2004 - AP® Physics C: Mechanics 2004 Free-Response...

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Unformatted text preview: AP® Physics C: Mechanics 2004 Free-Response Questions The materials included in these files are intended for noncommercial use by AP teachers for course and exam preparation; permission for any other use ® must be sought from the Advanced Placement Program . Teachers may reproduce them, in whole or in part, in limited quantities, for face-to-face teaching purposes but may not mass distribute the materials, electronically or otherwise. This permission does not apply to any third-party copyrights contained herein. These materials and any copies made of them may not be resold, and the copyright notices must be retained as they appear here. The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in 1900, the association is composed of more than 4,500 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three million students and their parents, 23,000 high schools, and 3,500 colleges through major programs and services in college admissions, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SAT®, the PSAT/NMSQT®, and the Advanced Placement Program® (AP®). The College Board is committed to the principles of excellence and equity, and that commitment is embodied in all of its programs, services, activities, and concerns. For further information, visit www.collegeboard.com Copyright © 2004 College Entrance Examination Board. All rights reserved. College Board, Advanced Placement Program, AP, AP Central, AP Vertical Teams, APCD, Pacesetter, Pre-AP, SAT, Student Search Service, and the acorn logo are registered trademarks of the College Entrance Examination Board. PSAT/NMSQT is a registered trademark jointly owned by the College Entrance Examination Board and the National Merit Scholarship Corporation. Educational Testing Service and ETS are registered trademarks of Educational Testing Service. Other products and services may be trademarks of their respective owners. For the College Board’s online home for AP professionals, visit AP Central at apcentral.collegeboard.com. TABLE OF INFORMATION FOR 2004 and 2005 CONSTANTS AND CONVERSION FACTORS 27 = 1.66 = 931 MeV/c ¥ 1 unified atomic mass unit, 10 - 1u UNITS Name Symbol 10 9 giga G kilogram kg 10 6 mega M 10 3 kilo k centi c milli m micro µ nano n pico p mn = 1.67 × 10 −27 kg second s Electron mass, me = 9.11 × 10 −31 kg ampere A e = 1.60 × 10 C kelvin N0 = 6.02 × 10 23 mol −1 R = Universal gas constant, K mole mol hertz 8.31 J / ( mol K ) ◊ Avogadro’s number, Hz Boltzmann’s constant, k B = 1.38 × 10 −23 J / K Speed of light, c = 3.00 × 10 8 m / s newton N Planck’s constant, h = 6.63 × 10 −34 J ⋅ s pascal Pa = 4.14 × 10 −15 eV ⋅ s hc = 1.99 × 10 −25 k = 1 / 4π J W θ sin θ cos θ tan θ C 0 0 1 0 V Ω 30 1/2 3 /2 3 /3 henry H 37 3/5 4/5 3/4 farad F tesla T 45 2 /2 2 /2 1 degree Celsius C 53 4/5 3/5 4/3 electronvolt eV 60 3 /2 1/2 3 90 k = µ 0 / 4π = 10 −7 (T ⋅ m) / A = G 6.67 ¥ 1 atmosphere pressure, VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES volt 2 = 9.0 × 10 9 N ⋅ m 2 / C 2 g = 9.8 m / s 10 11 - Acceleration due to gravity at the Earth’s surface, 10 −12 1 0 ∞ ' Universal gravitational constant, 10 −9 ohm C / N⋅m 2 µ 0 = 4π × 10 −7 (T ⋅ m) / A Vacuum permeability, Magnetic constant, 0 = 8.85 × 10 10 −6 coulomb 3 m / kg s ◊ Coulomb’s law constant, 0 10 −3 watt J⋅m −12 10 −2 joule = 1.24 × 10 3 eV ⋅ nm Vacuum permittivity, Symbol m Neutron mass, Magnitude of the electron charge, Prefix meter 2 −19 Factor kg m p = 1.67 × 10 −27 kg Proton mass, PREFIXES 2 1 atm = 1.0 × 10 5 N / m 2 2 = 1.0 × 10 5 Pa 1 electron volt, 1 eV = 1.60 × 10 −19 J 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. 2 ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2004 and 2005 = q t a= = w = w q = q + -= w + 0t 12 t 2 w 1 Ri FM = qv × B B•d = 1 f m k Bs = = = -= p m ˆ r e r2 Gm1m2 r 0 nI = B • dA dm dt dI = −L dt 12 U L = LI 2 e p g Gm1m2 0I F= Id ×B f = FG i 3 =− f w p 2 = Tp 1 = Rp Ri z = 2 i P = IV 12 kx 2 2 -= UG Rs = t a + 0 a Ts w= T A V = IR z u Us R= I kx Fs 0 dQ dt 1 1 Uc = QV = CV 2 2 2 I= m ¥= w= Â= Ú= K rp 12 I 2 1 1 = Cs i Ci m t = t =t ¥ r m Ci i ∑  Â= mr mr 2 Cp = d ∑ = r 2 dm a w u = w I net rcm L m D = F 0A r u I r Q V ∑ = r 2 0 q1 q 2 r Q q R r t U V = = = = = = = = = m= = k = u r C= 4 1 f Ú= ∑ 2 C= ∑ £ m ac UE = qV = r u = Ú= F dr 12 K m 2 dW P dt P Fv Ug mgh k N p D= = W = F fric p acceleration force frequency height rotational inertia impulse kinetic energy spring constant length angular momentum mass normal force power momentum radius or distance position vector period time potential energy velocity or speed work done on a system position coefficient of friction angle torque angular speed angular acceleration p = =u u dp dt F dt mv ma = = = = = = = = = L= m= N= P= p= r= r= T= t= U= = W= x= = = = = = ∑ + J p ( F Fnet - F ) = 2 0 a F f h I J K k e + u u 2 12 at 2 2 a x x0 0t + = u x0 at + x 0 ELECTRICITY AND MAGNETISM 1 q1 q 2 A = area F= 2 B = magnetic field 40r C = capacitance F d = distance E= q E = electric field = emf Q E • dA = F = force 0 I = current dV L = inductance E=− = length dr n = number of loops of wire qi 1 V= per unit length 4 0 i ri P = power p MECHANICS charge point charge resistance distance time potential or stored energy electric potential velocity or speed resistivity magnetic flux dielectric constant ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2004 and 2005 GEOMETRY AND TRIGONOMETRY area circumference volume surface area base height length width radius d f d f du dx du dx dn x nxn 1 dx dx e ex dx 1 d 1n x dx x d sin x cos x dx d cos x sin x dx 1 n1 xn dx x ,n n1 ex dx ex dx ln x x cos xdx sin x ( ( ( =) ( -=) = Ú = Ú Ú Ú 4 sin xdx -= = p q a b = p p p Ú b + p p p 90° q + a cos x 1 -π ( =) c b c = =) q q tan = =) cos - A= C= V= S= b= h= = w= r= = Rectangle A = bh Triangle 1 A = bh 2 Circle A = r2 C=2r Parallelepiped V = wh Cylinder V = r2 S = 2 r + 2 r2 Sphere 43 V= r 3 S = 4 r2 Right Triangle a 2 + b2 = c2 a sin = c CALCULUS 2004 AP® PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS PHYSICS C Section II, MECHANICS Time—45 minutes 3 Questions Directions: Answer all three questions. The suggested time is about 15 minutes for answering each of the questions, which are worth 15 points each. The parts within a question may not have equal weight. Show all your work in the booklet in the spaces provided after each part, NOT in this green insert. Mech. 1. A rope of length L is attached to a support at point C. A person of mass m1 sits on a ledge at position A holding the other end of the rope so that it is horizontal and taut, as shown above. The person then drops off the ledge and swings down on the rope toward position B on a lower ledge where an object of mass m2 is at rest. At position B the person grabs hold of the object and simultaneously lets go of the rope. The person and object then land together in the lake at point D, which is a vertical distance L below position B. Air resistance and the mass of the rope are negligible. Derive expressions for each of the following in terms of m1, m2, L, and g. (a) The speed of the person just before the collision with the object (b) The tension in the rope just before the collision with the object (c) The speed of the person and object just after the collision (d) The ratio of the kinetic energy of the person-object system before the collision to the kinetic energy after the collision (e) The total horizontal displacement x of the person from position A until the person and object land in the water at point D. Copyright © 2004 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). GO ON TO THE NEXT PAGE. 5 2004 AP® PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS Mech. 2. A solid disk of unknown mass and known radius R is used as a pulley in a lab experiment, as shown above. A small block of mass m is attached to a string, the other end of which is attached to the pulley and wrapped around it several times. The block of mass m is released from rest and takes a time t to fall the distance D to the floor. (a) Calculate the linear acceleration a of the falling block in terms of the given quantities. (b) The time t is measured for various heights D and the data are recorded in the following table. D (m) t (s) 0.5 0.68 1 1.02 1.5 1.19 2 1.38 i. What quantities should be graphed in order to best determine the acceleration of the block? Explain your reasoning. Copyright © 2004 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). GO ON TO THE NEXT PAGE. 6 2004 AP® PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS ii. On the grid below, plot the quantities determined in (b)i., label the axes, and draw the best-fit line to the data. iii. Use your graph to calculate the magnitude of the acceleration. (c) Calculate the rotational inertia of the pulley in terms of m, R, a, and fundamental constants. (d) The value of acceleration found in (b)iii, along with numerical values for the given quantities and your answer to (c), can be used to determine the rotational inertia of the pulley. The pulley is removed from its support and its rotational inertia is found to be greater than this value. Give one explanation for this discrepancy. Copyright © 2004 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). GO ON TO THE NEXT PAGE. 7 2004 AP® PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS Mech. 3. A uniform rod of mass M and length L is attached to a pivot of negligible friction as shown above. The pivot is L located at a distance from the left end of the rod. Express all answers in terms of the given quantities and 3 fundamental constants. (a) Calculate the rotational inertia of the rod about the pivot. (b) The rod is then released from rest from the horizontal position shown above. Calculate the linear speed of the bottom end of the rod when the rod passes through the vertical. (c) The rod is brought to rest in the vertical position shown above and hangs freely. It is then displaced slightly from this position. Calculate the period of oscillation as it swings. END OF SECTION II, MECHANICS Copyright © 2004 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). 8 ...
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