PHYS_123A_Final_Autumn_2023_with_Answers

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Print UW Net ID_______________________________________@uw.edu PHYS 123 A Autumn 2023 Final Exam 1 Mark all of your answers on the bubble sheet. All questions can have one or multiple correct answers, and you will get credit only when you identify all the correct answers without selecting any incorrect answers. I. [70 points total] 21 Lecture Questions 1. [3 points] A mass on a frictionless surface is attached to a horizontal spring with spring constant 𝑘 = 2 N/m . The spring is compressed by 𝑥 = 0.1 m and released from rest. By how much will the velocity of the mass change as it passes through 𝑥 = 0 , if it is instead compressed by 𝑥 = 0.2 m before being released? A. Increase by a factor of 2 B. Decrease by a factor of 2 C. Increase by a factor of 4 D. Increase by a factor of √2 E. It will remain the same. 2. [3 points] A simple pendulum is released from rest and undergoes oscillations of frequency 3.0 s -1 . The length of the string is decreased by a factor of 4.0. What is the new frequency of oscillations? A. Not enough information B. 1.5 s -1 C. 3.0 s -1 D. 6.0 s -1 E. 12.0 s -1 3. [4 points] Select all of the following functions of position, 𝑥 , and time, ? , (and all other variables representing constants) that represent solutions to the wave equation. A. ?(𝑥, ?) = 𝐴 (𝑥 − ??) ???(𝑥 − ??) B. ?(𝑥, ?) = 𝐴 𝑥 ???(𝑥 − ??) C. ?(𝑥, ?) = 𝐴 ?𝑥?(𝑥 − ??) ???(𝑥 − ??) D. ?(𝑥, ?) = (𝑥 − ??)/(𝑥 + ??) E. ?(𝑥, ?) = 𝐴 ?𝑖?(𝑥 − ??)

Print UW Net ID_______________________________________@uw.edu PHYS 123 A Autumn 2023 Final Exam 2 4. [3 points] Consider a wave propagating on a string approaching a splice from a lighter string to a heavier string, as shown below. The heavier string is twice the mass density of the lighter string. Select all of the true statements from below. A. The reflected wave on the light string will be inverted. B. The reflected wave on the light string will be upright. C. The transmitted wave will have four times the frequency of the incident wave. D. The transmitted wave will have the same frequency as the incident wave. E. The transmitted wave will have the same wavelength as the incident wave. 5. [4 points] You are tuning a guitar to middle C. A tuning fork with resonant frequency ? = 261.63 Hz (C) is struck, and when you pluck the guitar string, you hear a beat frequency of 2.60Hz. By how much should you change the tension of the string? Select one answer below. A. Increase by 1% B. Decrease by 1% C. Increase by 2% D. Decrease by 2% E. C or D 6. [3 points] Consider the following set up, illustrated at right. Surface waves are generated from two coherent sources, S1 and S2, separated by a small distance. The figure shows the crests (solid) and troughs (dashed) of the waves from S1 and S2 at an instant ? . Select all of the true statements about the system at a time ? + 𝑇 later, where 𝑇 is the period of the waves. A. Point A will have a minimum magnitude displacement. B. Point A will have neither a minimum or maximum magnitude displacement. C. Point B will have a minimum magnitude displacement. D. Point B will have a maximum magnitude displacement. E. Point C will have a maximum magnitude displacement.

Print UW Net ID_______________________________________@uw.edu PHYS 123 A Autumn 2023 Final Exam 3 7. [4 points] A U-tube with both sides open to the atmosphere is filled with water with mass density 𝜌 = 1000 kg/m 3 (figure a). Oil, with mass density 𝜌 = 717 kg/m 3 , is added to the left side, as in figure b. How much higher is the equilibrium height of the oil than the equilibrium height of the water, when the heights are measured with respect to the oil-water interface? A. Not enough information B. 39% higher C. 95% higher D. 139% higher E. 195% higher 8. [3 points] Initially a toy boat with a rock on board floats in a small tub of water. You remove the rock from the boat and place it in the water, where it sinks to the bottom of the tub. What happens to the water level in the tub? A. It rises. B. It falls. C. It stays the same. D. Not enough information

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Print UW Net ID_______________________________________@uw.edu PHYS 123 A Autumn 2023 Final Exam 4 9. [3 points] Water flows horizontally at velocity 𝑣 through a cylindrical pipe of cross- sectional diameter ? 1 . The pipe is then split into two equal segments, each with cross- sectional diameter ? 2 and the velocity in each segment is measured to be 2𝑣 . What can you conclude about the ratio of the diameters of the pipes? A. ? 2 / ? 1 = 1 B. ? 2 / ? 1 = 1/2 C. ? 2 / ? 1 = 1/4 D. ? 2 / ? 1 = 1/√2 E. Not enough information 10. [3 points] A beam of light in glass travels with a speed of 0.50 c and hits an interface with air. What is the minimum angle relative to the normal vector at the surface between the glass and the air at which no light is transmitted into the air? A. 45 o B. 35 o C. 30 o D. 50 o E. 60 o 11. [4 points] Two converging lenses, 1 and 2, are separated by 150 mm, with lens 1 on the left. The focal length of lens 1 is 100 mm and that of lens 2 is 200 mm. An object is placed 50 mm to the left of lens 1. How far from lens 2 should a screen be placed if the image formed by the two lenses is to be focused on the screen? A. 1000 mm B. 500 mm C. 300 mm D. 150 mm E. 450 mm

Print UW Net ID_______________________________________@uw.edu PHYS 123 A Autumn 2023 Final Exam 5 12. [4 points] A diverging mirror has a magnitude of focal length 700 mm. An object is located 350mm in front of the mirror. What is the magnification of the image formed? A. 0.33 B. 0.5 C. 0.67 D. 0.9 E. 1 13. [3 points] If the headlights on a car are separated by 1.3 m, what is the furthest distance down the road the car can be located for an eye to resolve the headlights if the angular resolution of the eye is 5.0 × 10 −4 rad, and the person has excellent vision? A. 5.0 km B. 1.3 km C. 2.6 km D. 0.65 km E. 4.8 km 14. [4 points] Monochromatic light shines down on a piece of glass that has a slight angle to horizontal that rests with the left side on a flat piece of glass and the right side raised by ℎ = 8.2 × 10 −7 ? , as shown at right. There is a small air gap between the pieces of glass. The image below shows the reflected light over the entire surface of the glass. What is the wavelength of the light? A. 4.7 × 10 −7 m B. 6.6 × 10 −7 m C. 1.1 × 10 −6 m D. 1.6 × 10 −6 m E. 3.3 × 10 −6 m

Print UW Net ID_______________________________________@uw.edu PHYS 123 A Autumn 2023 Final Exam 6 15. [4 points] A thermally insulated box contains gas (consisting of N particles) in thermal equilibrium (the temperature throughout the gas is same). The box has two compartments with 1/3 rd of the gas particles in compartment A (system A) and the rest of the gas in compartment B (system B). The partition between the compartments is free to move. Initially the volume of compartment B is 3 times the volume of compartment A, and the systems are allowed to reach an equilibrium, which is the final state. What is the change in entropy for the whole system (combination of A and B) during this process? A. Entropy does not change as the system is in thermal equilibrium. B. 𝑁 × ln (1.18) C. 𝑁 × ln (1.02) D. 𝑁 × ln (1.05) E. Entropy will increase but cannot be determined without more information. 16. [3 points] A monatomic ideal gas is in a fixed-volume flask. You increase the root-mean- square speed of the gas particles by a factor of 2. By what factor does the gas pressure change? A. 2 B. 4 C. √2 D. 8 E. Pressure does not change. 17. [3 points] A fixed amount of ideal gas is held in a rigid container that expands negligibly when heated. At 20.0 °C the gas pressure is p . What temperature does the gas need to reach to have a gas pressure of 2 p ? A. 40 o C B. 80 o C C. 313 o C D. 293 o C E. Insufficient information to determine

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Print UW Net ID_______________________________________@uw.edu PHYS 123 A Autumn 2023 Final Exam 7 18. [3 points] During an adiabatic process, an ideal gas does 25 J of work on its environment. What is the change in the internal (thermal) energy of the gas during this process? A. -25 J B. 25 J C. -50 J D. 50 J E. Cannot be determined 19. [3 points] A sample of an ideal gas with a degree of freedom of 5, initially has a volume of 1.00 L and a pressure of 100 Pa. If the gas expands isentropically to 1.15 L, what is the final pressure? A. 87 Pa B. 100 Pa C. 82.2 Pa D. 90 Pa E. 115 Pa

Print UW Net ID_______________________________________@uw.edu PHYS 123 A Autumn 2023 Final Exam 8 20. [3 points] A steady device in each cycle converts 140 J of work to thermal energy that is released into a reservoir at 340 K. Calculate the entropy change for the environment. A. 1.82 × 10 23 B. 2.98 × 10 22 C. 3.64 × 10 23 D. 1.50 × 10 22 E. Insufficient information to determine 21. [3 points] A heat engine that operates on a Carnot cycle has an efficiency of 0.5 when its low-temperature reservoir is at 10 o C. By how many degrees Celsius must you increase the temperature of the high-temperature reservoir to increase the efficiency to 0.6 if you continue to use the same low-temperature reservoir? A. 3 o C B. 5 o C C. 94 o C D. 125 o C E. 142 o C

Print UW Net ID_______________________________________@uw.edu PHYS 123 A Autumn 2023 Final Exam 9 II. [15 points total] 4 Lab Questions 22. [4 points] In a lab, a team measured a force acting on a surface, 𝐹 , and the area of the surface, 𝐴 . The team reports the pressure acting on the surface due to this force to be ? = 𝐹 𝐴 = 17.8 ± 0.5 N m 2 ⁄ . If the team measured the force to be 𝐹 = 32.51 ± 0.05 N, which of the following values with their uncertainties is consistent with their measurement of the area, 𝐴 ? A. 1.826 ± 0.002 m 2 B. 1.83 ± 0.05 m 2 C. 1.83 ± 0.03 m 2 D. 1.8 ± 0.2 m 2 E. 1.8 ± 0.5 m 2 23. [4 points] A monochromatic beam of light is incident on a mask containing four equally spaced slits. Each slit is very narrow and may be treated as a point source. The interference pattern observed on a distant screen is shown in the image upper right. Which points on the interference pattern could have the phasor diagram (phasors added head to tail) shown at bottom right? Note that points A and B are at minima, point C is at a secondary maximum, and point D is at a maximum. A. Point A B. Point B C. Point C D. Point D E. None of these points

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Print UW Net ID_______________________________________@uw.edu PHYS 123 A Autumn 2023 Final Exam 10 Use the following scenario for the next two questions. In a simulated multi-slit interference experiment, a lab team decided to measure the ratio of the amplitude at the principal maximum, A p , over the amplitude at the dimmest secondary maximum, A s , as the number of slits, N , are increased. 24. [3 points] In this experiment, which of the following statements is/are correct? Select all that apply. A. N is a dependent variable. B. N is a control variable. C. N is an independent variable. D. A s is a control variable. E. A p is a dependent variable. 25. [4 points] The graph below shows the result. The straight dotted line is the best-fit line. Which of the following statements can you conclude from this graph? Select all that apply. A. The best-fit line is a good fit. B. The best-fit line is not a good fit. C. A p / A s vs. N is consistent with a linear relationship. D. A p / A s vs. N is not consistent with a linear relationship. E. A p / A s vs. N must be a linear relationship.

Print UW Net ID_______________________________________@uw.edu PHYS 123 A Autumn 2023 Final Exam 11 III. [15 points total] 5 Tutorial Questions 26. [3 points] Two different springs are connected at a junction. A student generates a pulse at one end of the connected springs. The diagram below shows the shape of the springs a short time after the pulse reaches the junction, although the junction is not shown. You are not told which spring has a greater mass per unit length, or which end the student generated the pulse. Where is the junction located? A. Point A B. Point B C. Point C D. Point D E. This situation is not possible. 27. [3 points] Consider two point-sources (S1 and S2) oscillating up and down with an identical harmonic motion on a water surface producing a circular wave pattern. The diagram shows the wavefronts at ? = 0 where the solid lines represent the crests, and the dashed lines represent the troughs. Is position P a point of complete constructive interference, complete destructive interference, or half-way between constructive and destructive interference at ? = 𝑇 4 ⁄ , where 𝑇 is the period of the waves. A. Constructive interference B. Destructive interference C. Half-way between constructive and destructive interference D. The answer depends on the frequency of the waves.

Print UW Net ID_______________________________________@uw.edu PHYS 123 A Autumn 2023 Final Exam 12 28. [3 points] Light of wavelength 𝜆 is normally incident on a mask containing 4 identical, very narrow, evenly spaced slits. The interference pattern is viewed on a distant screen. Which of the following sets of values of 𝛿? adj correspond to all minima? Recall that 𝛿? adj denotes the difference between the path lengths from the two adjacent slits to a point on the screen. A. 𝜆 , 2𝜆 , 3𝜆 , 4𝜆 , 5𝜆 , … B. 𝜆 2 , 3𝜆 2 , 5𝜆 2 , 7𝜆 2 , 9𝜆 2 , … C. 𝜆 4 , 3𝜆 4 , 5𝜆 4 , 7𝜆 4 , 9𝜆 4 , … D. 𝜆 4 , 2𝜆 4 , 3𝜆 4 , 4𝜆 4 , 5𝜆 4 , … E. 𝜆 4 , 2𝜆 4 , 3𝜆 4 , 5𝜆 4 , 6𝜆 4 , … 29. A U-tube closed on one end with a stopper is partially filled with mercury. Water is then poured on top of the mercury on the left side of the tube. The surface of the water is at the same level as the stopper and open to the air as shown. Positions A and D are at the same height, and positions B and C are at the same height. Which of the following is the correct ranking of the pressures at these points? Note that the density of mercury is higher than that of water. A. ? B = ? C > ? A = ? D B. ? B = ? C > ? A > ? D C. ? B = ? C > ? D > ? A D. ? A > ? B > ? C > ? D E. ? D > ? C > ? B > ? A

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Print UW Net ID_______________________________________@uw.edu PHYS 123 A Autumn 2023 Final Exam 13 30. For the process represented in the PV diagram at right, which of the following statements are correct? Choose all that apply. A. The internal energy of the gas increases. B. The work done on the gas is positive. C. The energy transferred thermally to the gas is negative. D. The temperature of the gas increases. E. None of the above is correct.

PHYS_123A_Final_Autumn_2023_with_Answers

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