Q: A submarine is cruising at a depth of 300 m in seawater (density $$1030 \text{ kg/m}^3). $$Atmospheric pressure is $$1.01 \times 10^5$ Pa. What is the total pressure at this depth?

$$p = 1.01 \times 10^5$ \text{ Pa} + (1030 \text{ kg/m}^3)(9.80 \text{ m/s}^2)(300 \text{ m})$$

Q: A crown weighs 8.30 N in air and 7.81 N when suspended in water. What is the magnitude of the buoyant force acting on the crown?

$$F_b = 8.30 \text{ N} - 7.81 \text{ N} = 0.49 \text{ N}$$

Question 1

Which of the following statements best describes the atomic model of matter as it relates to the phases of matter?

Accepted Answer

The atomic model states that matter is made of basic particles whose arrangement and interactions determine whether the substance is a gas, liquid, or solid.

Question 2

The root-mean-square speed $$v_{rms} of $$gas particles is related to temperature by which equation?

Accepted Answer

$$v_{rms} = \sqrt{\frac{3k_B T}{m}}$$

Question 3

Which of the following is NOT an assumption of the ideal gas law?

Accepted Answer

Gas particles are always in a solid phase.

Question 4

A sealed container holds an ideal gas. If the initial pressure, volume, and temperature are $$p_i$$, $$V_i$$, and $$T_i$$, and the final values are $$p_f$$, $$V_f$$, and $$T_f$$, which equation correctly relates these quantities?

Accepted Answer

$$\frac{p_i V_i}{T_i} = \frac{p_f V_f}{T_f}$$

Question 5

On a pressure-volume ($$p$$-$$V) $$diagram, which type of process is represented by a vertical line?

Accepted Answer

A constant-volume process

Question 6

The work done by a gas during a constant-pressure process is given by which equation?

Accepted Answer

$$W_{gas} = p (V_f - V_i) = p \Delta V$$

Question 7

A liquid-filled cylinder has a cross-sectional area $$A$$ and height $$d. If $$the liquid has density $$\rho$$, what is the pressure at depth $$d$$ below the surface?

Accepted Answer

$$p = p_0$ + \rho g d$$

Question 8

A submarine is cruising at a depth of 300 m in seawater (density $$1030 	ext{ kg/m}^3). $$Atmospheric pressure is $$1.01 	imes 10^5$ Pa. What is the total pressure at this depth?

Accepted Answer

$$p = 1.01 	imes 10^5$ 	ext{ Pa} + (1030 	ext{ kg/m}^3)(9.80 	ext{ m/s}^2)(300 	ext{ m})$$

Question 9

According to Pascal's principle, what happens if the pressure at one point in an incompressible fluid is increased?

Accepted Answer

The pressure at every other point in the fluid increases by the same amount.

Question 10

A barometer measures atmospheric pressure using a column of liquid. If the liquid is mercury, which equation relates the atmospheric pressure to the height $$h of $$the column?

Accepted Answer

$$p_{atm} = \rho g h$$

Question 11

A block of wood floats in water with 5.8 cm submerged. In an unknown liquid, it floats with 5.0 cm submerged. If the density of water is $$1000 	ext{ kg/m}^3$$, what is the density of the unknown liquid?

Accepted Answer

$$\rho_{unknown} = \rho_{water} \frac{5.8}{5.0}$$

Question 12

Archimedes’ principle states that the buoyant force on an object immersed in a fluid is equal to:

Accepted Answer

The weight of the fluid displaced by the object

Question 13

A crown weighs 8.30 N in air and 7.81 N when suspended in water. What is the magnitude of the buoyant force acting on the crown?

Accepted Answer

$$F_b = 8.30 	ext{ N} - 7.81 	ext{ N} = 0.49 	ext{ N}$$

Question 14

An object will float in a fluid if:

Accepted Answer

The density of the object is less than the density of the fluid

Question 15

Which of the following best describes neutral buoyancy?

Accepted Answer

The density of the object equals the density of the fluid, so the object hangs motionless in the fluid.

Question 16

Which equation correctly defines mass density $$\rho$$?

Accepted Answer

$$\rho = \frac{m}{V}$$

Question 17

Which equation expresses the pressure $$p$$ exerted by a fluid on a surface of area $$A$$ due to a force $$F$$?

Accepted Answer

$$p = \frac{F}{A}$$

Question 18

In fluid dynamics, the equation of continuity for an incompressible fluid flowing through a tube of varying cross-section is:

Accepted Answer

$$A_1$$ $$v_1$$ = $$A_2$$ $$v_2$$

Question 19

A garden hose with an inside diameter of 16 mm fills a 10 L bucket in 20 s. What is the speed of water exiting the hose?

Accepted Answer

$$v = \frac{Q}{A}$$, where $$Q = \frac{10 	ext{ L}}{20 	ext{ s}} = 5.0 	imes 10$$^{-4}$$ 	ext{ m}^3/	ext{s}$$ and $$A = \pi (0.008 	ext{ m})^2$

Question 20

If the diameter of a nozzle attached to a hose is reduced by a factor of 2, what happens to the speed of water exiting the nozzle, assuming the flow rate remains constant?

Accepted Answer

The speed increases by a factor of 4.

Fluids: Properties, Pressure, Buoyancy, and Fluid Dynamics (Lecture 22, Sections 13.1-13.4)

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