_ap06_frq_physicsb_fo_51783

AP® Physics B

2006 Free-Response Questions

Form B

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TABLE OF INFORMATION FOR 2006 and 2007 CONSTANTS AND CONVERSION FACTORS UNITS 1 unified atomic mass unit, Proton mass, Neutron mass, Electron charge magnitude, 1 u=1.66×10−27kg=931MeVc2PREFIXES mp=1.67×10−27kg mn=1.67×10−27kg e=1.60×10−19C Electron mass, me=9.11×10−31kg Avogadro’s number, N0=6.02×1023mol−1 Universal gas constant, R=8.31 J(moliK) Boltzmann’s constant, kB=1.38×10−23J/K Name Symbol Factor Prefix Symbol giga G 109 meter m 6 10 mega M kilogram kg 103 kilo k second s 10-2 centi c 10-3 milli m ampere A 10-6 micro m kelvin 10-9 nano n mole mol -12 10 pico p hertz Hz newton N Speed of light, Planck’s constant, c=3.00×10m/s 8 h=6.63×10−34 Jis =4.14×10−15 eVishc=1.99×10−25 JimVacuum permittivity, Vacuum permeability, =1.24×103 eVinm ⑀0=8.85×10−12C2Nim2 VALUES OF pascal Pa TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES Coulomb’s law constant, k=14π⑀0=9.0×109 Nim2C2 µ0=4π×10(Tim)A G=6.67×10−11m3kgis2 g=9.8 ms2 −7joule J θ sin θ cos θ tan θ watt W 󰁄00 1 0 coulomb C volt V 30󰁄 1/2 3/2 3/3 KW ohm 37󰁄 3/5 4/5 3/4 henry H 󰁄 45 2/2 2/2 1 farad F tesla T 53󰁄 4/5 3/5 4/3 degree 󰁄C 60󰁄 3/2 1/2 3 Celsius electron- volt eV 90󰁄 1 0 • Magnetic constant, k′=µ0/4π=10−7(T⋅m)A Universal gravitational constant, Acceleration due to gravity at Earth’s surface, 1 atmosphere pressure, 1 electron volt, 1 atm=1.0×105 Nm2=1.0×10 Pa1 eV=1.60×10−19J 5 The following conventions are used in 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. For mechanics and thermodynamics equations, W represents the work done on a system. 2 ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2006 and 2007 NEWTONIAN MECHANICSu=u0+at x=x0+u0t+12at 2u2=u02+2a(x-x0) ÂF=Fnet=ma Ffric£mN u2ac= rt=rF sin q p =mv J=FDt=Dp K=12mu 2DUg=mgh W=FDrcosq Pavg=W DtELECTRICITY AND MAGNETISM a = acceleration A = area 1q1q2F =F = force B = magnetic field 4p⑀0r2f = frequency C = capacitance Fh = height d = distance E= qJ = impulse E = electric field e = emf K = kinetic energy 1q1q2 U=qV=Ek = spring constant F = force 4p⑀0r󰁁 = length I = current Vm = mass 󰁁 = length Eavg=- dN = normal force P = power P = power Q = charge qi1= Vp = momentum q = point charge 4p⑀0irir = radius or distance R = resistance Qr = position vector r = distance C= VT = period t = time t = time U = potential (stored) energy ⑀0AC= U = potential energy V = electric potential or du = velocity or speed potential difference 11u = velocity or speed W = work done on a system Uc=QV=CV2 22r = resistivity x = position DQm = coefficient of friction fm = magnetic flux Iavg=Dtq = angle t = torque r󰁁R= AÂV=IR P=IV Cp=P=Fucosq Fs=-kx ÂCi iUs=12kx 211=Â CsiCiRs=ÂRi im Ts=2pkTp=2p󰁁 g1=RpÂRi1i FB=quBsinq FB=BI󰁁sinq m0I 2pr1T= fFG=-Gm1m2r2B= fm=BAcosq UGGm1m2=- r eavg=-Dfm Dte3 =B󰁁u ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2006 and 2007 FLUID MECHANICS AND THERMAL PHYSICS WAVES AND OPTICS P=P0+rgh Fbuoy=rVg A1u1=A2u2 1P+rgy+ru2= const. 2D󰁁=a󰁁0DT H=P=kADT LF APV=nRT=NkBT Kavg=3kT2Burms=3RT=M3kBT mW=-PDV DU=Q+W e=ec= W QHTH-TC THA = area e = efficiency F = force h = depth H = rate of heat transfer k = thermal conductivity Kavg = average molecular kinetic energy 󰁁 = length L = thickness M = molar mass n = number of moles N = number of molecules P = pressure Q = heat transferred to a system T = temperature U = internal energy V = volume u= velocity or speed urms = root-mean-square velocity W = work done on a system y = height a = coefficient of linear expansion m= mass of molecule r= density u=fl n=c un1sinq1=n2sinq2 sinqc=n2 n1111+= sis0fhisiM==- h0s0R 2dsinq=ml f=d = separation f = frequency or focal length h = height L = distance M = magnification m = an integer n = index of refraction R = radius of curvature s = distance u = speed x = position l = wavelength q= angle xmϳmlL d GEOMETRY AND TRIGONOMETRYRectangle A=bh Triangle 1 A=bh 2Circle A=pr2 C=2pr Parallelepiped V=󰁁wh Cylinder V=pr2󰁁 ATOMIC AND NUCLEAR PHYSICS E=hf=pc Kmax=hf-f l=h pDE=(Dm)c2 E = energy f = frequency K = kinetic energy m = mass p = momentum l = wavelength f = work function A = area C = circumferenceV = volume S = surface area b = base h = height 󰁁 = length w = width r = radius S=2pr󰁁+2pr2 Sphere 4 V=pr3 3 S=4pr2 c aRight Triangle 90°q a2+b2=c2 b a sinq= c cosq=b c a tanq= b 4 2006 AP® PHYSICS B FREE-RESPONSE QUESTIONS (Form B) PHYSICS B SECTION II Time—90 minutes 6 Questions Directions: Answer all six questions, which are weighted according to the points indicated. The suggested time is about 17 minutes for answering each of questions 1-4, and about 11 minutes for answering each of questions 5-6. The parts within a question may not have equal weight. Show all your work in the goldenrod booklet in the spaces provided after each part, NOT in this lavender insert. 1. (15 points) A student wishing to determine experimentally the acceleration g due to gravity has an apparatus that holds a small steel sphere above a recording plate, as shown above. When the sphere is released, a timer automatically begins recording the time of fall. The timer automatically stops when the sphere strikes the recording plate. The student measures the time of fall for different values of the distance D shown above and records the data in the table below. These data points are also plotted on the graph. Distance of Fall (m) 0.10 0.50 1.00 1.70 2.00 Time of Fall (s) 0.14 0.32 0.46 0.59 0.63 (a) On the grid above, sketch the smooth curve that best represents the student’s data. © 2006 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). 5 GO ON TO THE NEXT PAGE. 2006 AP® PHYSICS B FREE-RESPONSE QUESTIONS (Form B) The student can use these data for distance D and time t to produce a second graph from which the acceleration g due to gravity can be determined. (b) If only the variables D and t are used, what quantities should the student graph in order to produce a linear relationship between the two quantities? (c) On the grid below, plot the data points for the quantities you have identified in part (b), and sketch the best straight-line fit to the points. Label your axes and show the scale that you have chosen for the graph. (d) Using the slope of your graph in part (c), calculate the acceleration g due to gravity in this experiment. (e) State one way in which the student could improve the accuracy of the results if the experiment were to be performed again. Explain why this would improve the accuracy. © 2006 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). 6 GO ON TO THE NEXT PAGE. 2006 AP® PHYSICS B FREE-RESPONSE QUESTIONS (Form B) 2. (15 points) A small block of mass M is released from rest at the top of the curved frictionless ramp shown above. The block slides down the ramp and is moving with a speed 3.5u0when it collides with a larger block of mass 1.5M at rest at the bottom of the incline. The larger block moves to the right at a speed 2u0 immediately after the collision. Express your answers to the following questions in terms of the given quantities and fundamental constants. (a) Determine the height h of the ramp from which the small block was released. (b) Determine the speed of the small block after the collision. (c) The larger block slides a distance D before coming to rest. Determine the value of the coefficient of kinetic friction m between the larger block and the surface on which it slides. (d) Indicate whether the collision between the two blocks is elastic or inelastic. Justify your answer. © 2006 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). 7 GO ON TO THE NEXT PAGE. 2006 AP® PHYSICS B FREE-RESPONSE QUESTIONS (Form B) 3. (15 points) Three electric charges are arranged on an x-y coordinate system, as shown above. Express all algebraic answers to the following parts in terms of Q, q, x, d, and fundamental constants. (a) On the diagram, draw vectors representing the forces F1 and F2 exerted on the +q charge by the +Q and –Q charges, respectively. (b) Determine the magnitude and direction of the total electric force on the +q charge. (c) Determine the electric field (magnitude and direction) at the position of the +q charge due to the other two charges. (d) Calculate the electric potential at the position of the +q charge due to the other two charges. (e) Charge +q is now moved along the positive x-axis to a very large distance from the other two charges. The magnitude of the force on the +q charge at this large distance now varies as 1/x3. Explain why this happens. © 2006 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). 8 GO ON TO THE NEXT PAGE. 2006 AP® PHYSICS B FREE-RESPONSE QUESTIONS (Form B) 4. (15 points) A ray of red light in air (l=650 nm) is incident on a semicircular block of clear plastic (n = 1.51 for this light), as shown above. The ray strikes the block at its center of curvature at an angle of incidence of 27°. (a) Part of the incident ray is reflected and part is refracted at the first interface. i. Determine the angle of reflection at the first interface. Draw and label the reflected ray on the diagram above. ii. Determine the angle of refraction at the first interface. Draw and label the refracted ray on the diagram above. iii. Determine the speed of the light in the plastic block. iv. Determine the wavelength of the light in the plastic block. (b) The source of red light is replaced with one that produces blue light (l=450 nm), for which the plastic has a greater index of refraction than for the red light. Qualitatively describe what happens to the reflected and refracted rays. (c) The semicircular block is removed and the blue light is directed perpendicularly through a double slit and onto a screen. The distance between the slits is 0.15 mm. The slits are 1.4 m from the screen. i. On the diagram of the screen below, sketch the pattern of light that you should expect to see. ii. Calculate the distance between two adjacent bright fringes. © 2006 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). 9 GO ON TO THE NEXT PAGE. 2006 AP® PHYSICS B FREE-RESPONSE QUESTIONS (Form B) 5. (10 points) A sample of ideal gas is taken through steps I, II, and III in a closed cycle, as shown on the pressure P versus volume V diagram above, so that the gas returns to its original state. The steps in the cycle are as follows. I. An isothermal expansion occurs from point A to point B, and the volume of the gas doubles. II. An isobaric compression occurs from point B to point C, and the gas returns to its original volume. III. A constant volume addition of heat occurs from point C to point A and the gas returns to its original pressure. (a) Determine numerical values for the following ratios, justifying your answers in the spaces next to each ratio. P i. B= PA ii. PC= PATB= TATC= TA iii. iv. (b) During step I, the change in internal energy is zero. Explain why. (c) During step III, the work done on the gas is zero. Explain why. © 2006 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). 10 GO ON TO THE NEXT PAGE. 2006 AP® PHYSICS B FREE-RESPONSE QUESTIONS (Form B) 6. (10 points) An electron of mass m is initially moving with a constant speed u, where u<