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Physics 1112 Spring 2010 University of Georgia Instructor: HBSchüttler PHYS 1112 Final Exam A Thu. April 29, 2010, 12:00pm-3:00pm This is a closed-book, closed-notes exam, but you are permitted to bring and use a copy of the official Formula Sheet for this exam, which you should have printed out from the PHYS1112 web page. The exam consists of 24 multiple-choice questions. Each question is worth one raw score point. There will be no penalty for wrong answers. No partial credit will be given. I recommend that you read all the questions at the start so that you can allocate your time wisely. (Answer the easy questions first!) You may use a scientific calculator for arithmetic only; your calculator must be non-graphing, non-programmable, and non-algebraic. You are not allowed to share your calculator. The use of cell phones, pagers, PDAs, or any other electronic devices (besides calculators) is forbidden. All such gadgets must be turned off and put away; distractions caused by these devices will not be tolerated. • Do not open the exam until you are told to begin. • Make sure the scantron sheet has your name and your UGA Card ID (810-...) number filled in. Make sure you also have entered your name, UGA Card ID number and signature on the exam cover page (this page!) below. • At the end of the exam period you must hand in both your scantron sheet and this entire exam paper, with the cover page signed and with your name and UGA Card ID (810-...) number filled-in. You may not keep any parts of this exam paper. • Your exam will not be graded, and you will receive a score of zero, if you do not hand in both a properly filled in scantron sheet and this entire exam paper, with properly filled-in and signed exam cover page. • You promise not to discuss the contents of this exam with anyone before the end of final exam week (May 10, 2010). By signing below, you indicate that you understand the instructions for this exam and agree to abide by them. You also certify that you will personally uphold the university standards of academic honesty for this exam, and will not tolerate any violations of these standards by others. Unsigned exams will not be graded. Name (please print): UGACard ID (810-...) #: Signature: 1 Physics 1112 Spring 2010 University of Georgia Instructor: HBSchüttler WORKSPACE 2 Physics 1112 Spring 2010 University of Georgia Instructor: HBSchüttler Conceptual Problems Problem 1: A student runs eastward at 4m/s, towards a vertical plane mirror, while the mirror, mounted on wheels, also travels eastward at 1 m/s (with both speeds given relative to the ground). The speed at which the student’s image moves and its direction, relative to the ground, is (A) (B) (C) (D) (E) 2m/s 6m/s 6m/s 7m/s 7m/s westward eastward westward eastward westward Problem 2: Sound waves (including ultrasound) have a speed of wave propagation vAir = 340m/s in air and vWater = 1500m/s in water. Also, sin(Θ) = vAir /vWater when Θ ∼ = 13.10o . A narrow ultrasound beam striking the flat water surface of your swimming pool (A) will undergo total internal reflection if incident from below the water surface with an angle of incidence of 7.7o . (B) will have an angle of refraction greater than the angle of incidence if the beam is incident from below the water surface; (C) will undergo total internal reflection if incident from below the water surface for any angle of incidence greater than 13.10o ; (D) will undergo total internal reflection if incident from above the water surface with an angle of incidence of 7.7o ; (E) will have an angle of refraction smaller than the angle of incidence if the beam is incident from below the water surface; Problem 3: In a two-source interference experiment two sources are oscillating in phase with the same period. The closest intensity minimum, counted from the central intensity maximum M and to the left of M, is located at point P, as shown in Fig. 2.01. A wave crest A from source 1 and a wave trough B from source 2 arrive simultaneously at P. Therefore, A and B must have departed from their respective sources as follows: Fig. 2.01 P Source 1 M Source 2 (A) A departed 3/2 period before B. 3 Physics 1112 Spring 2010 (B) (C) (D) (E) University of Georgia Instructor: HBSchüttler B departed 3/2 period before A. B departed 1/2 period before A. A departed 1/2 period before B. B departed 1 period before A. Problem 4: Q1 and Q2 in Fig. 2.15 are negative point charges. Assuming Q1 , Q2 and P are located at three corners of a square, as shown, which arrow drawn at P could correctly ~ generated by Q1 and Q2 at P ? represent the total electric field vector E Fig. 2.15 P (E) (C) (D) (A) (B) Q2 Q1 (A) (B) (C) (D) (E) Problem 5: Three different circuits, X, Y and Z, are built with the three resistors, R1 > 0, R2 > 0, and R3 > 0, and a battery of battery voltage E, as shown in Fig. 3.04. Let Io > 0, I1 > 0, I2 > 0, and I3 > 0 denote the currents through the battery, R1 , R2 , and R3 , respectively. Let V1 > 0, V2 > 0, and V3 > 0 denote the voltage drops across R1 , R2 , and R3 , respectively. Fig. 3.04 Io I2 I3 E I1 Io R2 R3 I2 Io R2 I1 E R1 (X) I3 R3 (Y) R1 I3 R3 I1 E I2 R1 R2 (Z) Which of the following statements is false ? (A) (B) (C) (D) (E) In In In In In circuit circuit circuit circuit circuit Z: V1 /R1 = E/(R1 + R2 ). X: V3 /E = R3 /(R1 + R2 + R3 ). Y : V1 /R1 = E[1/(R3 + R2 ) + 1/R1 ]. Y : I1 /(R2 + R3 ) = I2 /R1 . Z: V3 = V1 + V2 . Problem 6: A molecular ion beam containing four different types of ions, called P , Q, R and S here, enters a uniform magnetic field, as shown in Fig. 3.15, with B 6= 0 above the 4 Physics 1112 Spring 2010 University of Georgia Instructor: HBSchüttler ~ perpendicular to, and pointing out of, the plane of the drawing. lower horizontal line, and B The incident beam, below the lower horizontal line, is in the plane of the drawing. Fig. 3.15 B (out) P Q R S B=0 ~ The radii of the semicircular ion trajectories in the B-field, denoted by rP , rQ , rR and rS , respectively are observed to be in a ratio of rP : rQ : rR : rS = 3 : 2 : 1 : 4 , as indicated in Fig. 3.15. Assume all four ion types carry the same amount of charge per ~ ion, |q|, and they all enter the B-field with the same kinetic energy K. What is the ratio of the four ion masses, denoted by mP , mQ , mR and mS , respectively ? (A) (B) (C) (D) mP mP mP mP : : : : mQ mQ mQ mQ : : : : mR mR mR mR : : : : mS mS mS mS = 13 : 12 : 11 : 14 . =3 : 2 : 1 : 4 . √ √ √ √ = 3 : 2 : 1 : 4 . = √13 : √12 : √11 : √14 . (E) mP : mQ : mR : mS = 9 : 4 : 1 : 16 . Problem 7: In an electric generator, a single metallic wire loop, enclosing an area of 5cm2 ~ at 700RPM, produces a maximum induced and spinning in a uniform magnetic field B electromotoric force (EMF) of 6mV. What is the maximum induced EMF in a loop of ~ 10cm2 area, spinning at 2100RPM in the same B-field? (A) (B) (C) (D) (E) 48mV 36mV 9mV 4.5mV 1mV Problem 8: A beam of unpolarized light of intensity I0 is incident from the left upon a polarization filter PF1, with vertically oriented transmission axis T1 , followed by a second polarization filter PF2 with transmission axis T2 , located to the right of P F 1, as shown in Fig. 4.09. T2 is initially also oriented vertically ( parallel to T1 ); but it is then rotated around 5 Physics 1112 Spring 2010 University of Georgia Instructor: HBSchüttler the beam axis by 120o . Fig. 4.09 Before: After: T2 I0 I1 T1 I2 T2 Side View: Before 120o Rotation of T2 120o T2 Frontal View: Before and After 120o Rotation of T2 √ Recall that cos(30o ) = ( 3)/2 and cos(60o ) = 1/2. What is the light intensity I2 of the beam observed to the right of PF2, before and after the 120o -rotation of T2 ? (A) (B) (C) (D) (E) 0 before, 3I0 /8 after I0 /2 before, 3I0 /8 after I0 before, 3I0 /4 after I0 /2 before, I0 /8 after I0 before, I0 /4 after Numerical Problems Problem 9: The vacuum wavelength range of electromagnetic radiation visible to the human eye is 400nm to 700nm. A beam of monochromatic light with a frequency of 7.142 × 1014 Hz in air travels from air into water, with indices of refraction nAir = 1.00 and nWater = 4/3, in air and water, respectively. To an under-water human observer, the light beam while traveling in water will (A) have a wavelength of 420nm, have a frequency of 9.523 × 1014 Hz, and be visible to the human eye; (B) have a wavelength of 315nm, have the same frequency as in air, and be visible to the human eye; (C) have a wavelength of 420nm, have a frequency of 5.366 × 1014 Hz, and be visible to the human eye; (D) have a wavelength of 420nm, have the same frequency as in air, and be invisible to the human eye; (E) have a wavelength of 315nm, have the same frequency as in air, and be invisible to the human eye. Problem 10: The state highway patrol radar gun sends out a frequency of 8.25GHz. You’re approaching a radar speed trap driving 6.24m/s and the radar gun measures the frequency of the radar wave reflecting from your car. Assume c = 3.00 × 108 m/s. By what percentage is the reflected wave’s frequency different from the original frequency sent out by the gun? Would this percentage change if the radar gun sends out a different frequency, but your speed is the same ? 6 Physics 1112 Spring 2010 (A) (B) (C) (D) (E) University of Georgia Instructor: HBSchüttler 4.16 × 10−6 4.16 × 10−6 4.13 × 10−6 4.13 × 10−6 2.08 × 10−6 %, %, %, %, %, will will will will will not change with frequency change with frequency not change with frequency change with frequency not change with frequency Problem 11: A postage stamp placed 5.00cm to the left of a spherically curved mirror produces an image 40.0cm to the right of the mirror. What is the focal length of the mirror and where is its focal point F located ? (A) (B) (C) (D) (E) −5.71cm, −5.71cm, +5.71cm, +4.44cm, +4.44cm, F F F F F to to to to to left of mirror; right of mirror; left of mirror; right of mirror; left of mirror. Problem 12: In flint glass, the index of refraction is nR = 1.661 for red light, and nV = 1.696 for violet light, while nAir = 1.000 in air for all wavelengths. A beam of white light enters a triangular prism of flint glass from air at normal incidence at the front surface and then stikes the prism’s back surface at an angle of incidence φ = 22.0o as shown here: φ Red Violet The prism is surrounded by air. What is the angle of divergence, enclosed between the red and the violet beam after leaving the prism through the back surface ? (A) (B) (C) (D) (E) 0.1223o 0.2736o 0.4883o 0.9661o 2.073o Problem 13: If a diffraction grating with a line spacing of 1550nm is illuminated at normal incidence by coherent (laser) light with a wavelength of 550nm, at what angles θ, measured from the central (0th order) intensity maxium, will the 3rd order maxima be observed ? 7 Physics 1112 Spring 2010 (A) (B) (C) (D) (E) University of Georgia Instructor: HBSchüttler 3rd order maxima are not observable. ±66.44o ±50.23o ±39.18o ±26.78o Problem 14: Two identical point charges, spaced 56.2m apart, repel each other with a force of 160.0N. What is the amount of each point charge? (A) (B) (C) (D) (E) 3.5mC 5.5mC 7.5mC 9.5mC 11.5mC Problem 15: A charge of −18nC is uniformly spread out over a single thin, square-shaped sheet of aluminum foil with a side length of 1.5m. What is the strength and the direction of the electric field generated by that charge, very close to the surface and far from the edges of that foil? (Hint: Think of the aluminum foil as a single, uniformly charged planar surface.) (A) (B) (C) (D) (E) ~ pointing towards the foil 5752.0N/C, E ~ pointing away from the foil 5752.0N/C, E ~ pointing towards the foil 27.89N/C, E ~ pointing away from the foil 27.89N/C, E ~ pointing towards the foil 452.0N/C, E Problem 16: If the electric field strength between the capacitor plates in Fig. 2.13 is 683.V/m, what is the magnitude and the direction of the acceleration ~a of an electron traveling from A to B between the plates, assuming the electron is subject only to the electric force between the plates ? Fig. 2.13 ------------------------E B A E +++++++++++++++++++++++++++ (A) 5.00 × 1013 m/s2 , ~a pointing rightward (B) 5.00 × 1013 m/s2 , ~a pointing upward 8 Physics 1112 Spring 2010 University of Georgia Instructor: HBSchüttler (C) 12.0 × 1013 m/s2 , ~a pointing leftward (D) 12.0 × 1013 m/s2 , ~a pointing downward (E) 12.0 × 1013 m/s2 , ~a pointing upward Problem 17: A wire with a length 350m and a circular cross-section of diameter 0.17mm is made of dawgium alloy (a very poorly conducting metal!) with a resistivity of 3 × 10−6 Ω · m. Find the current flowing in this wire when it is connected to a 16V battery. [Hint: The area of a circle is A = (π/4)D2 .] (A) (B) (C) (D) (E) 86.5µA 0.346mA 3.46A 1.84kA 3.11GA Problem 18: In a Kirchhoff rule analysis, current arrows have been assigned to the I1 -, I2 and I3 -branches of a circuit for which a fragment (i.e., not the whole circuit) is shown in Fig. 3.10. Also assume that the voltage drop across R is defined as VR ≡ Va − Vb where Va and Vb are the electric potential values at points a and b. I1 I2 Fig. 3.10 a I3 R b Suppose R = 20Ω and VR = −40V and I2 = −6A for the arrow directions shown in Fig. 3.10. What is I1 ? Is the current |I1 | actually flowing towards or away from point a ? (A) (B) (C) (D) (E) I1 I1 I1 I1 I1 = +8A = −8A = +4A = −4A = −4A with with with with with |I1 | |I1 | |I1 | |I1 | |I1 | flowing flowing flowing flowing flowing towards a. away from a. towards a. away from a. towards a. 9 Physics 1112 Spring 2010 University of Georgia Instructor: HBSchüttler Problem 19: If a 15A current flows in a thin straight metal rod of length 4m through a uniform magnetic field of 90T and the direction of the current flow is at an angle of 35o from the direction of the magnetic field vector, what is the strength of the magnetic force exerted on the rod ? (A) (B) (C) (D) (E) 872N 1908N 3097N 4423N 6770N Problem 20: A very thin circular metal ring of radius R = 1.0m lies initially in the x − zplane and it is centered at the coordinate origin O ≡ (0, 0, 0), as shown in Fig. 3.21. A current I = 1.0A flows around the ring in the direction indicated in panel (B) of Fig. 3.21. (A) (B) z Fig. 3.21 z I y x z x y-z-Plane View z y y x x-z-Plane View This ring (and its magnetic field!) is then rotated by 20o around the x-axis, the rotation direction being counter-clockwise in the y−z-plane view shown in panel (A) of Fig. ~ ≡ (Bx , By , Bz ) due to I, at the center of the 3.21. The z-component of the magnetic field B ring, after the rotation, is: (A) (B) (C) (D) (E) Bz Bz Bz Bz Bz = +0.590µT = −0.590µT = +0.215µT = −0.215µT = +0.628µT Problem 21: A single conducting ring of wire encloses an area of 7.4 × 10−2 m2 and a resistance of 11.0Ω. Perpendicular to the plane of the loop is a uniform magnetic field, initially of strength 0.28T. At what rate (in T/s) must this field change if the induced current in the loop is to be 0.32A? 10 Physics 1112 Spring 2010 (A) (B) (C) (D) (E) University of Georgia Instructor: HBSchüttler 2.23µT/s 7.76mT/s 3.87T/s 47.6T/s 68.9T/s Problem 22: The electric motor in a toy train requires a voltage of 6.0V. Calculate the number of turns in the secondary coil for a transformer that has 2000 turns in its primary coil and will transform the 120V household voltage down to 6.0V. (A) (B) (C) (D) (E) 100 turns 1000 turns 2000 turns 40000 turns 320000 turns Problem 23: In the circuit in Fig. 4.03, the battery voltage is EB = 20V, and inductance L is a long, thin solenoid of length 1.5m, cross-sectional area 7.85 × 10−3 m2 , and 3800 turns. I Fig. 4.03 L EB Immediately after closing the switch, current I(t) in the circuit rises linearly with time t. At what rate ∆I/∆t does it rise? (A) (B) (C) (D) (E) 6820.A/s 211.A/s 39.3A/s 8.27A/s 0.482A/s Problem 24: A small 100% absorbing spherical object of mass 90 × 10−15 kg and radius 2.0 × 10−6 m is suspended against gravity (with g = 9.81m/s2 ) by the radiation pressure of an upward-directed laser beam. What is the intensity of the laser beam ? (Hint: A circle’s area is πR2 .) (A) (B) (C) (D) (E) 1.83W/m2 2.94kW/m2 5.88kW/m2 10.5MW/m2 21.1MW/m2 11