Physics 30 Released Item June 2001

ii Multiple Choice • Decide which of the choices best completes the statement or answers the question. • Locate that question number on the separate answer sheet provided and fill in the circle that corresponds to your choice. Example This examination is for the subject of A. science B. physics C. biology D. chemistry Answer Sheet A B C D Numerical Response • Record your answer on the answer sheet provided by writing it in the boxes and then filling in the corresponding circles. • If an answer is a value between 0 and 1 (e.g., 0.25), then be sure to record the 0 before the decimal place. • Enter the first digit of your answer in the left-hand box and leave any unused boxes blank. Examples Calculation Question and Solution If a 121 N force is applied to a 77.7 kg mass at rest on a frictionless surface, the acceleration of the mass will be _________ m/s 2 . (Record your three-digit answer in the numerical-response section on the answer sheet.) m F a = 2 m/s 557 1 kg 77.7 N 121 . a = = 0 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 . . 1 . 5 6 Record 1.56 on the answer sheet Calculation Question and Solution A microwave of wavelength 16 cm has a frequency, expressed in scientific notation, of b × 10 w Hz. The value of b is _______ . (Record your two-digit answer in the numerical-response section on the answer sheet.) λ c f = Hz 10 875 . 1 m 0.16 m/s 10 00 . 3 9 8 × = × = f 0 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 . . 1 . 9 Record 1.9 on the answer sheet

2 1. A 1 575 kg car, initially travelling at 10.0 m/s, collides with a stationary 2 250 kg car. The bumpers of the two cars become locked together. The speed of the combined cars immediately after impact is __________m/s. (Record your three-digit answer in the numerical-response section on the answer sheet.) 3. A 115 g arrow travelling east at 20 m/s imbeds itself in a 57 g tennis ball moving north at 42 m/s. The direction of the ball-and-arrow combination after impact is A. 46 ° N of E B. 46 ° E of N C. 25 ° E of N D. 25 ° N of E 4. In an inelastic collision, the energy that appears to be missing is converted into A. sound and momentum B. force and momentum C. sound and heat D. heat and force

5 7. The change in the kinetic energy of the car during the test drive is A. 9.60 × 10 3 J B. 1.15 × 10 5 J C. 1.73 × 10 5 J D. 1.80 × 10 5 J 8. The magnitude of the impulse on the car during the test drive is A. 4.80 × 10 3 kg . m/s B. 1.92 × 10 4 kg . m/s C. 2.40 × 10 4 kg . m/s D. 2.88 × 10 4 kg . m/s Use your recorded answer from Multiple Choice 8 to answer Numerical Response 3.* 3. The average net force on the car during the test drive, expressed in scientific notation, is a.bc × 10 d N. The values of a , b , c , and d are ____, ____, ____, and ____. (Record all four digits of your answer in the numerical-response section on the answer sheet.) *You can receive marks for this question even if the previous question was answered incorrectly.

8 Use the following information to answer the next four questions. To determine the electric force on a 2.5 × 10 –4 kg neutral pith ball, a student charges a Van de Graaff generator and suspends the pith ball by an insulating thread. 20 ° 30.0 cm Van de Graaff generator Pith ball 12. When the neutral pith ball is placed near the charged Van de Graaff generator, the pithball is attracted to the generator as a result of A. induction B. grounding C. conduction D. induction and grounding 13. The direction of the electrical force on the pith ball is A. → B. ← C. ↑ D. ↓

11 Use the following additional information to answer the next three questions. In Brent’s circuit, all bulbs are working and the brake switch is closed. 4. The reading on the ammeter is __________A. (Record your three-digit answer in the numerical-response section on the answer sheet.) 5. The voltage drop across one of the 12.0 Ω light bulbs is __________ V. (Record your three-digit answer in the numerical-response section on the answer sheet.) 17. The electrical power dissipated by the 4.00 Ω bulb is A. 5.76 W B. 8.64 W C. 14.4 W D. 144 W

14 Use the following information to answer the next two questions. A Mass Spectrometer A particular lithium sample contains two isotopes. These isotopes are singly charged in an ion generation and acceleration chamber. Since individual atoms are ionized at different points in the acceleration chamber, their speeds vary when they enter the velocity selection chamber. In the velocity selection chamber, the electric field strength is 5.95 × 10 2 N/C and the magnetic field strength is 1.55 × 10 –3 T. The velocity selection chamber allows ions of a certain speed to pass through undeflected. The beam of undeflected ions then enters the ion separation chamber where the magnetic field of 0.185 T splits the beam into two beams. Beam 1 curves through a radius of 0.131 m. Ion generation and acceleration chamber Velocity selection chamber Ion separation chamber Electron beam B 2 = 0.185 T B 1 = 1.55 × 10 –3 T E = 5.95 × 10 2 N/C Positive plate Negative plate Sample Beam 1 Beam 2 Ion detector and 20. The speed of the undeflected ionized lithium ions, Li + , as they leave the velocity selection chamber is A. 4.25 × 10 4 m/s B. 3.84 × 10 5 m/s C. 8.63 × 10 6 m/s D. 7.22 × 10 7 m/s

17 Use the following information to answer the next question. A proton enters a magnetic field at a right angle to the field. An alpha particle enters the same field at the same angle but with twice the speed. Once in the magnetic field, both particles move in a circular path. 24. The ratio of radius of the alpha particle’s path to the radius of the proton’s path is A. 1 : 1 B. 2 : 1 C. 4 : 1 D. 8 : 1 25. Which of the following forms of electromagnetic radiation has photons of lowest energy? A. Radio waves B. Ultraviolet light C. Gamma radiation D. Infrared radiation 8. If certain X-rays have a frequency of 2.15 × 10 20 Hz, then the period of these X-rays, expressed in scientific notation, is b × 10 –w s. The value of b is __________. (Record your three-digit answer in the numerical-response section on the answer sheet.)

18 26. Maxwell’s work contained the new idea that A. an electric current in a wire produces a magnetic field that circles the wire B. a current is induced in a conductor that moves across a magnetic field C. an electric field that changes with time generates a magnetic field D. two parallel, current-carrying wires exert a force on each other 27. Evidence of the wave-like properties of matter can be found in the A. refraction of light B. diffraction of electrons C. Compton scattering of X-ray photons D. conservation of momentum of photons 28. Which of the following types of radiation can be deflected by both electric fields and magnetic fields? A. X-rays B. Cathode rays C. Photon beams D. Electromagnetic waves

19 Use the following information to answer the next question. When a certain metal is struck by a photon with a frequency of 8.23 × 10 14 Hz, the metal emits an electron with a maximum speed of 2.45 × 10 5 m/s. 9. The work function for this metal is __________ eV. (Record your three-digit answer in the numerical-response section on the answer sheet.) 29. In his explanation of the photoelectric effect, Einstein proposed that A. the speed of light is constant B. light energy is concentrated in distinct “packets” C. light energy is evenly distributed over the entire wave front D. metallic surfaces emit electrons when illuminated with short-wavelength light Use the following information to answer the next question. Data Recorded in a Photoelectric Effect Experiment I The number of photoelectrons emitted each second II The maximum kinetic energy of the emitted photoelectrons III The charge on each of the emitted photoelectrons 30. The intensity of a light source that causes photoelectric emission is increased while the frequency of the light source is kept constant. This increase will result in an increase in A. I only B. II only C. I and II only D. II and III only

20 Use the following information to answer the next six questions. A sample of iodine-131 has an initial mass of 76.0 mg. The activity of the sample is measured and the amount of iodine-131 remaining in the sample is determined. The following graph was obtained. Mass of Iodine-131 Versus Elapsed Time Time (days) Mass of Iodine - 131 (mg) 0.0 5.0 10.0 15.0 20.0 25.0 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 A particular nucleus of iodine-131 decays by emitting a beta particle that travels at 2.34 × 10 5 m/s and gamma radiation that has a wavelength of 5.36 × 10 –12 m. Extra momentum and kinetic energy are carried off by a neutrino. 31. The half-life of iodine-131 is A. 8.0 days B. 12.0 days C. 16.0 days D. 24.0 days

21 Use your recorded answer from Multiple Choice 31 to answer Numerical Response 10.* 10. After 48.0 days the amount of iodine-131 that remains in the sample is __________ mg. (Record your three-digit answer in the numerical-response section on the answer sheet.) *You can receive marks for this question even if the previous question was answered incorrectly. 32. The energy emitted as gamma radiation during the transmutation of an iodine-131 nucleus is A. 3.55 × 10 –45 J B. 2.68 × 10 –27 J C. 1.24 × 10 –22 J D. 3.71 × 10 –14 J Use the following additional information to answer the next question. The momentum of the gamma ray photon and the beta particle can be calculated. The momentum of a gamma ray photon ( γ ) is determined by the equation λ h p = 33. For the decay of iodine-131, the relationship between the magnitude of the momentum of the gamma ray photon ( p γ ) and the magnitude of the momentum of the beta particle ( p β ) can be represented by the equation A. p γ = – p β B. p γ = p β C. p γ = (1.72 × 10 – 3 ) × p β D. p γ = (5.80 × 10 2 ) × p β

22 34. The equation for this radioactive decay is A. neutrino gamma beta Sb I 51 127 53 131 + + + → B. neutrino gamma beta Xe I 54 132 53 131 + + + → C. neturino gamma beta I I 53 132 53 131 + + + → D. neutrino gamma beta Xe I 54 131 53 131 + + + → 35. To protect lab technicians from harmful radiation, the equipment used in this experiment should be shielded with A. lead to stop the γ radiation B. paper to stop the β particles C. an electric field to stop the γ radiation D. a magnetic field to stop the β particles 11. An X-ray tube operates at an electrical potential difference of 1.00 × 10 5 V. The minimum wavelength of the X-ray radiation it produces, expressed in scientific notation, is b × 10 –w m. The value of b is __________. (Record your three-digit answer in the numerical-response section on the answer sheet.)

23 12. The voltage required to stop an alpha particle with an initial speed of 5.34 × 10 4 m/s is __________ V. (Record your three-digit answer in the numerical-response section on the answer sheet.) Use the following information to answer the next two questions. An electron in a hydrogen atom makes a transition from the third energy level to the ground state. 36. The frequency of light emitted when the electron drops from energy level n = 3 to n = 1 is A. 2.2 × 10 –8 Hz B. 1.0 × 10 7 Hz C. 5.5 × 10 14 Hz D. 2.9 × 10 15 Hz 37. In a hydrogen atom, the ratio of the radius of the third orbital to the radius of the first orbital is A. 9 : 1 B. 6 : 1 C. 3 : 1 D. 3 : 1 The written response questions follow on the next page.

24 Written Response — 15% 1. You have been given a large permanent magnet with a uniform magnetic field between its poles. In a preliminary experiment, the magnetic field of the permanent magnet was found to be at least 100 times the strength of Earth’s magnetic field. Using concepts discussed in the Physics 30 course, design a procedure to measure the magnitude of the magnetic field. Assume that the space between the poles is large enough to insert any necessary equipment. The description of your procedure must include • a label indicating the direction of the magnetic field between the poles of the magnet below • a list of the materials required • a labelled diagram showing your experimental design • a description of how to obtain the measurements required to calculate the magnitude of the magnetic field • a derivation of the formula used to determine the magnitude of the magnetic field NOTE: Marks will be awarded for the physics principles used in your response and for the effective communication of your response. N S

26 Use the following information to answer the next question. In a modified Millikan apparatus, a small, charged object that has a mass of 3.8 × 10 –15 kg is suspended by the electric field that is between charged parallel plates. The table below shows how the balancing voltage depends on the distance between the plates. Plate separation (mm) Balancing voltage (10 3 V) 11.1 20.0 24.0 28.1 35.1 50.0 1.39 2.21 2.78 3.11 4.22 ? Written Response — 15% 2. • Provide a graph of the balancing voltage as a function of the plate separation, with the manipulated variable on the horizontal axis. • Calculate the slope of the graph, and describe the physical quantity or quantities that this slope represents. • Using the slope, or another suitable averaging technique, determine the magnitude of the charge on the suspended mass. • Determine the balancing voltage required when the plates are separated by 50.0 mm. Clearly communicate your understanding of the physics principles that you are using to solve this question. You may communicate this understanding mathematically, graphically, and/or with written statements.

27 _____________________________________ (title) You may continue your answer on the next page.

PHYSICS DATA SHEET CONSTANTS Acceleration Due to Gravity or Gravitational Field Near Earth ............ a g or g = 9.81 m/s 2 or 9.81 N/kg Gravitational Constant ........................ G = 6.67 × 10 –11 N . m 2 /kg 2 Mass of Earth ...................................... M e = 5.98 × 10 24 kg Radius of Earth ................................... R e = 6.37 × 10 6 m Coulomb’s Law Constant .................... k = 8.99 × 10 9 N . m 2 /C 2 Electron Volt ....................................... 1 eV = 1.60 × 10 –19 J Elementary Charge .............................. e = 1.60 × 10 –19 C Index of Refraction of Air ................... n = 1.00 Speed of Light in Vacuum .................. c = 3.00 × 10 8 m/s Energy of an Electron in the 1st Bohr Orbit of Hydrogen ..................... E 1 = –2.18 × 10 –18 J or –13.6 eV Planck’s Constant ............................... h = 6.63 × 10 –34 J . s or 4.14 × 10 –15 eV . s Radius of 1st Bohr Orbit of Hydrogen r 1 = 5.29 × 10 –11 m Rydberg’s Constant for Hydrogen ...... R H = 1.10 × 10 7 m 1 Rest Mass Charge Alpha Particle ............... kg 10 65 . 6 27 – × = α m α 2 + Electron ........................ m e = 9.11 × 10 –31 kg e – Neutron ......................... m n = 1.67 × 10 –27 kg n 0 Proton ........................... m p = 1.67 × 10 –27 kg p + hypotenuse opposite = sin θ hypotenuse adjacent = cos θ adjacent opposite = tan θ C c B b A a sin sin sin = = C ab b a c cos 2 – 2 2 2 + = For any Vector R 2 2 y x R R R + = x y R R = θ tan θ cos R R x = θ sin R R y = x : [ x min , x max , x scl ] y : [ y min , y max , y scl ] Exponential Prefix Symbol Value pico ............. p .................. 10 –12 nano ............ n .................. 10 –9 micro ........... µ .................. 10 –6 milli ............. m ................. 10 –3 centi ............ c .................. 10 –2 deci ............. d .................. 10 –1 Exponential Prefix Symbol Value tera ............. T ................. 10 12 giga ............. G ................. 10 9 mega ........... M ................ 10 6 kilo ............. k ................. 10 3 hecto ........... h ................. 10 2 deka ............ da ................ 10 1

EQUATIONS t d v G G = ave t v v a i f – G G G = 2 i 2 1 t a t v d G G G + = T r v π 2 = 2 f 2 1 t a – t v d G G G = t v v d         + = 2 i f G G G ad v v 2 2 i 2 f + = r v a 2 c = a m F G G = v m t F G G ∆ = ∆ g m F G G = g N f F F µ = x k F G G – s = 2 2 1 g r m Gm F = 2 1 r Gm g = r mv F 2 c = 2 2 c 4 T mr F π = v m p G G = Fd W = θ cos Fd E W = ∆ = t E t W P ∆ = = 2 k 2 1 mv E = mgh E = p 2 p 2 1 kx E = k m T π 2 = g l T π 2 = f T 1 = λ f v = l ; l = λ = λ 4 2 1 1 1 2 2 1 2 1 2 1 sin sin n n v v = = = λ λ θ θ nl xd = λ n d θ λ sin = 0 i 0 i – d d h h m = = i 0 1 1 1 d d f + = W E hf + = max k W hf = 0 stop max k qV E = λ hc hf E = =         = 2 i 2 f H 1 – 1 1 n n R λ 1 2 1 E n E n = 1 2 r n r n = n N N       = 2 1 0 2 mc E = λ h p = pc E c hf p = = ; 2 2 1 e r q kq F = 2 1 r kq E = G q F E e G G = d V E = G q E V ∆ = 3 2 1 R R R R + + = 3 2 1 1 1 1 1 R R R R + + = max eff 707 . 0 I I = IR V = IV P = t q I = ⊥ = IlB F m ⊥ = qvB F m ⊥ = lvB V p s s p s p I I V V N N = = max eff 707 . 0 V V = Tear-out Page Fold and tear along perforation.

Tear-out Page Periodic Table of the Elements Fold and tear along perforation. 7 VIIB 6 VIB 5 VB 4 IVB 3 IIIB 2 IIA 1 IA 9 VIIIB 8 57 138.91 La Ac 89 (277.03) lanthanum 58 140.12 Ce Th 90 (232.04) thorium cerium 59 140.91 Pr 91 (231.04) Pa protactinium 60 144.24 Nd 92 238.03 U uranium neodymium 61 (144.91) Pm 93 (237.05) Np neptunium promethium 62 150.35 Sm 94 (244.06 ) Pu plutonium samarium praseodymium actinium cesium rubidium potassium sodium lithium hydrogen 1 1.01 H 3 6.94 Li 11 22.99 Na 19 39.10 K 37 85.47 Rb 55 132.91 Cs Fr barium strontium calcium magnesium beryllium yttrium scandium hafnium zirconium titanium 22 47.90 Ti 40 91.22 Zr 72 178.49 Hf 104 (266.11) Unq tantalum niobium vanadium 23 50.94 V 41 92.91 Nb 73 180.95 Ta 105 (262.11) Unp tungsten molybdenum chromium 24 52.00 Cr 42 95.94 Mo 74 183.85 W 106 (263.12) Unh rhenium technetium manganese 25 54.94 Mn 43 (98.91) Tc 75 186.21 Re 107 (262.12) Uns osmium ruthenium iron 26 55.85 Fe 44 101.07 Ru 76 190.20 Os 108 (265) Uno iridium rhodium cobalt 27 58.93 Co 45 102.91 Rh 77 192.22 I r 109 (266) Une francium radium 4 9.01 Be 12 24.31 Mg 20 40.08 Ca 38 87.62 Sr 56 137.33 Ba 88 (226.03) Ra 21 44.96 Sc 39 88.91 Y 57-71 89-103 87 (223.02) unnilquadium unnilpentium unnilhexium unnilseptium unniloctium unnilennium americium europium platinum palladium nickel 28 58.71 Ni 46 106.40 Pd 78 195.09 Pt 64 157.25 Gd 96 (247.07) Cm curium gadolinium gold silver copper 29 63.55 Cu 47 107.87 Ag 79 196.97 Au 65 158.93 Tb 97 (247.07) Bk berkelium mercury cadmium zinc 30 65.38 Zn 48 112.41 Cd 80 200.59 Hg 66 162.50 Dy 98 (242.06) Cf californium thallium indium gallium aluminum 5 10.81 B 13 26.98 Al 31 69.72 Ga 49 114.82 I n 81 204.37 Tl 67 164.93 Ho 99 (252.08) Es einsteinium holmium lead tin germanium 6 12.01 C Si 32 72.59 Ge 50 118.69 Sn 82 207.19 Pb 68 167.26 Er 100 (257.10) Fm fermium erbium bismuth antimony arsenic phosphorus nitrogen 7 14.01 N 15 30.97 P 33 74.92 As 51 121.75 Sb 83 208.98 Bi 69 168.93 Tm 101 (258.10) Md thulium polonium tellurium selenium sulphur oxygen 8 16.00 O 16 32.06 S 34 78.96 Se 52 127.60 Te 84 (208.98) Po 70 173.04 Yb 102 (259.10) No nobelium ytterbium astatine iodine bromine chlorine fluorine 9 19.00 F 17 35.45 Cl 35 79.90 Br 53 126.90 I 85 (209.98) At 71 174.97 Lu 103 (260.11) Lr lawrencium lutetium 2 4.00 He 10 20.17 Ne 18 39.95 Ar 36 83.80 Kr Xe 86 (222.02) Rn 63 151.96 Eu 95 (243.06) Am 18 VIIIA or O 17 VIIA 16 VIA 15 VA 14 IVA 13 IIIA 12 IIB 11 IB carbon boron 54 131.30 argon helium xenon radon neon krypton 10 VIIIB mendelevium terbium dysprosium silicon 14 28.09 lithium Name 3 6.94 Li Symbol Atomic number Atomic molar mass Key Based on 12 6 C ( ) Indicates mass of the most stable isotope

1 PHYSICS 30 DIPLOMA EXAMINATION JUNE 2001 Multiple Choice and Numerical Response Key and Written Response Scoring Guide

2 Physics 30 June 2001 Diploma Examination Multiple-Choice and Numerical-Response Keys Multiple Choice 1. B 20. B 2. D 21. C 3. A 22. A 4. C 23. C 5. C 24. C 6. B 25. A 7. C 26. C 8. B 27. B 9. B 28. B 10. C 29. B 11. A 30. A 12. A 31. A 13. B 32. D 14. C 33. D 15. D 34. D 16. A 35. A 17. A 36. D 18. D 37. A 19. D Numerical Response 4.12 1.01 232 4.65 1503* 3.24 1.20 1.19 7.20 1.24 9505 29.6 or 29.8 If MC 8 is A, the NR 3 is 3752, 3762 B, the NR 3 is 1503 C, then NR 3 is 1883 D, then NR 3 is 2252 If MC 20 is A, the NR 7 is 9.12 B, the NR 7 is 1.01 C, then NR 7 is 4.49 D, then NR 7 is 5.37 If MC 31 is A, the NR 10 is 1.19 B, the NR 10 is 4.75 C, then NR 10 is 9.50 D, then NR 10 is 19.0

3 Physics 30 — Holistic Scoring Guide Major Concepts: Magnetic field direction; Effect of an external magnetic field on moving charges; Experimental design Score Criteria 5 Excellent • The student provides a complete solution that covers the full scope of the question. – The reader has no difficulty following the strategy or solution presented by the student. – Statements made in the response are supported explicitly but may contain minor errors or have minor omissions. In the response, the student uses major physics principles such as balanced or unbalanced forces and conservation laws. The student applies knowledge from one area of physics to another. 4 Good • The student provides a solution to the significant parts of the question. – The reader may have some difficulty following the strategy or solution presented by the student. – Statements made in the response are supported implicitly and may contain errors. In the response, the student uses major physics principles. The response is mostly complete, mostly correct, and contains some application of physics knowledge. 3 Satisfactory • The student provides a solution in which he/she has made significant progress toward answering the question. – The reader has difficulty following the strategy or solution presented by the student. – Statements made in the response may be open to interpretation and may lack support. In the response, the student uses item-specific methods that reflect a knowledge-based approach, but the student does not apply them to the question. 2 Limited • The student provides a solution in which he/she has made some progress toward answering the question. – Statements made in the response lack support. In the response, the student uses an item-specific method. 1 Poor • The student provides a solution that contains a relevant statement that begins to answer the question. 0 Insufficient • The student provides a solution that is invalid for the question. NR No response is given.

4 Written Response — 15% 1. You have been given a large permanent magnet with a uniform magnetic field between its poles. In a preliminary experiment, the magnetic field of the permanent magnet was found to be at least 100 times the strength of Earth’s magnetic field. Using concepts discussed in the Physics 30 course, design a procedure to measure the magnitude of the magnetic field. Assume that the space between the poles is large enough to insert any necessary equipment. The description of your procedure must include • a label indicating the direction of the magnetic field between the poles of the magnet below • a list of the materials required • a labelled diagram showing your experimental design • a description of how to obtain the measurements required to calculate the magnitude of the magnetic field • a derivation of the formula used to determine the magnitude of the magnetic field NOTE: Marks will be awarded for the physics principles used in your response and for the effective communication of your response. A complete response should include the following content. The clarity of the response is considered in assigning a mark. Expected Content • Magnetic field direction • Effect of External Magnetic field on a moving charge • Experimental Design Sample Solution N S B

5 Experimental Design Method 1 – Circular Motion List: voltmeter metre stick power supply cathode ray tube Procedure: • place the cathode ray tube so that the electron beam is perpendicular to the magnetic field • connect the power supply to the cathode ray tube • connect a voltmeter in parallel to the power supply, record potential difference. This will be used to determine the speed of the electron • use a metre stick to measure the radius of curvature of the electron beam in the magnetic field × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × Accelerating voltage V × Indicates magnetic field perpendicularly into the page Electron beam Analysis: c m F F = or the magnetic force causes circular motion r mv Bvq 2 = qr mv B = Special Notes: Method 1 • The method of determining the speed of the electrons must be explicit • The method of measuring r must be explicit but does not need to be practical. For example, it is not necessary for the student to explicitly identify how the electron path will be observed • The electron path and magnetic field must be perpendicular • The direction of the magnetic field and path deflection must be consistent

6 Method 2 – Velocity Selector List: metre stick 2 voltmeters power supply variable power supply cathode ray tube with metal plates inside Procedure: • set up the cathode ray tube away from the magnetic field so that the electron beam is undeflected. Mark the position of the beam • record the voltage V 1 . This will be used to determine the speed of the electron • place cathode ray tube so that the electron beam is perpendicular to the magnetic field • adjust the variable power supply on the plates inside the CRT until the electron beam returns to its original path • record the voltage V 2 • measure the distance between the plates in the cathode ray tube. × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × Accelerating voltage V 2 V 1 × Indicates magnetic field perpendicularly into the page Electron beam Variable power supply Oppositely charged parallel plates Analysis: m e F F = or balanced forces d V E Bvq q E 2 , = = G G dv V B 2 = Special Notes: Method 2 • The method of determining the speed of the electrons must be explicit • The electron path and magnetic field must be perpendicular • The polarity on the power supplies must be consistent to accelerate the electrons and to produce an electric force in the opposite direction to the magnetic force • The direction of e m , F F and B must be consistent • The method of determine the position of the electron beam does not need to be practical. For example, it is not necessary for the student to explicitly identify how the electron path is observed.

7 Method 3 – Generator List: voltmeter Wire (or metal rod) ruler stopwatch or speed measuring devices Procedure: • measure length of wire (or rod) in the magnetic field • connect voltmeter across both ends of wire (or rod) • move wire (or rod) perpendicularly through the magnetic field at a uniform speed • determine speed using a measured distance with ruler and corresponding time interval with timer or use a speed measuring device • record induced voltage N S A F m F g Variable power supply Analysis: V = vlB and v = d/t B = V/vl Special Notes on Method 3 • timing devices may include radar gun, sonic ranger, stop watch • the length of the wire (or rod) in the magnetic field must be measured • the wire (or rod) must be moved perpendicular to the magnetic field

8 Method 4 – Current Balance 1 List: ammeter balance variable power supply wire (or rod) meter stick Procedure: • measure mass of wire or metal rod that will be levitated by the field • measure perpendicular length of magnetic field (This is the length of conductor in the magnetic field.) • complete a circuit with the variable power supply, the wire or metal rod and the ammeter all in series • place the wire or rod perpendicular to the magnetic field • adjust the current until the wire or metal rod is suspended in the magnetic field • record current N S A F m F g Variable power supply Analysis: g m F F = mg BIl = Il mg B = Special Notes: Method 4 • The length of the wire or metal rod in the magnetic field must be measured • The mass that will be lifted must be measured • The wire or rod must be perpendicular to the magnetic field • the direction of m F must be opposite gravity and consistent with the polarity of the power supply (i.e. the electron flow must be into the plane of the page through the wire)

9 Method 5 – Current Balance 2 List: ammeter balance wire or metal rod metre stick variable power supply string Procedure: • measure mass of wire or metal rod • measure perpendicular length of magnetic field (This is the length of conductor in the magnetic field.) • suspend the wire or rod from one arm of the balance • connect wires, rod, power supply and ammeter in series • zero the balance • adjust the current, record current • read the change in mass measured by the balance N S A Variable power supply F m Analysis: m F weight = ∆ BIl g m = ⋅ ∆ Il g m B ⋅ ∆ = Special Notes: Method 5 • The length of the wire or rod in the magnetic field must be measured • The wire or rod must be perpendicular to the magnetic field • Direction of forces do not matter. If m F is given, it must be consistent with the polarity of the power supply

10 Scoring Guide for Anaholistic Questions Major Concepts: Graphing data; Calculation of slope and identifying physics quantity; Balanced Forces; Data Analysis Score Criteria 5 In the response, the student • uses an appropriate method that reflects an excellent understanding of all major concepts • provides a complete description of the method used and shows a complete solution for the problem • states formulas explicitly • may make a minor error, omission, or inconsistency; however, this does not hinder the understanding of the physics content • draws diagrams that are appropriate, correct, and complete • may have an error in significant digits or rounding 4 In the response, the student • uses an appropriate method that reflects a good understanding of all major concepts or that reflects an excellent understanding of three of the major concepts • provides explanations that are correct and detailed • states most formulas explicitly and applies them correctly • makes minor errors, omissions, or inconsistencies in calculations and/or substitutions; however, these do not hinder the understanding of the physics content • draws most diagrams appropriately, correctly, and completely • may have errors in units, significant digits, rounding, or graphing 3 In the response, the student • uses an appropriate method that reflects a basic understanding of all four of the major concepts or that reflects a good understanding of three of the major concepts • uses an appropriate method that reflects an excellent understanding of two of the major concepts and that reflects a basic understanding of one of the two remaining concepts • uses formulas and/or diagrams that may be implicit, and these are applied correctly; however, errors in calculations and/or substitutions that hinder the understanding of the physics content are present • provides explanations that are correct but lack detail • has a major omission or inconsistency 2 In the response, the student • uses an appropriate method that reflects a basic understanding of three of the four major concepts or that reflects a good understanding of two of the major concepts • gives formulas and/or diagrams that are implicitly correct; however, they are not applied to determine the final solution or errors in the application of equations are present, but the answer is consistent with calculated results 1 In the response, the student • attempts at least two of the major concepts or uses an appropriate method that reflects a good understanding of one of the major concepts • makes errors in the formulas, diagrams, and/or explanations, and the answer is not consistent with calculated results 0 In the response, the student • identifies an area of physics that does not apply to the major concepts • uses inappropriate formulas, diagrams, and/or explanations NR No response is given.

11 Use the following information to answer the next question. In a modified Millikan apparatus, a small, charged object that has a mass of 3.8 × 10 –15 kg is suspended by the electric field that is between charged parallel plates. The table below shows how the balancing voltage depends on the distance between the plates. Plate separation (mm) Balancing voltage (10 3 V) 11.1 20.0 24.0 28.1 35.1 50.0 1.39 2.21 2.78 3.11 4.22 ? Written Response — 15% 2. • Provide a graph of the balancing voltage as a function of the plate separation, with the manipulated variable on the horizontal axis. • Calculate the slope of the graph, and describe the physical quantity or quantities that this slope represents. • Using the slope, or another suitable averaging technique, determine the magnitude of the charge on the suspended mass. • Determine the balancing voltage required when the plates are separated by 50.0 mm. Clearly communicate your understanding of the physics principles that you are using to solve this question. You may communicate this understanding mathematically, graphically, and/or with written statements.

12 Sample Solution • Provide a graph of the balancing voltage as a function of the plate separation, with the manipulated variable on the horizontal axis. Voltage as a Function of Plate Separation Voltage (10 3 V) Plate separation (10 –3 m) 0.0 1.0 2.0 3.0 4.0 5.0 6.0 0 10 20 30 40 50 • Calculate the slope of the graph and describe the physical quantity or quantities this slope represents. slope = rise/run = m ) 10 12 10 (38 V ) 10 4 . 1 10 4 . 4 ( 3 3 - 3 3 − × − × × − × = 1.15 × 10 5 V/m or consistent with graph The slope is the electric field between the plates or The slope is the gravitational force (weight) of the mass divided by the charge on the object

13 • Using the slope, or another suitable averaging technique, determine the magnitude of the charge on the suspended mass. Balanced forces gives: mg F = g and E q F = e and d V E = e g F F = d qV mg = V mgd q = Method 1 Using Slope slope = d V therefore, slope mg q = ) V/m 10 (1.15 ) m/s 81 . 9 )( kg 10 8 . 3 ( 5 2 15 × × = − q C 10 2 . 3 19 − × = q Method 2 Data Averaging C 10 98 . 2 V 10 39 . 1 m 10 1 . 11 ) m/s 81 . 9 )( kg 10 8 . 3 ( 19 3 3 2 15 1 − − − × = × × × × = q C 10 37 . 3 V 10 21 . 2 m 10 0 . 20 ) m/s 81 . 9 )( kg 10 8 . 3 ( 19 3 3 2 15 2 − − − × = × × × × = q C 10 22 . 3 V 10 78 . 2 m 10 0 . 24 ) m/s 81 . 9 )( kg 10 8 . 3 ( 19 3 3 2 15 3 − − − × = × × × × = q C 10 37 . 3 V 10 11 . 3 m 10 81 . 2 ) m/s 81 . 9 )( kg 10 8 . 3 ( 19 3 3 2 15 4 − − − × = × × × × = q C 10 10 . 3 V 10 22 . 4 m 10 51 . 3 ) m/s 81 . 9 )( kg 10 8 . 3 ( 19 3 3 2 15 5 − − − × = × × × × = q 5 C 10 604 . 1 18 − × = Σ = n q q C 10 2 . 3 19 − × = q

14 • Determine the balancing voltage required when the plates are separated by 50.0 mm. Method 1 Extrapolation from Graph The balancing voltage required for a plate separation of 50.0 mm can be found by reading up from 50.0 mm on the x -axis to the line of the graph and then left to the y -axis. The balancing voltage is V 10 8 . 5 3 × Method 2 Numerical Analysis d V = slope so d V (slope) = ) m 10 5.0 ( V/m) 10 (1.15 2 5 − × × = V V = V 10 8 . 5 3 ×

15 Special Case – Use of Graphing Calculator • Provide a graph of the balancing voltage as a function of the plate separation, with the manipulated variable on the horizontal axis. Balancing Voltage as a Function of Plate Separation y x x : [8.7, 37.5, 1] y : [0.9089, 4.7011, 1] x -axis is plate separation in mm (or 3 10 − m) y -axis is balancing voltage in 3 10 V • Calculate the slope of the graph and describe the physical quantity or quantities this slope represents. L1 = plate separation, d , in mm (or 3 10 − m) L2 = balancing voltage, V , in 10 3 V Using the linear regression function on the calculator ( ax + b ) L1, L2, Y gives slope = 1.16 × 10 5 V/m The slope is the electric field between the plates or The slope is the gravitational force (weight) of the mass divided by the charge on the object Notes 1. the definition (and units) of L1 and L2 and the order they are used in the linear regression must be consistent • Using the slope, or another suitable averaging technique, determine the magnitude of the charge on the suspended mass. Same as given in regular sample solution • Determine the balancing voltage required when the plates are separated by 50.0 mm. By extending window to include x = 50.0 mm and then using the trace function, the balancing voltage is V 10 8 . 5 3 ×