DO NOT OPEN EXAM UNTIL INSTRUCTED TO DO SO!

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1 DO NOT OPEN EXAM UNTIL INSTRUCTED TO DO SO! 11/11/09 PHYS260 EXAM II Prof. Hill NAME: (Print) (Sign) UID NO.: Tung-Chang Liu Sec 0201 (Tu 8) Sec 0202 (Tu 9) Alex Azatov Sec 0203 (Tu 11) Sec 0204 (W 10) INSTRUCTIONS This is a 70 min CLOSE-BOOK, CLOSED-NOTES AND CLOSED- ELECTRONIC INFORMATION EXAM worth 100 pts. Make sure to indicate your assumptions and identify clearly your final answer. DO ALL YOUR WORK IN THE EXAM BOOK(S). GROUND RULES: Put your name, section #, TA s name and UID # on this page and your exam book(s). Sign, this page and your exam book(s) acknowledging the Honor Pledge agreement. Turn in these pages along with your exam book(s). Do all scratch work in the exam book(s) on pages you should label scratch. Clearly indicate the problem number on each page of the exam book(s). Missing exams will be subject to loss of points! You are allowed one page ( ) of notes. You may use your calculator but no other devices can be used even if they have calculators built-in. No calculators are available to borrow. You can quote fundamental laws and use the results of derivations done in lecture or the text for this class (unless explicitly asked to derive on the exam). However, you must provide an argument as to why it is valid. Equations without justification will not receive full credit! You cannot quote from homework assignments but you can use the same approaches! DO NOT OPEN EXAM UNTIL INSTRUCTED TO DO SO!

2 Exam Score: Problem Score # # Total Bonus Please note, bonus scores are tabulated separately; they are not added to your total! Constants Liquids Density (gm/cm 3 ) Molecular Weight (g/mol) Specific Heat (J/g K) Lead Aircomposition21%O2+78%N2+~1%Ar Assumethevelocityofsoundinsillairis343m/s. Constants Boltzmann sconstant,kb UniversalGasConstant,R Value J/K 8.314J/mol K Avogadro snumber,na g 9.81m/s 2 1atm Elementarycharge(e) 1/4πε0 ElectronMass ProtonMass Pa C N m 2 /C Kg Kg 2

3 Problem1(25pts) (a) What is the thermal energy of air in a 10.0 m 10.0 m 10.0 m room at 25 C?(5pts) (b) Whatisthethermalenergyof100.0cm 3 ofleadat20 C(5pts)? (c) Ifthethermalenergyof1.00molofanensembleofagaswithmolarspecific heat(i.e.,cv)is12.5j/mol Kisincreasedby0.500J,byhowmuchdoesthe temperaturechange?(5pts) (d) You have 2.0 mol of gas A that initially has 5000 J of thermal energy. It interacts with 4.0 mol of gas B that initially has 8000 J of thermal energy. Assume CP = 20.8 J/mK for both gases. After equilibrium, what is the final temperature?(5pts) (e) Whatisthefinalthermalenergyofeachgasin(d)?(5pts) Problem2(20pts) Youhave2.00molofanidealgascontainedinavolumeof1.00m 3 thatundergoesa freeexpansionintoavolumeof2.00m 3. (a) Derive a formula for the change in entropy for this process. Explain your steps.(15pts) (b) Howmuchdoesitsentropychange?(5pts) Problem3(25pts) An early model of the atom, proposed by Rutherford after his discovery of the atomic nucleus, had a positive point charge +Ze (the nucleus) at the center of a sphere of radius R with uniformly distributed negative charge Ze, where Z is the atomicnumber,thenumberofprotonsinthenucleusandthenumberofelectrons inthenegativesphere. (a) Show, by derivation, that the electric field inside this atom is given by E = Ze 1 4πε 0 r r r ˆ 2 R 3 (15pts) (b) What is the net electric flux through a concentric sphere of radius r = R/2? (5pts). (c) What is the net electric flux through a cube with sides R/2 that is centered aboutthepointcharge?(5pts) 3

4 Problem4(30pts) Twoloudspeakersarelocatedonthey axisat(0.00m,+2.50m)and(0.00m, 2.50 m).thetwospeakersareinphaseandemitequal amplitudesoundwaveswitha frequencyof1.00khz.anobserveraislocatedonthex axisat(10.0m,0.00m).a secondobserver,b,islocatedinthexy planeat(10.0m,2.50m). (a) (b) (c) (d) (e) (f) Sketchthearrangement.(2pts) Write an expression for the amplitude of the composite sound wave heard at A? Assume each wave arrives ata with an amplitude a. Give youranswerintermsofa.(3pts) WhatisthephasedifferencebetweenthetwowavesatB?(5pts) Write an expression for the composite sound wave heard at B. Assume eachwavearrivesatbwithamplitudeaandgiveyouranswerintermsof a.(8pts) Nowassumethattheupperspeakerismovingwithavelocityparallelto thex axis, 50.0 x ˆ m/s,andthatthelowerspeakerisstationary.whatis the difference between the two frequencies heard at B? Justify your answer.(10pts) Whichspeakerin(d)hasthehigherfrequency?(2pts) 4

5 Bonus(10pts) The adjacent figure shows a mass m oscillating as a simple pendulum in an electric field produced by a very large plate. Imagine this pendulum being observed on the space shuttle. What is the angular frequencyforthisoscillation?justifyyouranswer. 5

PHYSICS 221, FALL 2010 FINAL EXAM MONDAY, DECEMBER 13, 2010

PHYSICS 221, FALL 2010 FINAL EXAM MONDAY, DECEMBER 13, 2010 Name (printed): Nine-digit ID Number: Section Number: Recitation Instructor: INSTRUCTIONS: i. Put away all materials except for pens, pencils,