Q: A submarine is submerged at a depth where the water pressure is 3.0 MPa. If the density of seawater is $$\rho = 1025\ \text{kg/m}^3$$ and atmospheric pressure is $$P_0 = 101$$,325\ \text{Pa}$$, what is the approximate depth of the submarine? (Use g = 9.8$$\ \text{m/s}^2$$)

$$h = \frac{P - P_0$}{\rho g} = \frac{3,000,000 - 101,325}{1025 \times 9.8} \approx 285\ \text{m}$$

Q: A patient receives an intravenous (IV) drip. The IV bag is hung 0.5 m above the insertion point. If the density of the saline solution is $$\rho = 1000\ \text{kg/m}^3$$, what is the pressure difference between the IV bag and the insertion point?

$$\Delta P = \rho g h = 1000 \times 9.8 \times 0.5 = 4900\ \text{Pa}$$

Q: A refrigerator removes 500 J of heat from its interior and expels 700 J to the kitchen. What is the work input required according to the first law of thermodynamics?

$$W = Q_{out} - Q_{in} = 700 - 500 = 200\ \text{J}$$

Q: A 0.5 kg mass attached to a spring oscillates with a period of 2 s. What is the spring constant $$k$$?

$$k = \frac{4\pi^2$ m}{T^2$} = \frac{4 \times \pi^2$ \times 0.5}{2^2$} \approx 4.93\ \text{N/m}$$

Q: A guitar string of length $$L = 0.65\ \text{m} is $$fixed at both ends. What is the wavelength of the fundamental mode?

$$\lambda = 2L = 2 \times 0.65 = 1.3\ \text{m}$$

Q: Two sound waves of frequencies 440 Hz and 444 Hz interfere. What is the beat frequency heard?

$$f_{\text{beat}} = |f_1$ - f_2$| = |440 - 444| = 4\ \text{Hz}$$

Question 1

A submarine is submerged at a depth where the water pressure is 3.0 MPa. If the density of seawater is $$ho = 1025\ 	ext{kg/m}^3$$ and atmospheric pressure is $$P_0 = 101$$,325\ 	ext{Pa}$$, what is the approximate depth of the submarine? (Use g = 9.8$$\ 	ext{m/s}^2$$)

Accepted Answer

$$h = \frac{P - P_0$}{ho g} = \frac{3,000,000 - 101,325}{1025 	imes 9.8} \approx 285\ 	ext{m}$$

Question 2

A patient receives an intravenous (IV) drip. The IV bag is hung 0.5 m above the insertion point. If the density of the saline solution is $$ho = 1000\ 	ext{kg/m}^3$$, what is the pressure difference between the IV bag and the insertion point?

Accepted Answer

$$\Delta P = ho g h = 1000 	imes 9.8 	imes 0.5 = 4900\ 	ext{Pa}$$

Question 3

A fluid flows through a horizontal pipe that narrows from radius $$r_1 to$$ $$r_2. If $$the speed at $$r_1 is$$ $$v_1$$, what is the speed at $$r_2$$ according to the continuity equation?

Accepted Answer

$$v_2$$ = $$v_1$$ \frac{$$r_1^2$$}{$$r_2^2$$}$$

Question 4

A 2 kg block of aluminum ($$c = 900\ 	ext{J/kg}\cdot	ext{K}) at$$ $$20^\circC is $$placed in 1 kg of water ($$c = 4186\ 	ext{J/kg}\cdot	ext{K}) at$$ $$80^\circC. $$What is the final equilibrium temperature, assuming no heat loss?

Accepted Answer

$$T_f = \frac{m_1$ c_1$ T_1$ + m_2$ c_2$ T_2$}{m_1$ c_1$ + m_2$ c_2$} = \frac{2 	imes 900 	imes 20 + 1 	imes 4186 	imes 80}{2 	imes 900 + 1 	imes 4186} \approx 62^\circ	ext{C}$$

Question 5

A refrigerator removes 500 J of heat from its interior and expels 700 J to the kitchen. What is the work input required according to the first law of thermodynamics?

Accepted Answer

$$W = Q_{out} - Q_{in} = 700 - 500 = 200\ 	ext{J}$$

Question 6

Which of the following best describes the second law of thermodynamics?

Accepted Answer

The entropy of an isolated system always increases or remains constant; it never decreases.

Question 7

A heat engine operates between a hot reservoir at $$T_H = 600\ 	ext{K}$$ and a cold reservoir at $$T_C = 300\ 	ext{K}. $$What is the maximum possible efficiency?

Accepted Answer

$$\eta = 1 - \frac{T_C}{T_H} = 1 - \frac{300}{600} = 0.5$$

Question 8

A 0.5 kg mass attached to a spring oscillates with a period of 2 s. What is the spring constant $$k$$?

Accepted Answer

$$k = \frac{4\pi^2$ m}{T^2$} = \frac{4 	imes \pi^2$ 	imes 0.5}{2^2$} \approx 4.93\ 	ext{N/m}$$

Question 9

A guitar string of length $$L = 0.65\ 	ext{m} is $$fixed at both ends. What is the wavelength of the fundamental mode?

Accepted Answer

$$\lambda = 2L = 2 	imes 0.65 = 1.3\ 	ext{m}$$

Question 10

Two sound waves of frequencies 440 Hz and 444 Hz interfere. What is the beat frequency heard?

Accepted Answer

$$f_{	ext{beat}} = |f_1$ - f_2$| = |440 - 444| = 4\ 	ext{Hz}$$

Question 11

A thin film of oil ($$n = 1.4) $$floats on water ($$n = 1.33). If $$light of wavelength $$\lambda = 560\ 	ext{nm} in $$air is incident, what minimum thickness will produce constructive interference in reflected light?

Accepted Answer

$$t = \frac{\lambda}{4n} = \frac{560}{4 	imes 1.4} \approx 100\ 	ext{nm}$$

Question 12

A lens has a focal length of $$f = 20\ 	ext{cm}. An $$object is placed $$60\ 	ext{cm}$$ from the lens. Where is the image formed?

Accepted Answer

$$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \Rightarrow d_i = \frac{1}{\frac{1}{f} - \frac{1}{d_o}} = \frac{1}{\frac{1}{20} - \frac{1}{60}} = 30\ 	ext{cm}$$

Question 13

A telescope uses an objective lens of focal length $$f_o = 100\ 	ext{cm}$$ and an eyepiece of focal length $$f_e = 2\ 	ext{cm}. $$What is the angular magnification?

Accepted Answer

$$M = \frac{f_o}{f_e} = \frac{100}{2} = 50$$

Question 14

A standing wave is formed on a string fixed at both ends. If the string length is $$L$$ and the speed of waves is $$v$$, what is the frequency of the second harmonic?

Accepted Answer

$$f_2$$ = \frac{2v}{L}$$

Question 15

A gas undergoes an isothermal expansion at $$T = 300\ 	ext{K}$$, doubling its volume. What is the change in entropy $$\Delta S$$ for 1 mole of ideal gas?

Accepted Answer

$$\Delta S = nR \ln \frac{V_f}{V_i} = 1 	imes 8.314 	imes \ln 2 \approx 5.76\ 	ext{J/K}$$

Question 16

A patient’s lung capacity is measured using a spirometer. If the pressure difference is $$200\ 	ext{Pa}$$ and the area of the mouthpiece is $$4 	imes 10$$^{-4}$$\ 	ext{m}^2$$, what is the force exerted by the air?

Accepted Answer

$$F = P 	imes A = 200 	imes 4 	imes 10$$^{-4}$$ = 0.08\ 	ext{N}$$

Question 17

A wave travels on a string with speed $$v = 20\ 	ext{m/s}$$ and frequency $$f = 50\ 	ext{Hz}. $$What is its wavelength?

Accepted Answer

$$\lambda = \frac{v}{f} = \frac{20}{50} = 0.4\ 	ext{m}$$

Question 18

A mirror forms an image of an object placed 30 cm in front of it. If the image is formed 30 cm behind the mirror, what type of mirror is it?

Accepted Answer

Plane mirror

Physics 2B: Fluids, Thermodynamics, SHM, and Waves – Course Syllabus and Structure

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