2008 Semifinal Exam AAPT UNITEDSTATES PHYSICS TEAM AIP 2008 Semifinal Exam DO NOT DISTRIBUTE THIS PAGE Important Instructions for the Exam Supervisor This examination consists of three parts. Part A has four questions and is allowed 90 minutes. Part B has two questions and is allowed 90 minutes. Part C has one question and is allowed 20 minutes.The answer for Part C will not be used for team selection,but will be used for special recognition from the Optical Society of America. The first page that follows is a cover sheet.Examinees may keep the cover sheet for all three parts of the exam. The three parts are then identified by the center header on each page.Examinees are only allowed to do one part at a time,and may not work on other parts,even if they have time remaining. Allow 90 minutes to complete Part A.Do not let students look at Part B or Part C.Collect the answers to Part A before allowing the examinee to begin Part B.Examinees are allowed a 10 to 15 minutes break between parts A and B. Allow 90 minutes to complete Part B.Do not let students look at Part C or go back to Part A.Collect the answers to part B before allowing the examinee to begin Part C.Examinees are allowed a 10 to 15 minutes break between Parts B and C. Allow 20 minutes to complete Part C.This part is optional;scores on Part C will not be used to select the US Team.Examinees may not go back to Part A or B. Ideally the test supervisor will divide the question paper into 4 parts:the cover sheet (page 2),Part A (pages 3-7),Part B(pages 8-10),and Part C(page 11).Examinees should be provided the parts individually,although they may keep the cover sheet. The supervisor must collect all examination questions,including the cover sheet,at the end of the exam, as well as any scratch paper used by the examinees.Examinees may not take the exam questions.The examination questions may be returned to the students after March 31,2008. Examinees are allowed calculators,but they may not use symbolic math,programming,or graphic features of these calculators.Calculators may not be shared and their memory must be cleared of data and programs.Cell phones,PDA's or cameras may not be used during the exam or while the exam papers are present.Examinees may not use any tables,books,or collections of formulas. Please provide the examinees with graph paper for Part A. Copyright C2008 American Association of Physics Teachers
2008 Semifinal Exam 1 AAPT UNITED STATES PHYSICS TEAM AIP 2008 Semifinal Exam DO NOT DISTRIBUTE THIS PAGE Important Instructions for the Exam Supervisor • This examination consists of three parts. • Part A has four questions and is allowed 90 minutes. • Part B has two questions and is allowed 90 minutes. • Part C has one question and is allowed 20 minutes. The answer for Part C will not be used for team selection, but will be used for special recognition from the Optical Society of America. • The first page that follows is a cover sheet. Examinees may keep the cover sheet for all three parts of the exam. • The three parts are then identified by the center header on each page. Examinees are only allowed to do one part at a time, and may not work on other parts, even if they have time remaining. • Allow 90 minutes to complete Part A. Do not let students look at Part B or Part C. Collect the answers to Part A before allowing the examinee to begin Part B. Examinees are allowed a 10 to 15 minutes break between parts A and B. • Allow 90 minutes to complete Part B. Do not let students look at Part C or go back to Part A. Collect the answers to part B before allowing the examinee to begin Part C. Examinees are allowed a 10 to 15 minutes break between Parts B and C. • Allow 20 minutes to complete Part C. This part is optional; scores on Part C will not be used to select the US Team. Examinees may not go back to Part A or B. • Ideally the test supervisor will divide the question paper into 4 parts: the cover sheet (page 2), Part A (pages 3-7), Part B (pages 8-10), and Part C (page 11). Examinees should be provided the parts individually, although they may keep the cover sheet. • The supervisor must collect all examination questions, including the cover sheet, at the end of the exam, as well as any scratch paper used by the examinees. Examinees may not take the exam questions. The examination questions may be returned to the students after March 31, 2008. • Examinees are allowed calculators, but they may not use symbolic math, programming, or graphic features of these calculators. Calculators may not be shared and their memory must be cleared of data and programs. Cell phones, PDA’s or cameras may not be used during the exam or while the exam papers are present. Examinees may not use any tables, books, or collections of formulas. • Please provide the examinees with graph paper for Part A. Copyright c 2008 American Association of Physics Teachers
2008 Semifinal Exam Cover Sheet 2 AAPT UNITEDSTATES PHYSICS TEAM AIP 2008 Semifinal Exam INSTRUCTIONS DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD TO BEGIN Work Part A first.You have 90 minutes to complete all four problems.Each question is worth 25 points.Do not look at Parts B or C during this time. After you have completed Part A you may take a break. Then work Part B.You have 90 minutes to complete both problems.Each question is worth 50 points. Do not look at Parts A or C during this time. Show all your work.Partial credit will be given.Do not write on the back of any page.Do not write anything that you wish graded on the question sheets. Start each question on a new sheet of paper.Put your school ID number,your name,the question number and the page number/total pages for this problem,in the upper right hand corner of each page.For example, School ID# Doe,Jamie A1-1/3 A hand-held calculator may be used.Its memory must be cleared of data and programs.You may use only the basic functions found on a simple scientific calculator.Calculators may not be shared.Cell phones,PDA's or cameras may not be used during the exam or while the exam papers are present. You may not use any tables,books,or collections of formulas. Questions with the same point value are not necessarily of the same difficulty. Part C is an optional part of the test.You will be given 20 additional minutes to complete Part C. Your score on Part C will not affect the selection for the US Team,but can be used for special prizes and recognition to be awarded by the Optical Society of America. In order to maintain exam security,do not communicate any information about the questions (or their answers/solutions)on this contest until after March 31,2008. Possibly Useful Information.You may use this sheet for all three parts of the exam. g=9.8 N/kg G=6.67×10-11N.m2/kg2 k=1/4xe0=8.99×109N.m2/C2 km Ho/4T 10-7 T.m/A c=3.00×108m/s kB=1.38×10-23J/K NA=6.02×1023(mol)-1 R=NAkB =8.31 J/(mol.K) σ=5.67×10-8J/(sm2.K4) e=1.602×10-19C 1eV=1.602×10-19J h=6.63×10-34J.s=4.14×10-15eV.s me=9.109×10-31kg=0.511MeV/c2(1+x)n≈1+nz for<1 sin0≈0-93forl0l<1 cos0≈1-号92for|9<1 Copyright C2008 American Association of Physics Teachers
2008 Semifinal Exam Cover Sheet 2 AAPT UNITED STATES PHYSICS TEAM AIP 2008 Semifinal Exam INSTRUCTIONS DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD TO BEGIN • Work Part A first. You have 90 minutes to complete all four problems. Each question is worth 25 points. Do not look at Parts B or C during this time. • After you have completed Part A you may take a break. • Then work Part B. You have 90 minutes to complete both problems. Each question is worth 50 points. Do not look at Parts A or C during this time. • Show all your work. Partial credit will be given. Do not write on the back of any page. Do not write anything that you wish graded on the question sheets. • Start each question on a new sheet of paper. Put your school ID number, your name, the question number and the page number/total pages for this problem, in the upper right hand corner of each page. For example, School ID # Doe, Jamie A1 - 1/3 • A hand-held calculator may be used. Its memory must be cleared of data and programs. You may use only the basic functions found on a simple scientific calculator. Calculators may not be shared. Cell phones, PDA’s or cameras may not be used during the exam or while the exam papers are present. You may not use any tables, books, or collections of formulas. • Questions with the same point value are not necessarily of the same difficulty. • Part C is an optional part of the test. You will be given 20 additional minutes to complete Part C. Your score on Part C will not affect the selection for the US Team, but can be used for special prizes and recognition to be awarded by the Optical Society of America. • In order to maintain exam security, do not communicate any information about the questions (or their answers/solutions) on this contest until after March 31, 2008. Possibly Useful Information. You may use this sheet for all three parts of the exam. g = 9.8 N/kg G = 6.67 × 10−11 N · m2/kg2 k = 1/4πǫ0 = 8.99 × 109 N · m2/C 2 km = µ0/4π = 10−7 T · m/A c = 3.00 × 108 m/s kB = 1.38 × 10−23 J/K NA = 6.02 × 1023 (mol)−1 R = NAkB = 8.31 J/(mol · K) σ = 5.67 × 10−8 J/(s · m2 · K4 ) e = 1.602 × 10−19 C 1eV = 1.602 × 10−19 J h = 6.63 × 10−34 J · s = 4.14 × 10−15 eV · s me = 9.109 × 10−31 kg = 0.511 MeV/c 2 (1 + x) n ≈ 1 + nx for |x| ≪ 1 sin θ ≈ θ − 1 6 θ 3 for |θ| ≪ 1 cos θ ≈ 1 − 1 2 θ 2 for |θ| ≪ 1 Copyright c 2008 American Association of Physics Teachers
2008 Semifinal Exam Part A 3 Part A Question Al Four square metal plates of area A are arranged at an even spacing d as shown in the diagram.(Assume that Ad2.) Plate I Plate 3 ate4 Plates 1 and 4 are first connected to a voltage source of magnitude Vo,with plate 1 positive;plates 2 and 3 are then connected together with a wire.The wire is subsequently removed.Finally,the voltage source attached between plates 1 and 4 is replaced with a wire.The steps are summarized in the diagrams below Step I Step 2 Step 3 Find the resulting potential difference AVi2 between plates 1 and 2;like wise find AV23 and AV34,defined similarly. Assume,in each case,that a positive potential difference means that the top plate is at a higher potential than the bottom plate. Copyright C2008 American Association of Physics Teachers
2008 Semifinal Exam Part A 3 Part A Question A1 Four square metal plates of area A are arranged at an even spacing d as shown in the diagram. (Assume that A ≫ d 2 .) Plate 1 Plate 2 Plate 3 Plate 4 d d d Plates 1 and 4 are first connected to a voltage source of magnitude V0, with plate 1 positive; plates 2 and 3 are then connected together with a wire. The wire is subsequently removed. Finally, the voltage source attached between plates 1 and 4 is replaced with a wire. The steps are summarized in the diagrams below. Step 1 Step 2 Step 3 Find the resulting potential difference ∆V12 between plates 1 and 2; like wise find ∆V23 and ∆V34, defined similarly. Assume, in each case, that a positive potential difference means that the top plate is at a higher potential than the bottom plate. Copyright c 2008 American Association of Physics Teachers
2008 Semifinal Exam Part A Question A2 A simple heat engine consists of a moveable piston in a cylinder filled with an ideal monatomic gas.Initially the gas in the cylinder is at a pressure Po and volume Vo.The gas is slowly heated at constant volume.Once the pressure reaches 32Po the piston is released,allowing the gas to expand so that no heat either enters or escapes the gas as the piston moves.Once the pressure has returned to Po the outside of the cylinder is cooled back to the original temperature,keeping the pressure constant.For the monatomic ideal gas you should assume that the molar heat capacity at constant volume is given by Cy=R,where R is the ideal gas constant.You may express your answers in fractional form or as decimals.If you choose decimals,keep three significant figures in your calculations.The diagram below is not necessarily drawn to scale. 32P0 Po Vo Vmax Volume a.Let Vax be the maximum volume achieved by the gas during the cycle.What is Vax in terms of Vo?If you are unable to solve this part of the problem,you may express your answers to the remaining parts in terms of Vmax without further loss of points. b.In terms of Po and Vo determine the heat added to the gas during a complete cycle. c.In terms of Po and Vo determine the heat removed from the gas during a complete cycle. d.What is the efficiency of this cycle? Copyright C2008 American Association of Physics Teachers
2008 Semifinal Exam Part A 4 Question A2 A simple heat engine consists of a moveable piston in a cylinder filled with an ideal monatomic gas. Initially the gas in the cylinder is at a pressure P0 and volume V0. The gas is slowly heated at constant volume. Once the pressure reaches 32P0 the piston is released, allowing the gas to expand so that no heat either enters or escapes the gas as the piston moves. Once the pressure has returned to P0 the outside of the cylinder is cooled back to the original temperature, keeping the pressure constant. For the monatomic ideal gas you should assume that the molar heat capacity at constant volume is given by CV = 3 2R, where R is the ideal gas constant. You may express your answers in fractional form or as decimals. If you choose decimals, keep three significant figures in your calculations. The diagram below is not necessarily drawn to scale. Pressure P 0 0 V0 32P Vmax Volume a. Let Vmax be the maximum volume achieved by the gas during the cycle. What is Vmax in terms of V0? If you are unable to solve this part of the problem, you may express your answers to the remaining parts in terms of Vmax without further loss of points. b. In terms of P0 and V0 determine the heat added to the gas during a complete cycle. c. In terms of P0 and V0 determine the heat removed from the gas during a complete cycle. d. What is the efficiency of this cycle? Copyright c 2008 American Association of Physics Teachers
2008 Semifinal Exam Part A 5 Question A3 A certain planet of radius R is composed of a uniform material that,through radioactive decay,generates a net power P.This results in a temperature differential between the inside and outside of the planet as heat is transfered from the interior to the surface. The rate of heat transfer is governed by the thermal conductivity.The thermal conductivity of a ma- terial is a measure of how quickly heat flows through that material in response to a temperature gradient. Specifically,consider a thin slab of material of area A and thickness Ax where one surface is hotter than the other by an amount AT.Suppose that an amount of heat AQ flows through the slab in a time At.The thermal conductivity k of the material is then k=414x △tA△T It is found that k is approximately constant for many materials;assume that it is constant for the planet. For the following assume that the planet is in a steady state;temperature might depend on position,but does not depend on time. a.Find an expression for the temperature of the surface of the planet assuming blackbody radiation,an emissivity of 1,and no radiation incident on the planet surface.You may express your answer in terms of any of the above variables and the Stephan-Boltzmann constant o. b.Find an expression for the temperature difference between the surface of the planet and the center of the planet.You may express your answer in terms of any of the above variables;you do not need to answer part (a)to be able to answer this part. Copyright C2008 American Association of Physics Teachers
2008 Semifinal Exam Part A 5 Question A3 A certain planet of radius R is composed of a uniform material that, through radioactive decay, generates a net power P. This results in a temperature differential between the inside and outside of the planet as heat is transfered from the interior to the surface. The rate of heat transfer is governed by the thermal conductivity. The thermal conductivity of a material is a measure of how quickly heat flows through that material in response to a temperature gradient. Specifically, consider a thin slab of material of area A and thickness ∆x where one surface is hotter than the other by an amount ∆T . Suppose that an amount of heat ∆Q flows through the slab in a time ∆t. The thermal conductivity k of the material is then k = ∆Q ∆t 1 A ∆x ∆T . It is found that k is approximately constant for many materials; assume that it is constant for the planet. For the following assume that the planet is in a steady state; temperature might depend on position, but does not depend on time. a. Find an expression for the temperature of the surface of the planet assuming blackbody radiation, an emissivity of 1, and no radiation incident on the planet surface. You may express your answer in terms of any of the above variables and the Stephan-Boltzmann constant σ. b. Find an expression for the temperature difference between the surface of the planet and the center of the planet. You may express your answer in terms of any of the above variables; you do not need to answer part (a) to be able to answer this part. Copyright c 2008 American Association of Physics Teachers
2008 Semifinal Exam Part A 6 Question A4 A tape recorder playing a single tone of frequency fo is dropped from rest at a height h.You stand directly underneath the tape recorder and measure the frequency observed as a function of time.Here t=0s is the time at which the tape recorder was dropped. t (s)f (Hz) 2.0 581 4.0 619 6.0 665 8.0 723 10.0 801 The acceleration due to gravity is g=9.80 m/s2 and the speed of sound in air is vsnd =340 m/s.Ignore air resistance.You might need to use the Doppler shift formula for co-linear motion of sources and observers in still air, f=snd土obs Usnd士Usrd where fo is the emitted frequency as determined by the source,f is the frequency as detected by the observer, and Usnd,Usre,and vobs are the speed of sound in air,the speed of the source,and the speed of the observer. The positive and negative signs are dependent upon the relative directions of the motions of the source and the observer. a.Determine the frequency measured on the ground at time t,in terms of fo,g,h,and vsnd.Consider only the case where the falling tape recorder doesn't exceed the speed of sound Usnd. b.Verify graphically that your result is consistent with the provided data. c.What (numerically)is the frequency played by the tape recorder? d.From what height h was the tape recorder dropped? Copyright C2008 American Association of Physics Teachers
2008 Semifinal Exam Part A 6 Question A4 A tape recorder playing a single tone of frequency f0 is dropped from rest at a height h. You stand directly underneath the tape recorder and measure the frequency observed as a function of time. Here t = 0 s is the time at which the tape recorder was dropped. t (s) f (Hz) 2.0 581 4.0 619 6.0 665 8.0 723 10.0 801 The acceleration due to gravity is g = 9.80 m/s 2 and the speed of sound in air is vsnd = 340 m/s. Ignore air resistance. You might need to use the Doppler shift formula for co-linear motion of sources and observers in still air, f = f0 vsnd ± vobs vsnd ± vsrc where f0 is the emitted frequency as determined by the source, f is the frequency as detected by the observer, and vsnd, vsrc, and vobs are the speed of sound in air, the speed of the source, and the speed of the observer. The positive and negative signs are dependent upon the relative directions of the motions of the source and the observer. a. Determine the frequency measured on the ground at time t, in terms of f0, g, h, and vsnd. Consider only the case where the falling tape recorder doesn’t exceed the speed of sound vsnd. b. Verify graphically that your result is consistent with the provided data. c. What (numerically) is the frequency played by the tape recorder? d. From what height h was the tape recorder dropped? Copyright c 2008 American Association of Physics Teachers
2008 Semifinal Exam Part A STOP:Do Not Continue to Part B If there is still time remaining for Part A,you should review your work for Part A,but do not continue to Part B until instructed by your exam supervisor. Copyright C2008 American Association of Physics Teachers
2008 Semifinal Exam Part A 7 STOP: Do Not Continue to Part B If there is still time remaining for Part A, you should review your work for Part A, but do not continue to Part B until instructed by your exam supervisor. Copyright c 2008 American Association of Physics Teachers
2008 Semifinal Exam Part B 8 Part B Question B1 A platform is attached to the ground by an ideal spring of constant k;both the spring and the platform have negligible mass;assume that your mass is mp.Sitting on the platform is a rather large lump of clay of mass me =rmp,with r some positive constant that measures the ratio me/mp.You then gently step onto the platform,and the platform settles down to a new equilibrium position,a vertical distance D below the original position.Throughout the problem assume that you never lose contact with the platform. h a.You then slowly pick up the lump of clay and hold it a height h above the platform.Upon releasing the clay you and the platform will oscillate up and down;you notice that the clay strikes the platform after the platform has completed exactly one oscillation.Determine the numerical value of the ratio h/D b.Assume the resulting collision between the clay and the platform is completely inelastic.Find the ratio of the amplitude of the oscillation of the platform after the collision(Ar)to the amplitude of the oscillations of the platform before the collision(Ai).Determine Ar/Ai in terms of the mass ratio r and any necessary numerical constants. c.Sketch a graph of the position of the platform as a function of time,with t=0 corresponding to the moment when the clay is dropped.Show one complete oscillation after the clay has collided with the platform.It is not necessary to use graph paper. d.The above experiment is only possible if the mass ratio r is less than some critical value re.Otherwise, despite the clay having been dropped from the height determined in part(a),the oscillating platform will hit the clay before the platform has completed one full oscillation.On your graph in part (c) sketch the position of the clay as a function of time relative to the position of the platform for the mass ratio r =re. Copyright C2008 American Association of Physics Teachers
2008 Semifinal Exam Part B 8 Part B Question B1 A platform is attached to the ground by an ideal spring of constant k; both the spring and the platform have negligible mass; assume that your mass is mp. Sitting on the platform is a rather large lump of clay of mass mc = rmp, with r some positive constant that measures the ratio mc/mp. You then gently step onto the platform, and the platform settles down to a new equilibrium position, a vertical distance D below the original position. Throughout the problem assume that you never lose contact with the platform. D h a. You then slowly pick up the lump of clay and hold it a height h above the platform. Upon releasing the clay you and the platform will oscillate up and down; you notice that the clay strikes the platform after the platform has completed exactly one oscillation. Determine the numerical value of the ratio h/D. b. Assume the resulting collision between the clay and the platform is completely inelastic. Find the ratio of the amplitude of the oscillation of the platform after the collision (Af) to the amplitude of the oscillations of the platform before the collision (Ai). Determine Af/Ai in terms of the mass ratio r and any necessary numerical constants. c. Sketch a graph of the position of the platform as a function of time, with t = 0 corresponding to the moment when the clay is dropped. Show one complete oscillation after the clay has collided with the platform. It is not necessary to use graph paper. d. The above experiment is only possible if the mass ratio r is less than some critical value rc. Otherwise, despite the clay having been dropped from the height determined in part (a), the oscillating platform will hit the clay before the platform has completed one full oscillation. On your graph in part (c) sketch the position of the clay as a function of time relative to the position of the platform for the mass ratio r = rc. Copyright c 2008 American Association of Physics Teachers
2008 Semifinal Exam Part B 9 Question B2 Consider a parallel plate capacitor with the plates vertical.The plates of the capacitor are rigidly supported in place.The distance between the plates is d.The plates have height h and area Ad2.Assume throughout this problem that the force of air resistance may be neglected;however,the force of gravity cannot be neglected.Neglect any edge effects as well as any magnetic effects. d/2 d a.A small metal ball with a mass M and a charge g is suspended from a string of length L that is tied to a rigid support.When the capacitor is not charged,the metal ball is located at the center of the capacitor-at a distance d/2 from both plates and at a height h/2 above the bottom edge of the plates. If instead a constant potential difference Vo is applied across the plates,the string will make an angle 0o to the vertical when the metal ball is in equilibrium. i.Determine 0o in terms of the given quantities and fundamental constants ii.The metal ball is then lifted until it makes an angle 6 to the vertical where 0 is only slightly greater than 0o.The metal ball is then released from rest.Show that the resulting motion is simple harmonic motion and find the period of the oscillations in terms of the given quantities and fundamental constants. iii.When the ball is at rest in the equilibrium position 0o,the string is cut.What is the maximum value for Vo so that the ball will not hit one of the plates before exiting?Express your answer in terms of the given quantities and fundamental constants. b.Suppose instead that the ball of mass M and charge g is released from rest at a point halfway between the plates at a time t=0.Now,an AC potential difference V(t)=Vo sinwt is also placed across the capacitor.The ball may hit one of the plates before it falls(under the influence of gravity)out of the region between the plates.If Vo is sufficiently large,this will only occur for some range of angular frequencies wmin Vg/h.Making these assumptions,find expressions for wmin and wmax in terms of the given quantities and or fundamental constants. c.Assume that the region between the plates is not quite a vacuum,but instead humid air with a uniform resistivity p.Ignore any effects because of the motion of the ball,and assume that the humid air doesn't change the capacitance of the original system. i.Determine the resistance between the plates. ii.If the plates are originally charged to a constant potential source Vo,and then the potential is removed,how much time is required for the potential difference between the plates to decrease to a value of Vo/e,where Ine =1? iii.If the plates are instead connected to an AC potential source so that the potential difference across the plates is Vo sinwt,determine the amplitude lo of the alternating current through the potential source. Copyright C2008 American Association of Physics Teachers
2008 Semifinal Exam Part B 9 Question B2 Consider a parallel plate capacitor with the plates vertical. The plates of the capacitor are rigidly supported in place. The distance between the plates is d. The plates have height h and area A ≫ d 2 . Assume throughout this problem that the force of air resistance may be neglected; however, the force of gravity cannot be neglected. Neglect any edge effects as well as any magnetic effects. h d/2 h/2 L h d Rigid Support String a. A small metal ball with a mass M and a charge q is suspended from a string of length L that is tied to a rigid support. When the capacitor is not charged, the metal ball is located at the center of the capacitor— at a distance d/2 from both plates and at a height h/2 above the bottom edge of the plates. If instead a constant potential difference V0 is applied across the plates, the string will make an angle θ0 to the vertical when the metal ball is in equilibrium. i. Determine θ0 in terms of the given quantities and fundamental constants. ii. The metal ball is then lifted until it makes an angle θ to the vertical where θ is only slightly greater than θ0. The metal ball is then released from rest. Show that the resulting motion is simple harmonic motion and find the period of the oscillations in terms of the given quantities and fundamental constants. iii. When the ball is at rest in the equilibrium position θ0, the string is cut. What is the maximum value for V0 so that the ball will not hit one of the plates before exiting? Express your answer in terms of the given quantities and fundamental constants. b. Suppose instead that the ball of mass M and charge q is released from rest at a point halfway between the plates at a time t = 0. Now, an AC potential difference V (t) = V0 sin ωt is also placed across the capacitor. The ball may hit one of the plates before it falls (under the influence of gravity) out of the region between the plates. If V0 is sufficiently large, this will only occur for some range of angular frequencies ωmin < ω < ωmax. You may assume that ωmin ≪ p g/h and ωmax ≫ p g/h. Making these assumptions, find expressions for ωmin and ωmax in terms of the given quantities and/or fundamental constants. c. Assume that the region between the plates is not quite a vacuum, but instead humid air with a uniform resistivity ρ. Ignore any effects because of the motion of the ball, and assume that the humid air doesn’t change the capacitance of the original system. i. Determine the resistance between the plates. ii. If the plates are originally charged to a constant potential source V0, and then the potential is removed, how much time is required for the potential difference between the plates to decrease to a value of V0/e, where ln e = 1? iii. If the plates are instead connected to an AC potential source so that the potential difference across the plates is V0 sin ωt, determine the amplitude I0 of the alternating current through the potential source. Copyright c 2008 American Association of Physics Teachers
2008 Semifinal Exam Part B 10 STOP:Do Not Continue to Part C If there is still time remaining for Part B,you should review your work for Part B,but do not continue to Part C until instructed by your exam supervisor.You may not return to Part A Copyright C2008 American Association of Physics Teachers
2008 Semifinal Exam Part B 10 STOP: Do Not Continue to Part C If there is still time remaining for Part B, you should review your work for Part B, but do not continue to Part C until instructed by your exam supervisor. You may not return to Part A Copyright c 2008 American Association of Physics Teachers
