Practice Test 1 PRACTICE TESTS PHYSICS B You must take the entire B exam as follows: First 90 minutes Section I – Multiple Choice 70 Questions No calculators allowed Percent of Total Grade – 50 2-minute interval Second 90 minutes Section II – Free Response 7 Questions Any battery-operated, hand-held calculator allowed Percent of Total Grade – 50 Each multiple-choice question has equal weight. Rulers or straight-edges may be used in both sections. However, calculators and the formula sheet provided may be used in Section II only, NOT in Section I. Show all work in answering the free response questions in Section II. Each question is worth either 10 or 15 points, and the suggested time for answering the question is about 1 minute per scoreable point. The parts within a question may not have equal weight. Calculators may not be shared. A table of information that may be helpful is on the following page. 361 Practice Test 1 TABLE OF INFORMATION CONSTANTS AND CONVERSION FACTORS 1 unified atomic mass unit u = 1.66x10-27 kg = 931 MeV/c2 Proton mass mp = 1.67x10-27 kg Neutron mass mn = 1.67x10-27 kg Electron mass me = 9.11x10-31 kg Electron charge e = 1.6x10-19 C Avogadro’s number No = 6.02x1023 mol-1 Universal gas constant R = 8.31 J/(mol K) Boltzmann’s constant kB = 1.38x10-23 J/K Speed of light c = 3x108 m/s Planck’s constant h = 6.63x10-34 J s = 4.14x10-15 eV s hc = 1.99x10-25 J m = 1.24x103 eV nm Vacuum permittivity εo = 8.85x10-12 C2/Nm2 Coulomb’s law constant K = 9.0x109 Nm2/C2 Vacuum permeability μo = 4πx10-7 T m/A Univ. gravitational constant G = 6.67x10-11 m3/kgs2 Acceleration due to gravity g = 9.8 m/s2 1 atmosphere pressure 1 atm = 1.0x10 5 Pa 1 electron volt 1eV = 1.6x10-19 J 1 angstrom 1 Å = 1x10 -10 m UNITS Name Symbol meter m kilogram kg second s ampere A Kelvin K mole mol hertz Hz newton N Pascal Pa Joule J watt W coulomb C volt V ohm Ω henry H farad F tesla T Celsius ºC electron-volt eV PREFIXES Factor Prefix 109 106 103 10-2 10-3 10-6 10-9 10-12 giga mega kilo centi milli micro nano pico Symbol G M K c m μ n p VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES θ sin cos tan θ θ θ 0º 0 1 0 30º ½ √3/2 √3/3 37º 3/5 4/5 ¾ 45º √2/2 √2/2 1 53º 4/5 3/5 4/3 60º √3/2 ½ √3 90º 1 0 ∞ The following conventions are used on this examination. I. Unless otherwise stated, the frame of reference of any problem is assumed to be inertial. II. The direction of any electric current is the direction of flow of positive charge (conventional current) III. For any isolated electric charge, the electric potential is defined as zero at an infinite distance from the charge. IV. The work done ON a thermodynamic system is defined as a positive quantity. 362 Practice Test 1 PHYSICS B SECTION I Time – 90 minutes 70 Questions Directions: Each of the questions or incomplete statements below is followed by five suggested answers or completions. Select the one that is best in each case and then fill in the corresponding oval on the answer sheet. Note: To simplify calculations, you may use g = 10 m/s2 in all problems. 1. The water in a river is running due west with a speed of 4 m/s. A boy in a boat tries to cross the river by rowing due south at 3 m/s. The velocity of the boat relative to the shore is (A) 12 m/s SW (B) 7 m/s SW (C) 5 m/s SW (D) 4/3 m/s SW (E) 1 m/s SW 4. Consider the following graphs of displacement x vs. time t and velocity v vs. time t. In which of the graphs does the moving object reverse its direction? x (A) (D) x t Questions 2 - 3. A child on a skateboard crosses a line on the sidewalk traveling with a speed of 2 m/s when he begins accelerating at a constant rate of 2 m/s2. (B) 2. What will be the child’s speed after 3 s? (A) 8 m/s (B) 9 m/s (C) 12 m/s (D) 15 m/s (E) 18 m/s t v t (C) (E) x v t t 3. How far past the line on the sidewalk will the child be after 3 s? (A) 8 m (B) 9 m (C) 12 m (D) 15 m (E) 18 m Y X 5. Consider the figure above which shows a ball that is projected and follows a parabolic path. Point Y is the highest point on the path, and air resistance is negligible. Which of the following best shows the direction of the acceleration of the ball at point X? (A) (D) (B) (E) (C) 363 Practice Test 1 Questions 6 - 8 relate to a ball thrown straight up, reaching its maximum height in 3 s. Air resistance may be neglected. 6. The initial velocity of the ball is most nearly (A) 10 m/s (B) 15 m/s (C) 30 m/s (D) 45 m/s (E) 60 m/s A B 10. Two blocks A and B are attached to a string that passes over a pulley of negligible mass and friction as shown. The two blocks do not have equal mass. Which of the following statements is true? (A) Block A is more massive than block B. (B) Block B is more massive than block A. (C) Both blocks will move with the same constant velocity. (D) Both blocks will move with the same constant acceleration. (E) Block A must have a greater acceleration than block B. 7. The magnitude of the acceleration of the ball at the instant it reaches its maximum height is most nearly (A) zero (B) 5 m/s2 (C) 10 m/s2 (D) 12 m/s2 (E) 20 m/s2 8. The maximum height of the ball is most nearly (A) 10 m (B) 15 m (C) 30 m (D) 45 m (E) 60 m Questions 11 – 12: A boat in still water of mass 1000 kg is being pulled by ropes tied to two cars, causing the boat to move along the dashed horizontal line as shown above. The ropes make an angle of 45 to the horizontal. The net force acting on the boat is 500 N. (sin 45 = cos 45 = 0.70, tan 45 = 1) 9. A block of mass m is at rest on a rough inclined plane. Which of the following diagrams best represents the correct directions for the normal, weight, and friction forces acting on the block? N (A) N (D) f 11. What is the tension in each rope? (A) 1000 N (A) 500 N (B) 350 N (C) 250 N (D) 100 N W f W (B) (E) f N 12. What is the acceleration of the boat? (A) 5 m/s2 (B) 3.5 m/s2 (C) 2.5 m/s2 (D) 2.0 m/s2 (E) 0.5 m/s2 f N W W (C) f W N 364 Practice Test 1 (A) The tension in the string is greater at point III than at point I. (B) The tension in the string is greater at point I than at point III. (C) The tension at point I is equal to the tension at point III. (D) The tension in the string is greatest at point II. (E) The tension in the string is the same at points I, II, and III. Questions 13 – 14: A 15 kg block rests on a surface of negligible friction and is pulled by a string which is passed over a pulley of negligible mass and connected to a hanging 5 kg block. 13. The net force acting on the 15 kg block is equal to (A) the weight of the 5 kg block. (B) the tension in the string. (C) the difference between the weight of the 15 kg block and the 5 kg block. (D) the sum of the weight of the 15 kg block and the 5 kg block. (E) the weight of the 15 kg block. 16. If the string were to break at point II, what would be the initial path of the ball? (A) (D) (B) (E) (C) 20N 14. In terms of the acceleration due to gravity g, the acceleration of the system is g (A) 5 g (B) 4 g (C) 3 (D) g (E) 3g B A 17. A board of negligible mass supports a mass weighing 20 N at a distance of 2 m from the support at point A. How much weight must be placed at point B which is 5 m from point A in order for the rod to remain horizontal? (A) 4 N (B) 8 N (C) 10 N (D) 40 N (E) 60 N Questions 15 – 16 A ball on the end of a string is being swung in a vertical circle as shown below. Points I, II, and III are labeled on the circle. I Questions 18 – 19. A ball of mass m is thrown horizontally at a vertical wall with a speed v and bounces off elastically and horizontally. II 18. What is the magnitude of the change in momentum of the ball? mv (A) 2mv (D) 4 (B) mv mv (C) zero (E) 2 III 15. Which of the following statements is true? 365 Practice Test 1 19. Which of the following force vs. time graphs below best represents the force acting on the ball while it is in contact with the wall? (A) (D) (B) 22. The change in the kinetic energy of the block is (A) Fd F (B) d (C) Ft F (D) t d (E) t (E) Questions 23 - 24: A red car and a blue car have the same mass and are moving on the highway. The red car is traveling at 60 miles per hour and the blue car is traveling at 30 miles per hour. (C) 23. The ratio of the red car’s momentum to the blue car’s momentum is (A) 4 (B) 2 (C) 1 (D) ½ (E) ¼ Questions 20 – 22: A horizontal force F acts on a block of mass m which is initially at rest on a floor of negligible friction. The force acts for a time t and moves the block a horizontal displacement d. 24. The ratio of the red car’s kinetic energy to the blue car’s kinetic energy is (A) 4 (B) 2 (C) 1 (D) ½ (E) ¼ 20. The acceleration of the block is (A) Ft (B) Fd F (C) m m (D) F d (E) t 25. A toy railroad car of mass 3 kg moving east collides with a 6 kg railroad car at rest, and the two cars lock together on impact and move away together toward the east at 2 m/s. The speed of the first car before the collision is (A) 2 m/s (B) 3 m/s (C) 4 m/s (D) 6 m/s (E) 9 m/s 21. The change in momentum of the block is (A) F t m t (C) Fd (D) Ft (E) mt (B) 366 Practice Test 1 4m 29. An ideal fluid passes from a narrow tube to a large tube as shown above. Which of the following statements is true? (A) The mass of the fluid passing through the tube is greater in the narrow portion than in the wide portion. (B) The mass of the fluid passing through the tube is greater in the wide portion than in the narrow portion. (C) The volume of the fluid passing through the tube is greater in the narrow portion than in the wide portion (D) The speed of the fluid is greater in the narrow portion than in the wide portion. (E) The pressure of the fluid is greater in the narrow portion than in the wide portion 26. A pendulum is dropped from a height of 4 m as shown above. The speed of the pendulum at the lowest point in the swing is most nearly (A) 6 m/s (B) 7 m/s (C) 8 m/s (D) 9 m/s (E) 10 m/s 27. The second law of thermodynamics (law of entropy) explains which of the following? (A) The heat lost by one object must be gained by another object. (B) Heat flows naturally from a hotter body to a cooler body. (C) Celsius degrees and Kelvin degrees are equivalent. (D) Heat can be transformed into work. (E) The average kinetic energy of molecules is proportional to temperature. Questions 30 – 31 A candle burns inside the metal container shown above. The base of the candle is insulated from the container. Three types of heat transfer are listed below. 28. A satellite is orbiting the Earth in an elliptical orbit. Which of the following must be true if the satellite’s speed is increasing? (A) The satellite’s distance from the Earth is increasing. (B) The satellite’s distance from the Earth is decreasing. (C) The kinetic energy of the satellite is decreasing. (D) The momentum of the satellite is decreasing. (E) The gravitational force acting on the satellite is decreasing. I. II. III. Radiation Conduction Convection 30. Heat can be transferred to the inside surface of the walls of the container by which of the above? (A) I only (B) I and II only (C) I and III only (D) II only (E) I, II, and III only 31. If you touch the outside surface of the metal container, your hand will become warmer directly by which of the above choices? (A) I only (B) I and II only (C) I and III only (D) II only (E) III only 367 Practice Test 1 32. If the average speed of the molecules of an ideal gas is doubled, the temperature of the gas (A) remains the same. (B) is doubled. (C) is halved. (D) is quadrupled. (E) is quartered. c p a b Questions 33 – 34 relate to a heat engine which uses heat to do 50 J of work, and then exhausts 100 J of energy into a cold reservoir. 36. Consider the graph of pressure vs. volume above. The gas represented by the graph begins at state a, and follows the arrows around the cycle, returning to state a. Which of the following statements is true? (A) Work is done by the gas in process ab. (B) Work is done on the gas in process ca. (C) No work is done on the gas during process bc (D) Heat is removed from the gas during process ca. (E) Process abc is adiabatic. 33. The heat added to the heat engine is (A) 150 J (B) 100 J (C) 50 J (D) 2 J (E) zero 34. The efficiency of the heat engine is (A) 25% (B) 33% (C) 50% (D) 75% (E) 100% Questions 37 – 39 relate to the two masses M1 and M2, which have a charge Q1 and Q2, respectively. The masses are initially separated by a distance r. 35. An ideal gas is enclosed in a container which has a fixed volume. If the temperature of the gas is increased, which of the following will also increase? I. The pressure against the walls of the container. II. The average kinetic energy of the gas molecules. III. The number of moles of gas in the container. (A) (B) (C) (D) (E) V M1 M2 r Q1 Q2 37. If the distance between the masses is doubled, which of the following is true? (A) the gravitational force will increase. (B) the electric force will increase. (C) the gravitational force will decrease but the electric force will remain the same. (D) the electric force will decrease, but the gravitational force will remain the same. (E) both the gravitational and electric forces will decrease. I only I and II only II and III only II only III only 38. If both masses are doubled, but the charge on each remains the same, which of the following is true? (A) the gravitational force will decrease. (B) the electric force will increase. (C) the gravitational force will increase but the electric force will remain the same. (D) the electric force will increase, but the gravitational force will remain the same. (E) both the gravitational and electric forces will decrease. 368 Practice Test 1 39. If the two charged masses above are placed in space so that no other forces affect them, and they remain at a distance r apart indefinitely, which of the following is true? (A) both charges are positive. (B) Q1 is positive and Q2 is negative. (C) Q1 is negative and Q1 is positive. (D) Q1 = Q2 (E) M1 = M2 A1 O 41. Which graph(s) can represent the potential energy of the spring and mass as a function of displacement x? (A) I only (B) I and II only (C) II only (D) III only (E) II and III only 42. Which graph(s) can represent the net force acting on the mass as a function of displacement x? (A) I only (B) I and II only (C) II only (D) III only (E) II and III only A2 Questions 40 – 42 refer to the diagram of a mass on a spring above. The mass is oscillating about point O on a surface of negligible friction, and the maximum displacements on either side of point O are labeled A1 and A2. The graphs below can represent quantities associated with the oscillation as a function of length x of the spring. I. +1 +2 43. Three charges of + 1 microcoulomb, + 2 microcoulombs, and – 2 microcoulombs are fixed at the vertices of an equilateral triangle as shown. The net force acting on the + 1 microcoulomb charge is directed in which direction? O II. -2 (A) (D) (B) (E) (C) O III. O 40. Which graph(s) can represent the kinetic energy of the spring and mass as a function of displacement x? (A) I only (B) I and II only (C) II only (D) III only (E) II and III only 369 Practice Test 1 + + + + + R + 44. A neutral electroscope consists of a metal sphere, a conducting rod, and two thin gold leaves, as shown above. If a positively charged rod is brought near the knob of the electroscope, which of the following statements is true? (A) The electroscope can be charged negatively without the positively charged rod touching the knob and using a only grounding wire. (B) The electroscope can be charged positively without the positively charged rod touching the knob and using only a grounding wire. (C) The leaves of the electroscope are negatively charged. (D) The knob of the electroscope is positively charged. (E) The electroscope has a net positive charge. Q + + + + + + + + Questions 46 – 47 An isolated conducting sphere of radius R is positively charged. Consider the following graphs: (A) (D) (B) (E) I II 45. An electron is placed in the center of the space between plates I and II above. The subsequent motion of the electron is described by which of the following? (A) The electron accelerates toward plate I. (B) The electron accelerates toward plate II. (C) The electron moves with constant velocity toward plate I. (D) The electron moves with constant velocity toward plate II. (E) The electron remains at rest halfway between the plates. (C) 46. Which of the graphs above best represents the electric field as a function of distance from the center of the sphere? 47. Which of the graphs above best represents the electric potential as a function of distance from the center of the sphere? 370 Practice Test 1 rA rB = 2rA rC = 2rB 1 48. Three resistors A, B, and C are made from the same material and have equal lengths but different radii. Which of the following is the relationship between the resistance of C compared to the resistance of A? (A) RC R A 2 Questions 52 – 53 refer to the circuit shown above. A 50-volt battery supplies 100 watts of power to each of the two identical light bulbs. The current passing through bulb 1 is 4 A. RC 4 R A (C) RC 16R A 1 (D) RC R A 4 1 RA (E) RC 16 (B) 52. The voltmeter across bulb 1 will read (A) 100 V (B) 50 V (C) 25 V (D) 4 V (E) zero 53. The current through bulb 2 is (A) 2 A (B) 4 A (C) 8 A (D) 100 A (E) zero 2 1 4V 3 54. The resistance of each bulb is most nearly (A) 25 (B) 20 (C) 6 (D) 4 (E) 2 4 Questions 49 – 51 Consider the capacitors in the circuit above. Each capacitor has a capacitance of 2 μF. 49. The total capacitance of the circuit is (A) 8 μF (B) 4 μF (C) 2/3 μF (D) 4/3 μF (E) 8/3 μF 50. The charge on capacitor 1 is (A) 8 μC (B) 4 μC (C) 2/3 μC (D) 4/3 μC (E) 8/3 μC Questions 55 – 56 A circuit consists of a fully-charged capacitor and a resistor as shown. The switch is initially open. 51. The charge on capacitor 2 is (A) 8 μC (B) 4 μC (C) 2/3 μC (D) 4/3 μC (E) 8/3 μC 371 Practice Test 1 55. Which of the graphs below represents the current I in the circuit as a function of time after the switch is closed? (A) (D) (B) (E) I P 59. A wire on the y – axis of a coordinate system has a current I in the +y direction as shown above. What is the direction of the magnetic field due to the wire at point P? (A) to the left (B) to the right (C) down into the page and perpendicular to the page (D) up out of the page and perpendicular to the page (E) toward the bottom of the page (C) d I (in) 56. Which of the graphs above represents the voltage V across the capacitor as a function of time after the switch is closed? I (out) 60. Two long parallel wires are separated by a distance d as shown above. One wire carries a steady current I into the plane of the page and the other wire carries an equal steady current I which is out of the page. The net magnetic field at a point halfway between the wires points in which of the following directions? B (A) (B) (C) (D) (E) zero Questions 61 – 62 relate to the standing wave in a string shown below. 57. A small particle enters a magnetic field B which is directed out of the page as shown. Which of the following particles would follow the path shown above while moving through the magnetic field? (A) proton (B) electron (C) neutron (D) x-ray (E) photon of red light L 58. A positive charge moves through a magnetic field of magnitude 10-2 T with a speed of 106 m/s when it experiences a force of 10-14 N. The magnitude of the charge is (A) 10-22 C (B) 10-18 C (C) 10-10 C (D) 10-6 C (E) 10-2 C A standing wave is produced in a string when a periodic wave is passed through the string and is reflected off the fixed end. The wavelength of the wave in the string shown above is 0.5 m, and the frequency of vibration is 120 Hz. 61. The speed of the wave is (A) 240 m/s (B) 120 m/s (C) 60 m/s (D) 30 m/s (E) 20 m/s 372 Practice Test 1 62. The length of the string is (A) 1.50 m (B) 0.75 m (C) 0.50 m (D) 0.25 m (E) 0.10 m Energy above ground state E4 = 8eV E3 = 7eV E2 = 5eV 63. Green light is passed through two narrow slits and forms a pattern of bright and dark lines on a screen. The phenomena primarily responsible for this pattern is (A) refraction (B) reflection (C) polarization (D) interference (E) intensity E1 = 0 Questions 67 – 68 refer to the energy level diagram for a hypothetical atom above. The energy for each level is given above ground state. 67. Which of the following photon energies could NOT be emitted from this atom after it has been excited to the 4th energy level? (A) 1 eV (B) 2 eV (C) 3 eV (D) 4 eV (E) 7 eV 64. Which of the graphs below represent the energy of a photon vs. its frequency? (A) (D) (B) 68. Which of the following transitions will produce the photon with the highest frequency? (A) n = 2 to n = 1 (B) n = 3 to n = 1 (C) n = 3 to n = 2 (D) n = 4 to n = 1 (E) n = 4 to n = 3 (E) (C) 69. In a radioactive decay process, the parent atom undergoes the following radioactive decays: alpha, alpha, beta. The atomic number of the final daughter element is how many atomic mass units less than the parent atom? (A) 2 (B) 3 (C) 4 (D) 5 (E) 7 Questions 65 – 66 relate to the converging lens and principal axis shown and the choices that follow. The focal length f and twice the focal length 2f are marked on one side of the lens. 1 3f 2 2f 3 4 5 70. Which of the following statements is true? (A) The binding energy of the nucleus is equal to the mass of the nucleus in atomic mass units. (B) The binding energy of the nucleus is equal to the mass of the nucleus in MeV (C) The atomic mass of a nucleus is greater than the sum of the masses of the individual nucleons. (D) The atomic mass of a nucleus is less than the sum of the masses of the individual nucleons (E) The mass defect of the nucleus is equal to the number of neutrons in the nucleus. f (A) Position 1 (B) Position 2 (C) Position 3 (D) Position 4 (E) Position 5 65. At which position could a candle be placed so that a virtual image would be formed? 66. At which position could a candle be placed so that an image smaller than the candle would be formed? 373 Practice Test 1 W F s F cos s 1 KE mv 2 2 1 1 2 2 W KE f KE0 mv f mv0 2 2 PE mgh NEWTONIAN MECHANICS v vo t v v o at a W g PE g mg h0 h f 1 (v o v)t 2 1 x v o t at 2 2 2 2 v v o 2 a x x PE0 KE0 PE f KE f W t P F v F cos v P F Fnet ma p = mv W mg f s max s FN ( static) J = Ft = p = mv f mv 0 f k k FN (kinetic) xcm FG Gm1 m2 r2 m1 x1 m2 x2 m1 m2 F x cg 2r T v2 ac r mv 2 Fc r GM E v r v W1 x1 W2 x 2 W1 W2 Fs kx 1 2 kx 2 x A cos t 2 2f T m TS 2 k PEelastic TP 2 T 374 1 f l g Practice Test 1 WAVES AND OPTICS 1 f T v f T FLUIDS AND THERMAL PHYSICS F A m V Pdepth P0 gh P sin D v f n n n 1,2,3,4,.. (vibrating string and open tube) 2L v f n n n 1,3,5,... (closed tube) 4L FB W fluid gV fluid 1 A1v1 2 A2 v 2 (mass flow rate) A1v1 A2 v 2 (volume flow rate) P1 1 1 v1 2 gy1 P2 v 2 2 gy 2 2 2 r i 1 R 2 ho d o hi d i f TK TC 273.15 L Lo T 1 1 1 do di f m PV nRT di do PiVi Pf V f (constant temperatur e) c f c n v n1 sin 1 n 2 sin 2 Vi Vf (constant pressure) Ti Tf KE avg v rms 1 3 2 mvrms k B T 2 2 v avg 2 3k B T 3RT M sin c ho d o hi d i U U f U i Q W W PV P(V f Vi ) e n2 n1 1 1 1 do di f W QH m T TC T e H 1 C TH TH 375 di do Practice Test 1 q t V R I L R A P IV Rs R1 R2 R3 ... I m sin , m 0,1,2,3,... d y tan L film t vacuum n m film , m 0,1,2,3,.. 2 (destructiv e interferen ce) 1 1 1 1 ... R p R1 R2 R3 1 m film 2 t , m 0,1,2,3,.. 2 (constructi ve interferen ce) m sin , m 0,1,2,3,.. W C P C1 C 2 C 3 ... 1 1 1 1 ... C s C1 C 2 C 3 q CV 1 1 1 Q2 CV 2 QV 2 2 2 C RC UE ELECTRICITY AND MAGNETISM F kq1 q 2 1 q1 q 2 2 40 r 2 r B F kq 1 q E 2 q0 r 40 r 2 FB q 0 v sin mv qB FB ILB sin r EPE V AB kq1 q 2 1 q1 q 2 r 4 0 r B W EPE B EPE A AB q0 q0 Vr kq 1 r 4 0 q r V s q CV E C 0A d 1 1 1 Q2 U E CV 2 QV 2 2 2 C 376 0 I 2r Practice Test 1 vBL E hf I hc c f E photon E f Ei R BA cos N t VS N S VP N P E mc 2 1u 1.6726 x10 27 kg 931.5 MeV A Z X IS NP IP NS P IV GEOMETRY AND TRIGONOMETRY Rectangle A bh 1 Triangle A bh 2 2 Circle A r and C 2r Parallelep iped V lwh ATOMIC AND NUCLEAR PHYSICS E hf c f Wo hf o h Cylinder V r 2 l and S 2rl 2r 2 4 Sphere V r 3 and S 4r 2 3 Right Triangle ho ha h 2 KEmax hf Wo eVstop p h 1 cos mc 2 h mv E pc 2 h sin o h ha cos h h tan o ha 377 h ho θ ha Practice Test 1 60˚ 25˚ 1. (15 points) A ball of mass 0.50 kg hangs from two strings at the angles shown. The longer string is 0.50 m long. (a) Determine the tension in each string. The shorter string is cut, and the longer string swings from a height h above the lowest point of the swing. 25˚ L=0.50 m Blade h (b) Determine i. the height h from which the ball is dropped. ii. the potential energy at the height h. iii. the speed of the ball as it passes through its lowest point. At the instant the ball passes through its lowest point, the string is cut by a razor blade at a height of 1.20 m above the floor. (c) Determine i. the time the ball is in the air. ii. the horizontal distance the ball travels before striking the floor. iii. the kinetic energy of the ball just before striking the floor. 378 Practice Test 1 2. (15 points) A cart of mass 1.0 kg can roll freely on small wheels on a curved track as shown above. The cart starts at a height of 0.80 m and rolls toward a cart of 3.0 kg attached to an uncompressed spring of negligible mass at the bottom of the ramp. The two blocks stick together on impact. A graph of Force F vs. displacement x for the spring is shown at the left. (a) Find the speed of the 1.0 kg cart at the bottom of the ramp. (b) Determine the speed of the two blocks immediately after the collision. (c) Using the graph at the left, determine the spring constant k. (d) Determine the maximum compression of the spring after the collision. (e) If the 3.0 kg block were removed and replaced with a plate of negligible mass, would the maximum compression of the spring increase, decrease, or remain the same as in part (d)? Justify your answer. 379 Practice Test 1 + + + 3. (15 points) A metal ball is fixed to a wall and charged to Q = +4 nC. An uncharged metal ball of mass m = 0.10 kg is hung by an insulating thread at a horizontal distance of d = 0.02 m from center of the fixed ball. (a) Assuming the hanging ball remains at a distance of 0.02 cm from the fixed ball, find i. the magnitude and direction of the electric field at the location of the hanging ball. ii. the electric potential at the location of the hanging ball. There is now a charge of q = +4 nC placed on the hanging ball. (b) If the force between the two charged balls is 1.60 x 10-4 N, determine the new horizontal separation distance x between the balls as a result of both of them having a charge. Neglect the small change in height of the hanging ball. (c) Determine the work required to separate the charge the additional distance Δx when the charge is placed on the hanging ball. The hanging ball is discharged, and it swings like a pendulum toward the fixed ball, touches it, and the balls are again separated to an equilibrium position. (d) Would the new equilibrium separation distance of the two balls be greater than, less than, or equal to the equilibrium separation distance determined in part (b)? Explain your answer. 380 Practice Test 1 cm 5 20 35 50 65 80 95 100 4. (10 points) A light bulb on a stand can be mounted on a 1.0-m long optical bench as shown above. A convex lens and a concave mirror, each of focal length 15 cm, and a screen can also be mounted on the bench. The convex lens is placed at the 50-cm mark of the bench, and the light bulb is placed at the 5-cm mark. (a) As the bulb is slowly moved toward the lens, describe the image formed by the lens. Be sure to discuss the characteristics and changes in the image in terms of size, whether the image is real or virtual, and its orientation. Note any significant object distances as the candle moves toward the lens. (b) On the diagram below, draw a sketch of the ray diagram for the bulb and lens when the bulb is placed 15-cm from the lens. Briefly describe the image formed by the lens. cm 5 20 35 65 80 95 50 The convex lens is removed, and the concave mirror is now placed at the 50-cm mark of the bench, and the light bulb is placed at the 5-cm mark. (c) As the bulb is slowly moved toward the mirror, describe the image formed by the mirror. Be sure to discuss the characteristics and changes in the image in terms of size, whether the image is real or virtual, and its orientation. Note any significant object distances as the candle moves toward the mirror. (d) The bulb is placed at an object distance which produces a real image on a screen. An opaque card is then placed over the top half of the mirror. Describe the changes in the real image, if any. 381 Practice Test 1 5. (10 points) A ball of mass 0.01 kg and radius 0.01 m is placed on the surface of a liquid with a density ρL = 1200 kg/m3. Determine (a) the density of the ball. (b) the buoyant force acting on the ball. (c) the acceleration of the ball as it descends through the liquid. 382 Practice Test 1 P B a b I 6. (10 points) A square loop of wire carries a current I = 0.20 A as it sits at rest in a uniform magnetic field B = 0.40 T directed into the page. The square is 0.15 m on each side. (a) Determine the magnitude and direction of the force acting on the side of the wire labeled ab. (b) Determine the magnitude and direction of the magnetic field Bw due to the current in the wire at point P, which is a perpendicular distance d = 0.05 m away from the wire. (c) Will this loop of wire tend to expand, contract, or remain the same size in this magnetic field? Explain. P v B I (d) An electron traveling at a speed of 3.0 x 104 m/s passes through the magnetic field through point P as shown above. i. Find the magnitude and direction of the magnetic force acting on the electron as it passes point P. ii. Draw arrows indicating the electric field that would need to be applied in order to keep the electron moving in a straight line. 383 Practice Test 1 7. (15 points) The electron energy levels for a mercury atom are shown below. E=0 E4 = - 4.95 eV E3 = -5.52 eV E2 = -5.74 eV E1 = - 10.38 eV An electron in the ground state absorbs a photon which causes the electron to be raised to the second energy level. (a) Determine the following for the absorbed photon. i. wavelength ii. frequency (b) State whether or not the absorbed photon is in the visible range. Explain your answer. The electron absorbs a second photon of energy 10.00 eV while it is in the second energy level of the atom. (c) Find the following for the electron after it absorbs the 10.00 eV photon. i. kinetic energy ii. speed iii. de Broglie wavelength 384 Practice Test 1 ANSWERS TO PRACTICE TEST 1 1. C 2. A 3. D 4. C 5. B 6. C 7. C 8. D 9. A 10. D 11. B 12. E 13. B 14. B 15. A 16. D 17. B 18. A 19. A 20. C 21. D 22. A 23. B 24. A 25. D 26. D 27. B 28. B 29. D 30. C 31. D 32. D 33. A 34. B 35. B 36. D 37. E 38. C 39. A 40. C 41. A 42. D 43. C 44. A 45. A 46. E 47. C 48. E 49. E 50. A 51. E 52. C 53. B 54. C 55. A 56. A 57. A 58. B 59. C 60. D Free Response Questions Solutions for Practice Test 1 1. (a) 5 points Drawing a free-body diagram for the ball: FT1 FT2 60º 25º W F x 0 FT 1x FT 2 x FT 1 cos 60 FT 2 cos 25 F y 0 FT 1 y FT 2 y W FT 1 sin 60 FT 2 sin 25 mg 385 61. C 62. B 63. D 64. D 65. E 66. A 67. D 68. A 69. B 70. D Practice Test 1 Solving these two equations simultaneously for the tension forces gives FT1 = 4.5 N and FT2 = 2.5 N (b) 5 points i. h L L sin 25 0.50m 0.50m sin 25 0.29m ii. U mgh 0.50kg 10m / s 2 0.29m 1.44 J iii. Conservation of energy U top K bottom mgh 1 2 mv 2 v 2 gh 2 10m / s 2 0.29m 2.4 m / s (c) 5 points 2y 21.2m 0.49 s i. t g 10m / s 2 ii. x vt 2.4 m / s 0.49s 1.18 m iii. 1 K floor U top K top mgy mv 2 2 1 2 0.50kg 10m / s 2 1.2m 0.50kg 2.4 m / s 7.44 J 2 2. (a) 3 points Conservation of energy 1 mgh mv 2 2 v 2 gh 2 10m / s 2 0.80m 4 m / s (b) 2 points Conservation of momentum mv m M v 1.0kg 4m / s 1.0 m / s v 4.0kg (c) 3 points The spring constant k is the slope of the F vs. x graph: k = 5 N/m (d) 4 points Conservation of energy 386 Practice Test 1 K U spring 1 m M v 2 1 kx2 2 2 x m M v 2 4kg 1m / s 2 0.89m k 5N /m (e) 3 points If the 3.0 kg mass were removed and replaced with a plate of negligible mass, then the potential energy of the 1.0 kg block at maximum height would equal the potential energy in the spring at maximum compression: 1 mgh kx 2 2 2mgh 21kg 0.80m x 0.57 m k 5N /m The compression of the spring would be smaller. 3. (a) 5 points Nm 2 9.0 x10 9 4 x10 9 C 2 C KQ 9 x10 4 N / C i. E 2 2 d 0.02m Nm2 9.0 x109 2 4 x10 9 C C KQ ii. V 1.8 x103V 0.02m d (b) 4 points KQq F 2 x KQq x F (c) 4 points Nm 2 9.0 x10 9 4 x10 9 C 4 x10 9 C 2 C 0.03m 1.60 x10 4 N Nm 2 Nm 2 9.0 x10 9 2 4 x10 9 C 9.0 x10 9 2 4 x10 9 C C C KQ KQ 9 W qV q 4 x10 C 0.02m 0.03m d2 d1 6 W 2.4 x10 J (d) 2 points Less than the original separation distance, since each charge would be +2 nC. 387 Practice Test 1 4. (a) 3 points The bulb begins at an object distance of 3 focal lengths, and the image begins as real, inverted, and smaller than the object. When the bulb is at 2f, the image is real, inverted, and the same size as the object. As the bulb moves toward f it becomes larger than the object and is real and inverted. The image disappears, and there is no image when the object distance is equal to the focal length. As the bulb moves inside the focal length, the image becomes upright, larger than the object, and virtual. (b) 3 points The bulb is placed at do = 15 cm = f : cm 5 20 35 65 80 95 The rays emerge from the lens parallel, and thus no image is formed. (c) 2 points As the bulb is moved toward the concave mirror, the images formed are exactly the same at the same locations as the convex lens in part (a). (d) 2 points A real image will still be formed as it would be if half the mirror were not blocked, but the image would be dimmer. 5. (a) 3 points 0.01 kg m m b 2387.3 kg / m 3 4 4 V r 3 0.01m3 3 3 (b) 3 points Fbuoy liquid gVdisplaced fluid 1200 kg / m3 10m / s 2 4.19 x10 6 m3 0.05 N (c) 4 points W Fbuoy 0.10 N 0.05 N F a net 5.0 m / s 2 downward. m m 0.01 kg 388 Practice Test 1 6. (a) 3 points F ILB 0.20 A0.15m0.40T 1.2 x10 2 N directed down to the bottom of the page by the right-hand rule. (b) 2 points I 4x10 7 Tm / A 0.20 A B o 8x10 7 T 2d 2 0.05m (c) 2 points By the right-hand rule, the forces are inward on all sides of the loop, so the loop will tend to contract. (d) 3 points i. The electron experiences a force from the magnetic field of 0.40 T and the magnetic field due to the current in the wire, which is negligible. F evB 1.6 x10 19 C 3.0 x10 4 0.40T 1.9 x10 15 N ii. The magnetic force on the electron is downward by the left-hand rule, so the electric force to keep the electron moving in a straight line would point upward. Since the electric field points in the direction a positive charge would experience a force, the electric field should point downward in order to apply an upward force to the electron. 7. (a) 6 points i. E E 2 E1 5.74eV 10.38eV 4.64eV hc 1240 eV nm 267.24nm 2.67 x10 7 m E 4.64 eV 3.00 x10 8 m / s 1.12 x1015 Hz ii. f 7 2.67 x10 m c (b) 2 points This photon is not in the visible range of wavelengths, which is 400 nm to 700 nm. (c) 7 points i. K 10.00eV 5.74eV 4.26 eV 6.82 x10 19 J ii. v 2K m 2 6.82 x10 19 J 1.22 x10 6 m / s 9.11x10 31 kg 6.62 x10 34 J s h 5.94 x10 10 m 31 6 mv 9.11x10 kg 1.22 x10 m / s This wavelength is in the x-ray range. iii. 389 Practice Test 1 Practice Test 1 Scoring Worksheet – AP Physics B Section I: Multiple Choice ( ___________ ) – (1/4 x _________ ) x 1.2857 = __________= ___________ Number correct Number MultipleWeighted (out of 70) wrong Choice Section I Score Score Section II: Free Response Question 1 ____________ x 1.0000 = ____________ (out of 15) Question 2 ____________ x 1.0000 = ____________ (out of 15) Question 3 ____________ x 1.0000 = ____________ (out of 15) Question 4 ____________ x 1.0000 = ____________ (out of 10) Question 5 ____________ x 1.0000 = ____________ (out of 10) Question 6 ____________ x 1.0000 = ____________ (out of 15) Question 7 ____________ x 1.0000 = ____________ (out of 10) Sum = ____________ Weighted Section II Score Composite Score __________ + ___________ = _______________ Weighted Weighted Composite Score Section I Section II Score Score Possible scoring range: 106 – 180 = 5; 83 – 105 = 4; 54 – 82 = 3; 40 – 53 = 2; 0 – 39 = 1 390
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