AP Physics C: Mechanics 2004 Free-Response Questions

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1 AP Physics C: Mechanics 004 Free-Response Questions The materials inclue in these files are intene for noncommercial use by AP teachers for course an exam preparation; permission for any other use must be sought from the Avance Placement Program. Teachers may reprouce them, in whole or in part, in limite quantities, for face-to-face teaching purposes but may not mass istribute the materials, electronically or otherwise. This permission oes not apply to any thir-party copyrights containe herein. These materials an any copies mae of them may not be resol, an the copyright notices must be retaine as they appear here. The College Boar is a not-for-profit membership association whose mission is to connect stuents to college success an opportunity. Foune in 900, the association is compose of more than 4,500 schools, colleges, universities, an other eucational organizations. Each year, the College Boar serves over three million stuents an their parents, 3,000 high schools, an 3,500 colleges through major programs an services in college amissions, guiance, assessment, financial ai, enrollment, an teaching an learning. Among its best-known programs are the SAT, the PSAT/NMSQT, an the Avance Placement Program (AP ). The College Boar is committe to the principles of excellence an equity, an that commitment is emboie in all of its programs, services, activities, an concerns. For further information, visit Copyright 004 College Entrance Examination Boar. All rights reserve. College Boar, Avance Placement Program, AP, AP Central, AP Vertical Teams, APCD, Pacesetter, Pre-AP, SAT, Stuent Search Service, an the acorn logo are registere traemarks of the College Entrance Examination Boar. PSAT/NMSQT is a registere traemark jointly owne by the College Entrance Examination Boar an the National Merit Scholarship Corporation. Eucational Testing Service an ETS are registere traemarks of Eucational Testing Service. Other proucts an services may be traemarks of their respective owners. For the College Boar s online home for AP professionals, visit AP Central at apcentral.collegeboar.com.

2 TABLE OF INFORMATION FOR 004 an 005 CONSTANTS AND CONVERSION FACTORS - unifie atomic mass unit, u kg 93 MeV/ c Proton mass, m p kg Neutron mass, m n kg Electron mass, m e kg Magnitue of the electron charge, e C Avogaro s number, N mol Universal gas constant, R 83. J/ ( mol K ) Boltzmann s constant, k B J/K Spee of light, c ms / Planck s constant, h Js ev s 5 hc J m ev nm Vacuum permittivity, C / N m 9 Coulomb s law constant, k / 4π Nm / C 7 Vacuum permeability, µ 0 4π 0 ( Tm) / A Magnetic constant, k' µ / 4π 0 7 ( T m) / A 0 Universal gravitational constant, G m 3 / kg s Acceleration ue to gravity at the Earth s surface, g 98. m/s atmosphere pressure, atm N / m Pa electron volt, ev J UNITS Name Symbol meter kilogram secon ampere kelvin mole hertz newton pascal joule watt coulomb volt ohm henry fara tesla egree Celsius electronvolt m kg s A K mol Hz N Pa J W C V Ω H F T C ev PREFIXES Factor Prefix Symbol 0 9 giga G 0 6 mega M 0 3 kilo k 0 centi c 0 milli m 0 6 micro µ 0 9 nano n 0 pico p VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES θ sin θ cos θ tan θ / 3 / 33 / 37 3/5 4/5 3/4 45 / / 53 4/5 3/5 4/ / / The following conventions are use in this examination. I. Unless otherwise state, the frame of reference of any problem is assume to be inertial. II. The irection of any electric current is the irection of flow of positive charge (conventional current). III. For any isolate electric charge, the electric potential is efine as zero at an infinite istance from the charge.

3 ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 004 an 005 MECHANICS u u0 + at a acceleration F force x x0 + u0t + at f frequency h height u u0 + a( x - x0) I rotational inertia Â F Fnet ma J impulse K kinetic energy p F k spring constant l length J Ú F Dp L angular momentum m mass p mv N normal force Ffric mn P power p momentum W ÚF r r raius or istance K m r position vector u T perio W t time P U potential energy u P Fv velocity or spee W work one on a system DUg mgh x position m coefficient of friction u ac w r r q angle t torque t r F w angular spee Â t tnet Ia a angular acceleration I Ú r m Â mr rcm Âmr Âm u r w L r p Iw K w w w0 + a q q0 + w0t + at F U T T T s s s F U p G G I t kx kx p w f m p k - p g Gm m r Gm m r - - l rˆ ELECTRICITY AND MAGNETISM qq A area F 4p r B magnetic fiel 0 E F C capacitance istance q E electric fiel Q e emf E A F force 0 I current V E L inuctance r l length q n number of loops of wire i V per unit length 4p 0 i ri P power qq Q charge UE qv 4p 0 r q point charge C Q R resistance r istance V t time k 0 A U potential or store energy C V electric potential u velocity or spee Cp Ci r resistivity i f m magnetic flux k ielectric constant Cs i Ci Q I Uc QV CV rl R A V IR R R s i i R R p i i P IV FM qv B B m I 0 F z I B Bs m0ni fm z B A fm e e L I UL LI 3

4 ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 004 an 005 GEOMETRY AND TRIGONOMETRY CALCULUS Rectangle A bh Triangle A bh Circle A pr C pr Parallelepipe V lwh Cyliner V pr l S prl + pr Sphere V 4 3 pr 3 S 4pr Right Triangle a + b c sin q a c b cos q c tan q a b A area C circumference V volume S surface area b base h height l length w wih r raius q c b 90 a f f u x u x ( x n ) nx n- x ( e x x ) e x ( n x) x x ( sin x) cos x x ( cos x) -sinx x, n n+ Ú xx x n π - n + x x Ú ex x ln x x cos xx sin x Ú sin xx e Ú Ú - cos x 4

5 004 AP PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS PHYSICS C Section II, MECHANICS Time 45 minutes 3 Questions Directions: Answer all three questions. The suggeste time is about 5 minutes for answering each of the questions, which are worth 5 points each. The parts within a question may not have equal weight. Show all your work in the booklet in the spaces provie after each part, NOT in this green insert. Mech.. A rope of length L is attache to a support at point C. A person of mass m sits on a lege at position A holing the other en of the rope so that it is horizontal an taut, as shown above. The person then rops off the lege an swings own on the rope towar position B on a lower lege where an object of mass m is at rest. At position B the person grabs hol of the object an simultaneously lets go of the rope. The person an object then lan together in the lake at point D, which is a vertical istance L below position B. Air resistance an the mass of the rope are negligible. Derive expressions for each of the following in terms of m, m, L, an g. (a) The spee 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 spee of the person an object just after the collision () 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 isplacement x of the person from position A until the person an object lan in the water at point D. Copyright 004 by College Entrance Examination Boar. All rights reserve. Visit apcentral.collegeboar.com (for AP professionals) an (for AP stuents an parents). 5 GO ON TO THE NEXT PAGE.

6 004 AP PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS Mech.. A soli isk of unknown mass an known raius R is use as a pulley in a lab experiment, as shown above. A small block of mass m is attache to a string, the other en of which is attache to the pulley an wrappe aroun it several times. The block of mass m is release from rest an takes a time t to fall the istance 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 measure for various heights D an the ata are recore in the following table. D (m) t (s) i. What quantities shoul be graphe in orer to best etermine the acceleration of the block? Explain your reasoning. Copyright 004 by College Entrance Examination Boar. All rights reserve. Visit apcentral.collegeboar.com (for AP professionals) an (for AP stuents an parents). 6 GO ON TO THE NEXT PAGE.

7 004 AP PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS ii. On the gri below, plot the quantities etermine in (b)i., label the axes, an raw the best-fit line to the ata. iii. Use your graph to calculate the magnitue of the acceleration. (c) Calculate the rotational inertia of the pulley in terms of m, R, a, an funamental constants. () The value of acceleration foun in (b)iii, along with numerical values for the given quantities an your answer to (c), can be use to etermine the rotational inertia of the pulley. The pulley is remove from its support an its rotational inertia is foun to be greater than this value. Give one explanation for this iscrepancy. Copyright 004 by College Entrance Examination Boar. All rights reserve. Visit apcentral.collegeboar.com (for AP professionals) an (for AP stuents an parents). 7 GO ON TO THE NEXT PAGE.

8 004 AP PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS Mech. 3. A uniform ro of mass M an length L is attache to a pivot of negligible friction as shown above. The pivot is locate at a istance 3 L from the left en of the ro. Express all answers in terms of the given quantities an funamental constants. (a) Calculate the rotational inertia of the ro about the pivot. (b) The ro is then release from rest from the horizontal position shown above. Calculate the linear spee of the bottom en of the ro when the ro passes through the vertical. (c) The ro is brought to rest in the vertical position shown above an hangs freely. It is then isplace slightly from this position. Calculate the perio of oscillation as it swings. END OF SECTION II, MECHANICS Copyright 004 by College Entrance Examination Boar. All rights reserve. Visit apcentral.collegeboar.com (for AP professionals) an (for AP stuents an parents). 8

AP Physics C: Electricity and Magnetism 2004 Free-Response Questions

AP Physics C: Electricity and Magnetism 2004 Free-Response Questions AP Physics C: Electricity an Magnetism 004 Free-Response Questions The materials inclue in these files are intene for noncommercial use by AP teachers for course an exam preparation; permission for any