PY205 Matter & Interactions Final Exam, 2005 May 5

Transcription

1 1 PY05 Matter & Interactions Final Exam, 005 May 5 Print your name and circle your section! *** 3 point deduction if you do not circle correct lecture section *** 004 Schaefer 10:15, 005 Weninger 11:0, 006 Nardelli 1:5, 007 Ramakrishnan 1:30, 008 Sherwood :35, 01 Beichner 11:0, 014 Chilton 11:0, H001 Gould 10:15 I hae neither gien nor receied unauthorized aid on this test. Signature: When you turn in the test (including formula page) you must show an NCSU photo ID to identify yourself. Do not use other paper. If you need more space, write on the extra page and indicate that you did this. Read all problems carefully before attempting to sole them. You must show all your work. Use correct ector notation. Your work must be legible, and the organization must be clear. Correct answers without adequate explanation will be counted wrong. Incorrect explanations mixed in with correct explanations will be counted wrong. Cross out anything you don t want us to read! Make explanations complete but brief. Do not write a lot of prose. Include diagrams where appropriate to explain your work. ( )( ) Show what goes into a calculation, not just the final number: 5 4 ( 10 )( 4 10 ) = 5 10 If you don t show your calculation, and the final result is wrong, you lose all credit. If you do show a correct calculation, and the final result is wrong due to a calculator mistake, you will lose ery little. Gie standard SI units with your results. Unless specifically asked to derie a result, you may start from any formula on the formula sheet. If you cannot do some portion of a problem, inent a symbol for the quantity you can t calculate (explain that you re doing this), and do the rest of the problem. 4 1 (5 pts): 6 (15) (5 pts): 7 (15) 3 (15 pts): 8 (0) 4 (5 pts): 9 (5) 5 (15 pts): Total (140 pts):

2 Problem 1 (5 pts) The diagram depicts two pucks on a frictionless table. Puck is four times as massie as puck 1. Starting from rest, the pucks are pushed across the table by two equal forces. Which puck has the greater kinetic energy after one second? Briefly explain your reasoning. Problem (5 pts) The diagram depicts two pucks on a frictionless table. Puck is four times as massie as puck 1. Starting from rest, the pucks are pushed across the table by two equal forces. Which puck has the greater kinetic energy upon reaching the finish line? Briefly explain your reasoning.

3 3 Problem 3 (15 pts) A 0.6 kg basketball is rolling by you at 3.5 m/s. As it goes by, you gie it a kick perpendicular to its path. Your foot is in contact with the ball for 0.00 s. The ball eentually rolls at a 0º angle from its original direction. The oerhead iew is approximately to scale. The arrow represents the force your toe applies briefly to the basketball. (a) (5 pts) Circle the letter corresponding to the correct oerhead iew of the ball s path: A B C A B 0 0 (b) (10 pts) Determine the magnitude of the aerage force you applied to the ball. You may if you wish make the approximation that the change in speed of the basketball is negligible. C 0

4 4 Problem 4 (5 pts) A spring with stiffness 10 N/m is attached to a 30 gram mass that can oscillate horizontally on a nearly frictionless surface. The relaxed length of the spring is 0 cm. Initially the spring is elongated to 8 cm and the mass is released from rest. (a) (5 pts) What is the period of the oscillation? (b) (1 pts) What is the speed of the mass when the spring has a length of 17 cm? (c) (4 pts) Draw and label graphs of kinetic energy, potential energy, and the sum of the kinetic energy and potential energy, as a function of time, for one period starting from when you release the mass. Energy Did you label the 3 cures? t (d) (4 pts) If we consider this system as a model for a single quantum oscillator, what is the energy spacing between the quantized energy leels?

5 Problem 5 (15 pts) Here is a portion of a program for Rutherford scattering (alpha particle interacting with gold nucleus). Complete the missing pieces. (Not shown are the statements that set the initial conditions before the while loop.)... alpha.m = 4*1.7e-7 gold.m = 197*1.7e-7 deltat = 1e-3 while t < 1e-0: r = alpha.pos - gold.pos rmag = sqrt(r.x** + r.y** + r.z**) 5 rhat = Fmag = 9e9*79**(1.6e-19)**/rmag** F = alpha.p = gold.p = alpha.pos = gold.pos = t = t+deltat

6 Problem 6 (15 pts) (a) (3 pts) What is the minimum kinetic energy an electron must hae to be able to ionize a hydrogen atom? 6 (b) (8 pts) If electrons of energy 1.8 ev are incident on a gas of hydrogen atoms in their ground state, what is the highest energy leel in hydrogen that can be excited and what are the energies of the photons that are emitted? (c) (4 pts) If instead of electrons, photons of all energies between 0 and 1.8 ev are incident on a gas of hydrogen atoms in their ground state, what are the energies at which the photons are absorbed? For each absorption energy, state whether it is in the isible region.

7 7 Problem 7 (15 pts) Tarzan is hanging at rest from a tree limb. Then he lets go and falls to the ground. Just before he lets go, his center of mass is at a height h 1 aboe the ground and the bottom of his dangling feet are at a height h aboe the ground. When he first hits the ground he has dropped a distance h, so his center of mass is ( h1 h ) aboe the ground. Then his knees bend and he ends up at rest in a crouched position with his center of mass a height h 3 aboe the ground. Your results must be expressed using the ariables gien in this problem (h 1, h, and h 3 ) and g. (a) (7 pts) Consider the point particle system. What is the speed at the instant just before Tarzan s feet touch the ground? (b) (8 pts) Consider the real system. What is the net change in internal energy for Tarzan from just before his feet touch to the ground to when he is in the crouched position?

8 Problem 8 (0 pts) A deice consisting of four heay balls connected by low-mass rods is free to rotate about an axle. It is initially not spinning. A small bullet traeling ery fast buries itself in one of the balls. Information about the situation is gien in the diagram. The axle of the deice is at the origin < 0, 0, 0 >, and the bullet strikes at location < 0.87, 0.410, 0 > m. Just after the impact, what is the angular speed of the deice? Note that this is an inelastic collision; the system s temperature increases. 400 m/s kg 0.6 kg 1.6 kg 0.3 m 0.5 m 1.6 kg 0.6 kg rotates on frictionless axle 8

9 9 Problem 9 (5 pts) A nanoparticle containing 6 atoms can be modeled as an Einstein solid of 18 1 independent oscillators. The eenly spaced energy leels of each oscillator are 4 10 J apart. 1 1 (a) (10 pts) When the nanoparticle s energy is in the range 5 ( 4 10 ) J to 6 ( 4 10 ) approximate temperature? J, what is the 1 1 (b) (5 pts) When the nanoparticle s energy is in the range 8 ( 4 10 ) J to 9 ( 4 10 ) approximate temperature? J, what is the 1 1 (c) (10 pts) When the nanoparticle s energy is in the range 5 ( 4 10 ) J to 9 ( 4 10 ) J, what is the approximate heat capacity per atom? Note that between parts (a) and (b) the aerage energy increased from 5.5 quanta to 8.5 quanta. As a check, compare your result with the high temperature limit of 3k.

10 FUNDAMENTAL PHYSICAL LAWS Principle of relatiity: Physical laws work in the same way for obserers in uniform motion as for obserers at rest. The superposition principle: the effectie force on an object is the net force, the ector sum of all forces acting on the object, each force unaffected by the presence of other interactions. The momentum principle, and the definition of momentum. (These must be memorized.) The energy principle, and the definitions of work and energy. (These must be memorized.) The angular momentum principle. (This must be memorized.) The relationship among position, elocity, and time. (This must be memorized.) The second law of thermodynamics or the entropy principle: If a closed system is not in equilibrium, the most probable consequence is that the entropy will increase. K = K + K = K + K + K total trans rel to cm trans rot MULTIPARTICLE SYSTEMS ib total 1 P K total = M totalcm = nonrelatiistically M Lrot 1 Ptotal = M total cm nonrelatiistically K rot = = Iω I I = m1 r 1 + mr + m3r LA = ra p for a point particle τ A = r A F L = L + L = R P + L for a multiparticle system L = I ω A trans, A rot ( cm, A total ) rot E ( pc) = ( mc ) ; E = pc for massless photon ( q + N ) 1! Ω = q!( N 1)! F F gra electric EVALUATING GENERAL PHYSICAL QUANTITIES S = k ln Ω 1 ds T = de EVALUATING SPECIFIC PHYSICAL QUANTITIES Mm GMm = G ; can be approximately mg U gra = ; change can be approximately (mgy) r r 1 = 4πε 0 Qq r U electric 1 = 4πε 1 Fspring = k s s, opposite the stretch U spring = k s s + U 0 U U U F =<,, > Power = energy/time (watts = joules/second) x y z Perpendicular component of d p / dt (toward the center of the kissing circle): p R R is the radius of the kissing circle (There may also be a parallel component of d p / dt ) 0 Qq r F / A r Y = r L / L = π = ω T k s x = Acos t m 1 air resistance: F = CρA ˆ sliding friction: f µfn oscillator: k s k E N = N h ; classically s 13.6 ev ω = hydrogen atom: E N = (N = 1,,...) m m N rot total 11

11 Macro/micro connections: 1 m macro measurement of density = 3 (micro quantities) d k s,interatomic macro measurement of Young s modulus Y = (micro quantities) d atomic k s macro measurement of speed of sound = d (micro quantities) m E 1 C = (high-temperature limit: k per quadratic energy term; solid is 3k/atom) T A component of angular momentum is an integer or half-integer multiple of h. The square magnitude of angular momentum has quantized alues L = l( l + 1) h, where l has integer (0, 1,,...) or half-integer alues (1/, 3/, 5/,...). Sphere Cylinder or disk Thin rod (about axis shown) Solid cylinder (about axis shown) I = MR 5 1 I = MR 1 I = ML 1 1 I = ML MR 11 G = N m /kg g = 9.8 N/kg 34 h = J s 1 4πε 0 = N m /C CONSTANTS 34 h = J s 8 c = 3 10 m/s 3 k = J/K 19 proton or positron charge: e = coulomb 19 1 ev = J Aogadro s number = molecules/mole m proton m neutron m hydrogen atom = kg/mole 7 = atoms/mole 31 kg m electron = 9 10 kg M Earth = M Moon = kg Radius of Earth = m 7 10 kg Distance from Earth to Moon = m M Sun = 10 kg Distance from Earth to Sun = m Typical atomic radius r 1 10 m Proton radius 1 10 R m A 1/ 3 r m, ( ) Heat capacity of water = 4. (J/K)/gram. Energy of isible light is from about 1.8 ev to about 3.1 ev. Effectie stiffness of interatomic bond in aluminum is 16 N/m, lead is 5 N/m. Mass of one mole of atoms: carbon 1 grams (0.01 kg) nitrogen 14 grams (0.014 kg) oxygen 16 grams (0.016 kg) aluminum 7 grams (0.07 kg) iron 56 grams (0.056 kg) lead 07 grams (0.07 kg) nucleus