MECH + E&M - 1998

MECH + E&M - 1998 - 1 998 The College Board Advanced...

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 12
Background image of page 13
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 998 The College Board Advanced Placement Examination PHYSICS C SECTION II TABLE OF INFORMATION FOR 1998 CONSTANTS AND CONVERSION FACTORS UNITS PREFIXES l unified atomic mass unit. lu = 1.66 X 10—27 kg Name MID-‘21 F—aqp—r Pmfix 34m = 93t MeV/cz meter in 109 giga G Proton mass. mp = 157 x 10'27 kg kilogram kg 106 mega M Neutron mass, : ’27 3 . mfl 1.67 x 10 kg second S 10 kilo 1: El t mass. _ -31 “C m“ mE - 9.11 x 10 kg A 10.2 cemi c Magnitude of the electron charge, 8 = 1.60 X 10-19C amp“: -3 . . Avogadro's number, No x 602 X 1013 moi-1 kelvin K 10 “1111‘ m . _6 _ Universal as constant, = . 10 micro u g R 8.31 J/(rnol K) mole m0] Boltzmann's constant, k5 = 133 x 1043 J/K 10-9 mm H . s hertz Hz Speed “fight. 6 = 3.0% 10 m/s 10-12 pm p Planck‘s constant, _ ~34 . newton N h ‘ 6'63 x 10 15 J 5 mm Pa VALUES OF TRIGONOMETRIC FUNCTIONS = 4.]4x 10— eV ' s P ‘ FOR COMMON ANGLES he = 1.99x10‘25 J ' m joule J = 1.24><103 eV - rim watt w Vacuum permittivity, 50 = 335 x 10"” CQ/N . m2 “Dummb C Coulomb's law constant, k : 1/4n50 = 90X 109 N . mq/C? VD“ V Vacuum permeability, p0 = 4It x 10-7 (T . m) /A ohm Q 35 Magnetic constant, kt : “0/4” = {077(1- . m) /A henry H Universal gravitational constant, G = 6.67 X 10-” [If/kg . 52 farad F @2 Via/2 ACCBleml-iotia due]:1 to gravity tesla T att 6 art 'ssu ace, _ 2 g ' 9'3 m” degree 4/5 3/5 1 atmosphere pressure, 1 atm = 1.0 x 10’ N/m2 Celsius °c . 5 = 1.0x 10 Pa clean-0m -19 volt 6V lelectron volt, iev = Léox 10 J l angstrom. HR = Ix io’“’m The following conventions are used in this examination. 1. Unless otherwise stated, the frame of reference of any problem is assumed to be inertial, 11. The direction of any electric current is the direction of flow of positive charge (conventional current). 111. For any isolated electric charge, the electric potential is defined as zero at an infinite distance from the charge. Copyright © 1998 by College Entrance Examination Board and Educational Testing Service. All rights reserved. ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 1998 MECHANICS ELECTRICITY AND MAGNETISM 1; = no + at a = acceleration F: —— ‘1qu A = area 1 F = force 47”” r B = magnetic field 5 = so + not + E at2 f 2 frequency E = E C = capacitance h = height :1 d = distance 32 = 302 + gag; _ so) I = rotational inertia E = electric field J: impulse fiE-dA =62 5=emf 2F = FM! 2 ma K = kinetic energy 0 F = force d k = spring constant _ d_V I = current F = a]; f = length E _ '— dr L = inductance L = angular momentum E = length J = I F d? = AP m = mass V: L 23 n = number of loops of wire .. N = normal force 47‘“) r per unit length p — mv P _ _ 1 qu .— -. power U = qV _ — — P — power an'c S W p = momentum 47*" r Q = charge a . r = distance q = point charge W _ IF ds 3 = displacement C = g R = resistance 1 2 T = eriod :- = distance K_§mr’i t=ti3me C=K€0A t=time dW ‘ U = potential energy d U = potential or stored energy = E?- v = velocity or speed Cp = 2 Cl. V = electric potential W = work 1- v = velocity or speed Aug = mgh x = displacement . I 1 1 p = resistivity 2 u = coeff1c1ent of friction E = 6 rpm = magnetic flux 1: 2 s ,- r . . ac = — = (,3 ,- 9 = angle x = dielectric constant r 't = torque 1' = r x F to = angular speed (1 = angular acceleration ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 1998 GEOMETRY AND TRIGONOMETRY Rectangle A = area A = bh C = circumference Triangle V = volume 1 S = surface area A _ E bk [7 = base Circle h = height A = m2 E = length C = 2m w = width Parallelepiped r = radius V = Ewh Cylinder 2 V = m f S = 21:14? + 21tr2 Sphere _E 3 V—3n: S=41tr Right Triangle CALCULUS df_fl.fl nix—dot dx d x_ x a(e)—e d 1 E(lnx)—:t- i (sin x) - cos x dx _ % (cos x) = —sin x J'xfldx= 1 11+] 1: ,nat-l n+1 Iexdx=ex Idi=1n lxl x Icosxdx=sinx Isinxdx=—cosx 1 998 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 pink booklet in the spaces provided after each part, NOT in this green insert. Air Track Mech. 1. Two gliders move freely on an air track with negligible friction, as shown above. Glider A has a mass of 0.90 kg and glider B has a mass of 0.60 kg. Initially, glider A moves toward glider B, which is at rest. A spring of negligible mass is attached to the right side of glider A. Strobe photography is used to record successive positions of glider A at 0.10 5 intervals over a total time of 2.00 3, during which time it collides with glider B. The following diagram represents the data for the motion of glider A. Positions of glider A at the end of each 010 s interval are indicated by the symbol A against a metric ruler. The total elapsed time I after each 0.50 s is also indi- cated. 1.10 1.20 A A A A A A A A A A A A A A A A A A A A A 0.00s 0.505 . 1.003 1.505 2.005 r (a) Determine the average speed of glider A for the following time intervals. i. 0.105t00.305 ii. 0.905t01.108 iii. 1.70 s to 1.90 s GO ON TO THE NEXT PAGE Copyright © 1998 by College Entrance Examination Board and Educational Testing Service. All rights reserved. 1998 PHYSICS C—MECHANICS (b) On the axes below, sketch a graph. consistent with the data above, of the speed of glider A as a function of time t for the 2.00 s interval. ) \II S S {t {x .t I f.- G .A P . T. 3 VA 0 .m 0 F. I 0 r. O N l1l—II1I1I1II1IJIJII1I1|I-II-I1JII1 u p lltdll_ll1l1llqllulJlJI-I.II1II-II_I1J'I1 . __ _ __ _ __ _ _. . __ _ 7. s . _ __ _ __ _ __ _ __ _ _ 0. EL ||_Lt_ __I.‘ _ __ _“|_ __ e __ _|__ __ __ _|#_I__t_ u” .- _ ._.IHII_ _IJ|._.I_I4l—ui_ fiJI... ..nL II._.I_I4 _IJlflJlfith 1|. ._ut_ .._. T _ _ __ _ ._ _ _, _ __ _ _ L _ _ __ _ __ _ ._ _ _, fl _ nu II_LI_I__|__I_tF.I__|_LI_ m II_LI_I__|__I_|F_I__1_.|_ q..._._ln__tJ._._._.fil_fl_._. m e fi_._._IJfiJ._._n—_Il_fll_._. T __ __ .. __ __ __ __ . f .m ._ F. __ _. __ __ ._ _ Mu IIPLIFtrLIPLIeLILIrLIrLIk s t IIhLIpirLlrLlhtrplrLlrle nu _ __ ._ _ __ __ . __ __ m f _ __ ._ _ __ __ . __ __ _ _ __ _ __ _ __ _ __ _ _ a o _ _ __ _ __ . __ _ ._ _ _ nu |t+LI+ITL|TLI+IT+ITL1+LI+ m n InTLI+ITLITLI+IT+ITLIr11+ nu . _ __ _ __ _ __ _ _. h _ D. .m . _ __ _ ._ __ _ __ _ __ d _ _fl __ _ ._ __ . __ _ mw W a _ __ __ _ a. _ __ __ _ _ m ItrLILIrLIrletT+IrLIrLI+ . t n ItrIT+IrLIrLt+ITLIrLIrLI+ . _ __ __ __ __ __ .fl. _ l .1 nm . __ __ __ __ .. __ _n 1 _ __ __ _ __ __ _ _. __ m _ __ __ __ _ __ __ _ __ II14I4I14|14t4114|14|+4l4 t a t|+J|4|14|14|+I14I14|flJI4 .. __ __ __ __ ___ __ fl S _ ___ n. __ ._ __ ___ II_LI_I__I._1_IF_I__I__ _ Y a I|__I_IF_ _LI_iF_I__I_LI_ .._474 uIJfi_Afli_ fiJlfl .1 B ._.l_._._|_I1_._._n—_1|_«._._. _ __ __ _ __ __ _ __ __ w . __ __ _ __ __ . __ __ IIrLtFIFLIrLielrptrLlrLt» .m r IIhLiFIrLIrLlhIFFlrLIrLtk __ __ __ __ _fl __ __ _ d R _. __ __ __ __ _. __ _ _ __ _. _ __ __ _ __ __ e H _ _. __ _ ,_ __ _ __ __ IIrLlpIrLIrLtklrplrLlrLrp m g IlrLtFIFLLrLIhIFFtrLIrLIh __ _ __ _ _. _ __ _ __ _ m f. .. __ _ __ _ __ _ __ __ . __ _ __ __ __ __ ._ _ 0 .1 0 __ __ __ ._ __ __ __ _ n II+LI+ITLIr1|+IT+tTLIrL1+ 0 .d |I+IT+ITL1TLI+|T+ITLITLI+ fl __ _. _. _. ._ __ __ _ It B e __ __ ._ __ __ ._ __ _ 1 _ __ __ _ __ __ ._ _ __ r e _ __ __ __ . _n __ . __ II+LI+IT4ITLI+|T+IT¢I+LI+ e w. II+LI+ITLITLt+IT+tTLI+L1+ _ __ __ _ __ __ . __ __ M e _ __ _. __ _ __ __ _ __ ._ fl. __ __ __ __ __ _ 1 h ._ __ __ __ ._ __ __ _ IIfiJt4114|thal14t14|1J|4 g t IlfiJt4|14I14|4114|14114|4 _ __ __ . __ _. _ __ __ d d _ __ u. _ _. __ . __ __ _ __ __ . __ __ __ _ __ IlrLlhlrutrLlwtrplrLirle _ _ .w h . n. __ _ ,_ __ . __ _— _ _ e W __ __ _. __ __ __ ___ P r ILILLLL:ELLLIELLL S g . ___ __ d. __ _ _. 0 e a _ __ _ __ __ __ _ __ 0 i, m h tIrIFFIFLtr4IrITLI L 5 . C _ _ _ _ _ _ _ _ _ . 0 m a __ __ __ __ ._ n 1 k II+LI+1TLITLI+IT+I fl 5 __ ._ __ __ __ k M _ ___ __ __ __ w 0 IIfiIW4I1JI1414I14I l __ __ __ ._ __ w m _ ._ __l__I_t__ a |1H|14|14 HJ A 14| S m e . __ ._ . __ __ d x IIPIFFIFLIPLIFIFF IIIIII II c a \J _ _ __ _ __ . __ _ h e S __ _ ._ __ _. __ 0 t m m 0 e S n /I\ 0 0 0 U 0 v fie fl .3 11 1... 0 \I} C ( 1998 PHYSICS C—MECHANICS A graph of the total kinetic energy K for the two-glider system over the 2.00 s interval has the following shape. K0 is the total kinetic energy of the system at time I = 0. KO) 0 0.50 1.00 1.50 2.00 (d) i. Is the collision elastic? Justify your answer. ii. Briefly explain why there is a minimum in the kinetic energy curve at t = 1.00 s. GO ON T0 THE NEXT PAGE Mech. 2. 1998 PHYSICS C—MECHANICS A space shuttle astronaut in a circular orbit around the Earth has an assembly consisting of two small dense spheres, each of mass m, whose centers are connected by a rigid rod of length l2 and negligible mass. The astronaut also has a device that will launch a small lump of clay of mass m at speed 110 . Express your answers in terms of m, U0 , l2, and fundamental constants. I-——9~——-I m.—.m it C m (3) Initially, the assembly is “floating” freely at rest relative to the cabin, and the astronaut launches the clay lump so that it perpendicularly strikes and sticks to the midpoint of the rod, as shown above. i. Determine the total kinetic energy of the system (assembly and clay lump) after the collision. ii. Determine the change in kinetic energy as a result of the collision. I—— 9 ————-| m.——.m Too 0 (b) The assembly is brought to rest, the clay lump removed, and the experiment is repeated as shown above, with the clay lump striking perpendicular to the rod but this time sticking to one of the spheres of the assembly. i. Determine the distance from the left end of the rod to the center of mass of the system (assembly and clay . lump) immediately after the collision. (Assume that the radii of the spheres and clay lump are much smaller than the separation of the spheres.) ii. On the figure above, indicate the direction of the motion of the center of mass immediately after the collision. iii. Determine the speed of the center of mass immediately after the collision. iv. Determine the angular speed of the system (assembly and clay lump) immediately after the collision. v. Determine the change in kinetic energy as a result of the collision. GO ON TO THE NEXT PAGE Mech. 3. 1998 PHYSICS C—MECHANICS Block 1 of mass m] is placed on block 2 of mass m2, which is then placed on a table. A string connecting block 2 to a hanging mass M passes over a pulley attached to one end of the table, as shown above. The mass and friction of the pulley are negligible. The coefficients of friction between blocks 1 and 2 and between block 2 and the tabletop are nonzero and are given in the following table. Coefficient Between Coefficient Between Blocks 1 and 2 Block 2 and the Tabletop Static ,uxz Kinetic ,un Express your answers in terms of the masses, coefficients of friction, and g, the acceleration due to gravity. (51) Suppose that the value of M is small enough that the blocks remain at rest when released. For each of the following forces, determine the magnitude of the force and draw a vector on the block provided to indicate the direction of the force if it is nonzero. i. The normal force N] exerted on block 1 by block 2 ii. The friction force fi exerted on block 1 by block 2 1998 PHYSICS 'C—MECHANICS iii. The force Texerted on block 2 by the string iv. The normal force N2 exerted on block 2 by the tabletop v. The friction force f2 exerted on block 2 by the tabletop (b) Determine the largest value of M for which the blocks can remain at rest. (c) Now suppose that M is large enough that the hanging block descends when the blocks are released. Assume that blocks l and 2 are moving as a unit (no slippage). Determine the magnitude 0 of their acceleration. (cl) Now suppose that M is large enough that as the hanging block descends, block 1 is slipping on block 2. Determine each of the following. i. The magnitude a} of the acceleration of block 1 ii. The magnitude (:2 of the acceleration of block 2 STOP END OF SECTION II, MECHANICS 1 998 PHYSICS C SECTION II, ELECTRICITY AND MAGNETISM Time—45 minutes 3 Questions 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 pink booklet in the spaces provided after each part, NOT in this green insert. E&M. 1. Note: Figure not drawn to scale. The small sphere A in the diagram above has a charge of 120 ttC. The large sphere BI is a thin shell of nonconducting material with a net charge that is uniformly distributed over its surface. Sphere B, has a mass of 0.025 kg, a radius of 0.05 m, and is suspended from an uncharged, nonconducting thread. Sphere BI is in equilibrium when the thread makes an angle 6 = 20° with the vertical. The centers of the spheres are at the same vertical height and are a horizontal distance of 1.5 m apart, as shown. (a) Calculate the charge on sphere Bl. (b) Suppose that sphere BI is replaced by a second suspended sphere 82 that has the same mass, radius, and charge, but that is conducting. Equilibrium is again established when sphere A is 1.5 m from sphere 32 and their centers are at the same vertical height. State whether the equilibrium angle 62 will be less than, equal to, or greater than 20°. Justify your answer. GO ON TO THE NEXT PAGE 1998 PHYSICS C—E 8: M The sphere 32 is now replaced by a very long, horizontal. nonconducting tube, as shown in the top view below. The tube is hollow with thin walls of radius R = 0.20 m and a uniform positive charge per unit length of]. = +0.10 [AC/m. / Tube (radius R) Top View (c) Use Gauss‘s law to show that the electric field at a perpendicular distance r from the tube is given 1.8 x 103 l" by the expression E = N/C, where r>R and r is in meters. ((1) The small sphere A with charge 120 [JC is now brought into the vicinity of the tube and is held at a distance of r = 1.5 In from the center of the tube. Calculate the repulsive force that the tube exerts on the sphere. (e) Calculate the work done against the electrostatic repulsion to move sphere A toward the tube from a distance r = 1.5 m to a distance r = 0.3 m from the tube. GO ON TO THE NEXT PAGE E&M.2. 1998 PHYSICS C—E & M R1=IOQ S 3 Al e=2ov C=15uF L=2.0H R2=200 In the circuit shown above, the switch S is initially in the open position shown, and the capacitor is uncharged. A voltmeter (not shown) is used to measure the correct potential difference across resistor R1 . (a) (b) (C) (d) (6) (f) On the circuit diagram above, draw the voltmeter with the proper connections for correctly measuring the potential difference across resistor R1. At time t = 0, the switch is moved to position A. Determine the voltmeter reading for the time immediately after t = 0. After a long time, a measurement of potential difference across R1 is again taken. Determine for this later time each of the following. i. The voltmeter reading ii. The charge on the capacitor At a still later time t = T, the switch S is moved to position 3. Determine the voltmeter reading for the time immediately after t = T. A long time after t = T, the current in R1 reaches a constant final value If. i. Determine If. ii. Determine the final energy stored in the inductor, Write, but do not solve, a differential equation for the current in resistor R! as a function of time t after the switch is moved to position B. GO ON TO THE NEXT PAGE 1998 PHYSICS C—E 8: M E & M. 3. A conducting bar of mass m is placed on two long conducting rails a distance it apart. The rails are inclined at an angle 9 with respect to the horizontal, as shown above, and the bar is able to slide on the rails with negligible friction. The bar and rails are in a uniform and constant magnetic field of magnitude B oriented perpendicular to the incline. A resistor of resistance R connects the upper ends of the rails and completes the circuit as shown. The bar is released from rest at the top of the incline. Express your answers to parts (a) through (d) in terms of m, 9, 6, B, R, and g. (3) Determine the current in the circuit when the bar has reached a constant final speed. (h) Determine the constant final speed of the bar. (c) Determine the rate at which energy is being dissipated in the circuit when the bar has reached its constant final speed. ' (d) Express the speed of the bar as a function of time I from the time it is released at t = 0. (6) Suppose that the experiment is performed again, this time with a second identical resistor connecting the rails at the bottom of the incline. Will this affect the final speed attained by the bar, and if so, how? Justify your answer. STOP END OF SECTION II, ELECTRICITY AND MAGNETISM ...
View Full Document

This note was uploaded on 02/19/2011 for the course PHYS 102 taught by Professor Allen during the Spring '11 term at Northwestern IA.

Page1 / 13

MECH + E&M - 1998 - 1 998 The College Board Advanced...

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online