:

How many feet of water pressure does a column of mercury of height 1.0 m exert?

Q23:

A gate that is 2.00 m wide and 1.00 m high is located in a vertical wall that is part of a water container. The top of the wall is at the level of the water’s surface. Calculate the magnitude of the hydrostatic force acting on the gate.

Q24:

The specific gravity of an oil is 0.750. Calculate the pressure represented by a 5.00 cm column of the oil.

Q25:

A semicircular tunnel is built under a lake. The tunnel is 487.7 m long and has a diameter of 9.14 m. The distance from the top of the tunnel to the water surface is 36.58 m. Calculate the magnitude of the hydrostatic force acting on the roof of the tunnel.

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