# 2002 - Physics C Mechanics TABLE OF INFORMATION FOR 2002...

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Unformatted text preview: Physics C: Mechanics TABLE OF INFORMATION FOR 2002 UNITS CONSTANTS AND CONVERSION FACTORS 1 unified atomic mass unit, 1 u = 1.66  10 -27 = 931 MeV/c Proton mass, PREFIXES Name Symbol meter kilogram Factor Prefix Symbol m 10 9 giga G kg 10 6 mega M 10 3 kilo k kg 2 m p = 1.67 × 10 −27 kg Neutron mass, mn = 1.67 × 10 −27 kg second s Electron mass, me = 9.11 × 10 −31 kg ampere A 10 −2 centi c Magnitude of the electron charge, e = 1.60 × 10 −19 C kelvin K 10 −3 milli m micro µ Avogadro’s number, N0 = 6.02 × 10 mol 23 −1 mol hertz Hz 10 −9 nano n 10 −12 pico p 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 Vacuum permittivity, Coulomb’s law constant, Vacuum permeability, Magnetic constant, Universal gravitational constant, Acceleration due to gravity at the Earth’s surface, 1 atmosphere pressure, 0 k = 1 / 4π = 8.85 × 10 C / N⋅m 0 k = µ 0 / 4π = 10 (T ⋅ m ) / A G = 6.67  10 -11 m 3 / kg ¼ s 2 g = 9.8 m / s V Ω H farad −7 0 henry µ 0 = 4π × 10 −7 (T ⋅ m ) / A C ohm = 9.0 × 10 N ⋅ m 2 / C 2 θ volt 9 W coulomb 2 J watt = 1.24 × 10 3 eV ⋅ nm 2 VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES joule hc = 1.99 × 10 −25 J ⋅ m −12 10 mole R = 8.31 J / ( mol ¼ K ) Universal gas constant, −6 F tesla T 45o o = 1.0 × 10 Pa tan θ 0 1 0 3 /2 3 /3 1/2 37o 3/5 degree Celsius o C 53o eV 60 o 90o 1 atm = 1.0 × 10 5 N / m 2 cos θ 30o electronvolt 2 sin θ 2 /2 4/5 4/5 2 /2 3/4 1 3/5 4/3 3 /2 1/2 3 1 0 ∞ 5 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 2002 MECHANICS a = acceleration F = force 1 x = x 0 + u 0 t + at 2 f = frequency 2 h = height 2 u 2 = u 0 + 2a x - x 0 I = rotational inertia Ê F = Fnet = ma J = impulse K = kinetic energy dp F= k = spring constant dt l = length J = F dt = Dp L = angular momentum p = mv m = mass N = normal force F fric  mN P = power W = F dr p = momentum 1 2 r = radius or distance K = mu 2 r = position vector dW T = period P= dt t = time P=F v U = potential energy u = velocity or speed DUg = mgh W = work done on a system u 2 = w2r x = position ac = r m = coefficient of friction t=rF q = angle Ê t = t net = Ia t = torque 2 2 w = angular speed I = r dm = Ê mr a = angular acceleration rcm = Ê mr Ê m u = rw L = r  p = Iw 1 K = Iw 2 2 w = w0 + at q = q 0 + w0 t + 1 at 2 2 Fs = - kx 1 Us = kx 2 2 2p 1 T= = f w m Ts = 2 p k l Tp = 2 p g Gm1m2 \$ FG = r r2 Gm1m2 UG = r u = u 0 + at 0 I I I  5 ELECTRICITY AND MAGNETISM q1 q 2 A = area 2 B = magnetic field r 0 C = capacitance F d = distance E= q E = electric field e = emf Q E • dA = F = force 0 I = current dV L = inductance E=− l = length dr n = number of loops of wire per qi 1 V= unit length 4 p 0 i ri P = power 1 F= 4p ∑ UE = qV = 1 4p 0 q1 q 2 r Q C= V kA C= 0 d C p = ∑ Ci i 1 1 =∑ Cs i Ci dQ dt 1 1 Uc = QV = CV 2 2 2 rl R= A V = IR I= Rs = ∑ Ri i 1 1 =∑ Rp i Ri P = IV FM = qv × B B • d ø = m0 I I F = I dø × B Bs = m0 nI I fm = B • dA dfm dt dI e = −L dt 12 U L = LI 2 e=− 3 Q= q= R= r= t= U= V= υ= r= fm = k= 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 2002 GEOMETRY AND TRIGONOMETRY Rectangle A = bh Triangle 1 A = bh 2 Circle A = pr 2 C = 2 pr Parallelepiped V = lwh Cylinder V = pr 2 l S = 2 prl + 2 pr 2 Sphere 4 V = pr 3 3 S = 4 pr 2 Right Triangle a 2 + b2 = c2 a sin q = c cos q = area circumference volume surface area base height length width radius c q a 90 b b c tan q = A= C= V= S= b= h= l= w= r= a b CALCULUS df d f du = dx du dx 27 27 dn n -1 x = nx dx dx e = ex dx d 1 (1n x) = dx x d (sin x) = cos x dx d (cos x) = - sin x dx 1 n +1 xn dx = x , n  -1 n +1 e x dx = e x I I I dx = 1n x x cos x dx = sin x I I sin x dx = - cos x 4 2002 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 pink booklet in the spaces provided after each part, NOT in this green insert. Mech 1. A crash test car of mass 1,000 kg moving at constant speed of 12 m/s collides completely inelastically with an object of mass M at time t = 0. The object was initially at rest. The speed u in m/s of the car-object system after the collision is given as a function of time t in seconds by the expression u= 8 . 1 + 5t (a) Calculate the mass M of the object. (b) Assuming an initial position of x = 0, determine an expression for the position of the car-object system after the collision as a function of time t. (c) Determine an expression for the resisting force on the car-object system after the collision as a function of time t. (d) Determine the impulse delivered to the car-object system from t = 0 to t = 2.0 s. Copyright © 2002 by College Entrance Examination Board. All rights reserved. Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board. 5 GO ON TO THE NEXT PAGE. 2002 AP® PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS Mech 2. The cart shown above is made of a block of mass m and four solid rubber tires each of mass m/4 and radius r. 1 ML2 , where M is the mass and L is Each tire may be considered to be a disk. (A disk has rotational inertia 2 the radius of the disk.) The cart is released from rest and rolls without slipping from the top of an inclined plane of height h. Express all algebraic answers in terms of the given quantities and fundamental constants. (a) Determine the total rotational inertia of all four tires. (b) Determine the speed of the cart when it reaches the bottom of the incline. (c) After rolling down the incline and across the horizontal surface, the cart collides with a bumper of negligible mass attached to an ideal spring, which has a spring constant k. Determine the distance x m the spring is compressed before the cart and bumper come to rest. (d) Now assume that the bumper has a non-neglible mass. After the collision with the bumper, the spring is compressed to a maximum distance of about 90% of the value of x m in part (c). Give a reasonable explanation for this decrease. Copyright © 2002 by College Entrance Examination Board. All rights reserved. Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board. 6 GO ON TO THE NEXT PAGE. 2002 AP® PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS Mech 3. An object of mass 0.5 kg experiences a force that is associated with the potential energy function 4.0 U ( x) = , where U is in joules and x is in meters. 2.0 + x (a) On the axes below, sketch the graph of U(x) versus x. (b) Determine the force associated with the potential energy function given above. (c) Suppose that the object is released from rest at the origin. Determine the speed of the particle at x = 2 m. In the laboratory, you are given a glider of mass 0.5 kg on an air track. The glider is acted on by the force determined in part (b). Your goal is to determine experimentally the validity of your theoretical calculation in part (c). (d) From the list below, select the additional equipment you will need from the laboratory to do your experiment by checking the line next to each item. If you need more than one of an item, place the number you need on the line. ___ Meterstick ___ Stopwatch ___ Photogate timer ___ String ___ Balance ___ Wood block ___ Spring ___ Set of objects of different masses (e) Briefly outline the procedure you will use, being explicit about what measurements you need to make in order to determine the speed. You may include a labeled diagram of your setup if it will clarify your procedure. END OF SECTION II, MECHANICS Copyright © 2002 by College Entrance Examination Board. All rights reserved. Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board. 7 GO ON TO THE NEXT PAGE. ...
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