Q: A block of wood has dimensions $$0.75\,\mathrm{m} \times 0.45\,\mathrm{m} \times 0.12\,\mathrm{m}$$ and a mass of $$37.8\,\mathrm{kg}. $$What is the density of the wood?

$$\rho = \dfrac{37.8}{0.75 \times 0.45 \times 0.12} = 933\,\mathrm{kg/m^3$}$$

Q: A cubical box (side $$20.0\,\mathrm{cm}) is $$completely submerged in a fluid. The pressure at the bottom is $$106.8\,\mathrm{kPa}$$ and at the top is $$100.0\,\mathrm{kPa}. $$What is the density of the fluid?

$$\rho = \dfrac{106800 - 100000}{0.2 \times 9.8} = 417\,\mathrm{kg/m^3$}$$

Q: A U-tube manometer contains mercury ($$\rho_{Hg} = 13,600\,\mathrm{kg/m^3$}) $$and water ($$\rho_{w} = 1000\,\mathrm{kg/m^3$}). If $$the height difference of mercury is $$0.025\,\mathrm{m}$$, what is the pressure difference between the two sides?

$$\Delta P = (\rho_{Hg} - \rho_{w})gh = (13,600 - 1000) \times 9.8 \times 0.025 = 3,136\,\mathrm{Pa}$$

Q: A person floats in a swimming pool with $$97.1\% of $$their body submerged. If the density of water is $$1000\,\mathrm{kg/m^3$}$$, what is the density of the person?

$$\rho_{person} = 0.971 \times 1000 = 971\,\mathrm{kg/m^3$}$$

Q: A chunk of ice floats in fresh water. If the density of ice is $$917\,\mathrm{kg/m^3$}$$ and water is $$1000\,\mathrm{kg/m^3$}$$, what percentage of the ice is above the water?

$$\dfrac{1000 - 917}{1000} \times 100\% = 8.3\%$$

Q: Water flows through a pipe with a diameter of $$15.0\,\mathrm{cm} at a $$speed of $$2.0\,\mathrm{m/s}. $$What is the speed of water in a constricted section with a diameter of $$5.0\,\mathrm{cm}$$?

$$v_2$$ = $$v_1$$ \dfrac{$$A_1$$}{$$A_2$$} = 2.0 \times \dfrac{$$(0.15)^2$$}{$$(0.05)^2$$} = 18\,\mathrm{m/s}$$

Q: A tower open to the atmosphere at the top contains water. The water velocity at the top is $$0.0\,\mathrm{m/s}$$ and at the bottom is $$2.0\,\mathrm{m/s}. If $$the height difference is $$10.0\,\mathrm{m}$$, what is the pressure difference between the bottom and the top?

$$\Delta P = \dfrac{1}{2}\rho(v_2$^2 - v_1$^2) + \rho g h = \dfrac{1}{2}1000(4-0) + 1000 \times 9.8 \times 10 = 5000 + 98000 = 103000\,\mathrm{Pa}$$

Question 1

A block of wood has dimensions $$0.75\,\mathrm{m} 	imes 0.45\,\mathrm{m} 	imes 0.12\,\mathrm{m}$$ and a mass of $$37.8\,\mathrm{kg}. $$What is the density of the wood?

Accepted Answer

$$ho = \dfrac{37.8}{0.75 	imes 0.45 	imes 0.12} = 933\,\mathrm{kg/m^3$}$$

Question 2

Which of the following best describes the physical meaning of density?

Accepted Answer

The amount of mass per unit volume.

Question 3

A gauge reads a pressure of $$700\,\mathrm{kPa}$$ inside a basketball. If the atmospheric pressure is $$101\,\mathrm{kPa}$$, what is the absolute pressure inside the ball?

Accepted Answer

$$P_{abs} = 700\,\mathrm{kPa} + 101\,\mathrm{kPa} = 801\,\mathrm{kPa}$$

Question 4

A cubical box (side $$20.0\,\mathrm{cm}) is $$completely submerged in a fluid. The pressure at the bottom is $$106.8\,\mathrm{kPa}$$ and at the top is $$100.0\,\mathrm{kPa}. $$What is the density of the fluid?

Accepted Answer

$$ho = \dfrac{106800 - 100000}{0.2 	imes 9.8} = 417\,\mathrm{kg/m^3$}$$

Question 5

While swimming below the surface, you let out a small bubble of air. As the bubble rises toward the surface, what happens to its diameter?

Accepted Answer

It increases.

Question 6

A U-tube manometer contains mercury ($$\rho_{Hg} = 13,600\,\mathrm{kg/m^3$}) $$and water ($$\rho_{w} = 1000\,\mathrm{kg/m^3$}). If $$the height difference of mercury is $$0.025\,\mathrm{m}$$, what is the pressure difference between the two sides?

Accepted Answer

$$\Delta P = (ho_{Hg} - ho_{w})gh = (13,600 - 1000) 	imes 9.8 	imes 0.025 = 3,136\,\mathrm{Pa}$$

Question 7

A hydraulic lift is used to lift a $$2100\,\mathrm{kg}$$ car. If the small piston has an area of $$0.015\,\mathrm{m^2$}$$ and the large piston has an area of $$0.45\,\mathrm{m^2$}$$, what force must be applied to the small piston?

Accepted Answer

$$F_1$$ = \dfrac{$$A_1$$}{$$A_2$$} $$F_2$$ = \dfrac{0.015}{0.45} 	imes 2100 	imes 9.8 = 686\,\mathrm{N}$$

Question 8

A person floats in a swimming pool with $$97.1\% of $$their body submerged. If the density of water is $$1000\,\mathrm{kg/m^3$}$$, what is the density of the person?

Accepted Answer

$$ho_{person} = 0.971 	imes 1000 = 971\,\mathrm{kg/m^3$}$$

Question 9

A chunk of ice floats in fresh water. If the density of ice is $$917\,\mathrm{kg/m^3$}$$ and water is $$1000\,\mathrm{kg/m^3$}$$, what percentage of the ice is above the water?

Accepted Answer

$$\dfrac{1000 - 917}{1000} 	imes 100\% = 8.3\%$$

Question 10

Water flows through a pipe with a diameter of $$15.0\,\mathrm{cm} at a $$speed of $$2.0\,\mathrm{m/s}. $$What is the speed of water in a constricted section with a diameter of $$5.0\,\mathrm{cm}$$?

Accepted Answer

$$v_2$$ = $$v_1$$ \dfrac{$$A_1$$}{$$A_2$$} = 2.0 	imes \dfrac{$$(0.15)^2$$}{$$(0.05)^2$$} = 18\,\mathrm{m/s}$$

Question 11

A tower open to the atmosphere at the top contains water. The water velocity at the top is $$0.0\,\mathrm{m/s}$$ and at the bottom is $$2.0\,\mathrm{m/s}. If $$the height difference is $$10.0\,\mathrm{m}$$, what is the pressure difference between the bottom and the top?

Accepted Answer

$$\Delta P = \dfrac{1}{2}ho(v_2$^2 - v_1$^2) + ho g h = \dfrac{1}{2}1000(4-0) + 1000 	imes 9.8 	imes 10 = 5000 + 98000 = 103000\,\mathrm{Pa}$$

Question 12

During a hurricane, the air pressure outside a house drops to $$95000\,\mathrm{Pa}$$ while inside it remains at $$101300\,\mathrm{Pa}. If $$the area of a window is $$2.0\,\mathrm{m^2$}$$, what is the net force on the window?

Accepted Answer

$$F = (101300 - 95000) 	imes 2.0 = 12,600\,\mathrm{N}$$

Question 13

A water fountain shoots water to a height of $$2.0\,\mathrm{m}. $$What is the speed of water as it leaves the nozzle?

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 2.0} = 6.3\,\mathrm{m/s}$$

Question 14

Blood flows through the pulmonary artery with a radius of $$0.012\,\mathrm{m}$$ and a pressure difference of $$400\,\mathrm{Pa}$$ over a length of $$0.06\,\mathrm{m}. If $$the viscosity of blood is $$2.72 	imes 10$$^{-3}$$\,\mathrm{Pa \cdot s}$$, what is the speed of blood flow?

Accepted Answer

$$v = \dfrac{\Delta P \cdot r^2$}{8 \eta L} = \dfrac{400 	imes (0.012)^2$}{8 	imes 2.72 	imes 10$$^{-3}$$ 	imes 0.06} = 1.23\,\mathrm{m/s}$$

Fluids: Density, Pressure, and Applications in Physics

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