UIC PHYSICS 105 Fall 2014 Final Exam

Transcription

1 UIC: Physics 105 Final Exam Fall 2014 Wednesday, December 10 # LAST Name (print) FIRST Name (print) Signature: UIN #: Giving or receiving aid in any examination is cause for dismissal from the University. Any other violation of academic honesty can have the same effect. Page 1 of 9

2 MCQ/SP POINTS SCORE Multiple Choice Problem SP1 Problem SP2 Problem SP3 Problem SP4 Problem SP Total 100 Page 2 of 9

3 MULTIPLE CHOICE QUESTIONS Identify the choice that best completes the statement or answers the question MCQ01 [3 points]: The motion of a 2.0-kg particle connected to a spring is described by 0.10 m sin. What is the magnitude of the maximum force on the block from the spring? (A) 0.5 N (B) 1.0 N (C) 1.5 N (D) 2.0 N Answer (D): Magnitude of the max. restoring force: where. From equation: A = 0.10 and = rad/s = 2.0 N MCQ02 [3 points]: In MCQ01, at what time (in s) the particle s potential energy equal to its kinetic energy? (A) 0.00 (B) 0.25 Answer (B): (C) 0.50 From equation (D) 1.0 sin and cos UK sin cos or tan 1 or t = 0.25 s MCQ03 [3 points]: Two circus clowns (each having a mass of 50 kg) swing on two flying trapezes (negligible mass, length 25 m) shown in the figure to the right. At the peak of the swing, one grabs the other, and the two swing back to one platform. The time for the forward and return motion is (A) 10 s (B) 15 s (C) 20 s (D) 25 s (E) 50 s Answer (A): For a simple pendulum 2 2. = 10 s MCQ04 [3 points]: Three physical pendulums, with masses m1, m2 = 2m1, and m3 = 3m1, have the same shape and size, and are suspended at the same point. Rank them according to their periods, from shortest to longest. (A) 1, 2, 3 (B) 3, 2, 1 Answer (E): For a physical pendulum 2, where. So, for the physical (C) 2, 3, 1 pendulums of the same shape and size their periods are the same. (D) 2, 1, 3 (E) All the same MCQ05 [2 points]: A sinusoidal force with a given amplitude is applied to an oscillator. To maintain the largest amplitude oscillation the frequency of the applied force should be: (A) half the natural frequency of the oscillator Answer (B): The largest amplitude oscillation (B) the same as the natural frequency of the oscillator happen when the driving frequency matches the (C) twice the natural frequency of the oscillator oscillator s natural frequency. (D) unrelated to the natural frequency of the oscillator (E) determined from the maximum speed desired Page 3 of 9

4 MCQ06 [3 points]: A wave is generated in a rope, which is represented by the solid line in the diagram to the right. As wave moves to the right, point P on the rope is moving toward which position? (A) A (B) B Answer (D): See diagram (C) C (D) D MCQ07 [2 points]: A source of frequency f sends waves of wavelength λ traveling with speed v in some medium. If the frequency is changed from f to 2f, then the new wavelength and new speed are (respectively): (A) 2λ, v (B) λ/2, v Answer (B): (C) λ, 2v In the same medium, when frequency changes the wave speed does not (D) λ, v/2 2 So, the new wavelength is /2 and speed does not change, i.e. (E) λ/2, 2v MCQ08 [2 points]: A wire, 4.0 m long, with a mass of 60. g, is under tension. A transverse wave is propagated on the wire, for which the frequency is 330 Hz, the wavelength is 0.20 m, and the amplitude is 7.0 mm. The time for a crest of the transverse wave to travel the length of the wire, in ms, is closest to: (A) 61 (B) 53 (C) 82 (D) 75 (E) 68 Answer (A): = 66 m/s s = 61 ms MCQ09 [2 points]: A crane lifts a mass m = kg using a steel cable whose mass per unit of length is kg/m. What is the speed of transverse waves on this cable? (A) 578 m/s (B) 225 m/s (C) 1220 m/s (D) 194 m/s (E) 1880 m/s Answer (D):, where... = 194 m/s MCQ10 [2 points]: A transverse traveling sinusoidal wave on a string has a frequency of 100. Hz, a wavelength of m, and an amplitude of 2.0 mm. The maximum transverse velocity in m/s of any point on the string is: (A) 0.2 (B) 1.3 Answer (B): m/s (C) 4 (D) 15 (E) 25 Page 4 of 9

5 MCQ11 [3 points]: A stationary source generates 5.0 Hz water waves whose speed is 2.0 m/s. A boat is approaching the source at 10. m/s. The frequency of these waves, as observed by a person in the boat, is: (A) 5.0Hz (B) 15 Hz (C) 20 Hz (D) 25 Hz (E) 30 Hz Answer (E): The source is stationary and the listener moves approaching the source = 30 Hz. MCQ12 [2 points]: A standing wave: (A) can be constructed from two similar waves traveling in opposite directions (B) must be transverse (C) must be longitudinal (D) has motionless points that are closer than half a wavelength (E) has a wave velocity that differs by a factor of two from what it would be for a traveling wave MCQ13 [3 points]: If you hold a 1.2-m aluminum rod in the center and hit one end with a hammer, it will oscillate like an open pipe. Antinodes of pressure correspond to nodes of molecular motion, so there is a pressure antinode in the center of the bar. The speed of sound in aluminum is 5150 m/s. What would be the bar s lowest frequency of oscillation? (A) 2.1 khz (B) 2.4 khz (C) 3.3 khz (D) 4.8 khz Answer (A): The rod length is, so = 2.4 m the lowest frequency. 2.1 khz MCQ14 [3 points]: You are listening to an A note played on a violin string. Let the subscript s refer to the violin string and a refer to the air. If the wave speed on the string is not the same as the speed of sound in air, then: (A) fs = fa but λs λa (B) fs = fa and λs = λa (C) λs = λa but fs fa (D) λs λa and fs fa Answer (A): / and So, f = fs = fa and MCQ15 [2 points]: An organ pipe with one end closed and the other open has length L. Its fundamental frequency is proportional to: (A) L Answer (B): (B) 1/L For a pipe with one end closed its fundamental frequency is /4, so 1/ (C) 1/L 2 (D) L 2 (E) Page 5 of 9

6 MCQ16 [2 points]: The pressure exerted on the ground by a man is greatest when: (A) he stands with both feet flat on the ground (B) he stands flat on one foot Answer (C): (C) he stands on the toes of one foot / where A is contact area the pressure exerted on the (D) he lies down on the ground ground is greatest when he stands on the toes of one foot. (E) all of the above yield the same pressure MCQ17 [3 points]: The density of water is 1.0 g/cm 3. The density of the oil in the left column of the U-tube shown to the right is: (A) 0.20 g/cm 3 (B) 0.80 g/cm 3 (C) 1.0 g/cm 3 (D) 1.3 g/cm 3 (E) 5.0 g/cm 3 MCQ18 [3 points]: A rod of length L = 24. cm floats vertically in water as shown in the figure to the right. If it has a cross-sectional area of 1.0 cm 2 and rod /water = 0.60, what length, Lw, is submerged? (A) 9.6 cm (B) 14 cm (C) 18 cm (D) 19 cm Answer (B): The pressure at points corresponding to the lowest level of oil is the same in both arms of the U-shaped tube, i.e and g/cm 3 Answer (B):,, where, and cm MCQ19 [2 points]: Water flows through a cylindrical pipe of varying cross section. The velocity is 3.0 m/s at a point where the pipe diameter is 1.0 cm. At a point where the pipe diameter is 3.0 cm, the velocity is: (A) 9.0 m/s (B) 3.0 m/s (C) 1.0 m/s (D) 0.33 m/s (E) 0.11 m/s Answer (B): According to continuity equation, where and m/s MCQ20 [3 points]: A person blows across the top of one arm of a U-tube partially filled with water. The water in that arm: (A) drops slightly (B) rises slightly (C) remains at the same height (D) rises if the blowing is soft but drops if it is hard (E) rises if the blowing is hard but drops if it is soft Answer (B): Initially the level of water is the same in both arms of the U-tube. When the person blows, say, near left arm the air moves with speed v L across the top, which is greater than speed of air across the top of the right arm, v R. According to Bernoulli s equation:, i.e. if v L >v R, then and the water in the left arm will rise slightly Page 6 of 9

7 SHORT PROBLEMS You must show your work and write your answers clearly and legibly SP1: A block of mass m is attached to a massless spring with spring constant k, and is set oscillating over a frictionless horizontal surface as shown in Figure (a). Figure (b) shows the block s kinetic energy versus its position x. At x = 5 cm, the block s kinetic energy Ks = 3 J. (a) [6 points] What is the spring constant? From the diagram (Fig (b)). 800 N/m 4J and amplitude of oscillation A = 0.1 m (b) [6 points] If the block s maximum acceleration is 40 m/s 2 what is the mass of the block? The magnitude of the maximum restoring force is. 2 kg SP2: The equation of a transverse wave traveling along a very long string is given by, sin where x and y are expressed in centimeters and t is in seconds. (a) [6 points] If the linear density of a string = kg/m and the tension in the string is N, what is the wavelength (in meters) of the wave? From the equation follows that s The wave propagates along the string at speed and / m Page 7 of 9

8 (b) [5 points] If the maximum transverse speed of a particle in the string is 75 cm/s, what is the amplitude A (in meters) of the wave? The maximum transverse speed:,. So,,/2/ 0.75/ m SP3 [7 points]: In order to be able to determine her speed, a skydiver carries a tone generator. A friend on the ground at the landing site has equipment for receiving and analyzing sound waves. While the skydiver is falling at terminal speed, her tone generator emits a steady tone of frequency fe = 1260 Hz. Assume that the air is calm and the sound speed of 343 m/s is independent of altitude. If her friend on the ground (directly beneath the skydiver) receives waves of frequency fr = 2890 Hz, what is the skydiver's speed of descent? Since the diver, who is the source of the sound waves, is moving towards her friend on the ground, who is the receiver of the waves, the Doppler formula takes the form: Solving for, we have m/s SP4 [6 points]: An organ pipe that is closed at one end has a fundamental frequency of 175 Hz. There is a leak in the church roof, and some water gets into the bottom of the pipe, as shown in the figure to the right. The organist then finds that this organ pipe has a frequency of 230 Hz. What is the depth, h, of the water in the pipe? The speed of sound in air v = 346 m/s. For a pipe closed at one end the fundamental frequency is: (1) where L is the length of the pipe without water. With water at bottom:, From (1) and (2) 4 4., Solving for, we have, (2) 0.12 m Page 8 of 9

9 SP5 consists of two independent parts: (a) [6 points] An incompressible liquid ( = 900. kg/m 3 ) is initially at rest in the vertical portion of the pipe shown in the figure to the right, where L = 2.0 m. The force exerted by the liquid on the valve is 944 N. Use Patm = Pa and g = 10. m/s 2. Find the diameter of the pipe. Top: Valve: /, where m (b) [7 points] A Venturi meter is used to measure the flow speed of a fluid in a pipe. The meter is connected between two sections of the pipe as shown in the figure to the right. The cross section area A of the entrance and exit of the meter is equal to 64 cm 2 and matches the pipe s cross-sectional area. Between the entrance and exit, the fluid flows from the pipe with speed va and then through a narrow throat of crosssectional area a = 32 cm 2 with speed va. A manometer connects the wider portion of the meter to the narrower portion. Suppose that the fluid is fresh water ( = kg/m 3 ). If the pressure in the wide part of the pipe is 55 kpa and 41 kpa in the throat, what is the rate of the water flow (in m 3 /s)? [Hint: First, find the speed of water in wider portion of the meter va] According to Bernoulli s equation: (1) According to continuity equation: (2) From (1) and (2) 3.1 m/s. So, m 3 /s Page 9 of 9