T1 - PHYS 2211 Test 1 September 17th, 2009 Name (print)......

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Unformatted text preview: PHYS 2211 Test 1 September 17th, 2009 Name (print)... ___________ __ Instructions 0 Read all problems carefully before attempting to solve them. 0 Your work must be legible, and the organization must be clear. 0 You must ShOW all work, including correct vector notation. 0 Correct answers without adequate explanation will be counted wrong. 0 Incorrect work or explanations mixed in with correct work will be counted wrong. Cross out anything you don’t want us to read! 0 Make explanations correct but brief. Don’t write a lot of prose. 0 Include diagrams! —3 6 0 Show what goes into a calculation, not just the final number, e.g.: $61-53 = W = 5 X 104 0 Give standard SI units with your results. Unless specifically asked to derive a result, you may start from the formulas given on the formula sheet, including equations corresponding to the fundamental concepts. If a formula you need is not given, you must derive it. If you cannot do some portion of a problem, invent a symbol for the quantity you can’t calculate (explain that you are doing this), and use it to do the rest of the problem. Honor Pledge “In accordance with the Georgia Tech Honor Code, I have neither given nor received unauthorized aid on this test.” ’ Sign your name on the line above PHYS 2211 Do not write on this page! Problem 1 (25 pts) Problem 2 (25 pts) Problem 3 (25 pts) Problem 4 (25 pts) Problem 1 (25 Points) (a)(4pts) Write down the definition of the momentum of a particle valid at all speeds. Please define and describe any quantities you use in your definition. Your answer must be exactly correct to receive credit, including arrows for vectors, correct subscripts, etc. There is no partial credit. .3 I: Mcméai‘VM C: Spied cc . . ( l M: MASS W9“ 6 6:. .3 1’ Q _ ‘ , Ni V ~ valacdx; l“ ‘32.. (b)(6pts) Below are several snapshots of a particle taken at equal time intervals. Circle the trajectories that indicate an interaction is takififlg‘fiieogbetween the particle and itsqsurseumhings. was I'iifiisififiiefiiisiiai (c)(10pts) Write down any one of the valid forms of the momentum principle. If you write more than one and any of them are incorrect, the whole problem will be marked as incorrect. Your answer must be exactly correct to receive credit, including arrows for vectors, correct subscripts, etc. There is no partial credit. t, I FM“ = 73+. ‘: + (d)(5pts) Two students are late for class and collide with each other. The collision last, for a very short time but is sufficient to bring the students to a standstill. During the collision the collision force on one of the students was determined to be F =< —F2, 0, 0 >. What was the collision force on the other student? Please explain how you know this. Tint. £9? (Q cn 0 S +U Gig/l Eta Ono», TL‘S IN] frat (jut: reciprocily / Newim'i LQHVUM Problem 2 (25 Points) In the accompanying figure a 0.4 kg hockey puck sliding along the ice with velocity < 10, 0,0 > m/s. As the puck slide past location < 1,0, 3 > In on the rink, a player strikes the puck with a sudden constant force < 400, 0, 800 > N. “Na. (a)(10pts) In the space below, make a sketch of the path of the puck before and after it is hit. Note that the impact of the hockey stick is very sudden. When sketching the path of the puck you can treat this collision as if it occurs instantaneously. towgi o \n (b)(10pts) The hockey stick was in contact with the puck for only a brief moment Atl = 0.01 s. What is the position of the puck after this time has passed? 7‘ Freer a” <mqugwm‘i/ML a 0‘ (Wt/in? A a» :. <FX.ORF;>A{§ x§»d:NC§.I‘GJE1 Vxng ’: V)“; «1- Z; W$%E M «4) MA? :— Vmw V1.5 : Wm + E Aid i‘dt Nd‘l‘bhi t a, \g a “no, I Z a... - VHS ~» . ~— W‘ » ~ [Oms‘g + 900“ (0.0%} s V m, a ‘ . f ‘i. mud-{k flAUG ‘ » 1- O I g a: 3 : W h I , 7 P ‘ c «c M m ‘2 2m 2mm?) P A T’s ‘ - x 2: W‘Sm . i w - Q ~1- VM m: ~ ’ Q 2 T1 1— % M; +1£Ew N1 = 0.0.9:“ + «ow-30,0w0ses) +1619?“ 0, ‘7 (0.03531 1, may Mk9 r (046.03.?) am} (c)(5pts) After losing contact With the hockey stick, the puck travels across the ice for a time Atg = 2 8. What is the position of the puck after this time has passed? .45 Fm} :0 =5 A3 :0 “*3 Van :Cchs'iflw "1‘ QUE 0.20%3‘9 Problem 3 (25 Points) Here is a portion of the trajectories of two asteroids interacting gravitationally and far from anything else. The asteroids are moving away from each other, with positions marked at times t1, t2, and t3. At each of these positions, draw vectors of appropriate lengths and directions for the forces acting on each of the asteroids at that location. Label these vectors "F”. At the same locations draw vectors of appropriate ’7 7’ lengths and directions for the momenta of each of the asteroids at that location, and label them p . (”Appropriate lengths” means that larger magnitudes are represented by longer vectors.) Problem 4 (25 Points) The two Apollo astronauts on the airless Moon did the simple experiment of dropping a coffee filter of mass m and observing that it took 1.6 s to fall 2 m. This close to the surface of the moon the force of gravity on the coffee filter can be approximated as constant. (a)(9pts) When the astronaut released the coffee filter it had zero initial speed. Starting from the momen- tum principle, show that the time t it takes a coffee filter to fall a distance h on the surface of the Moon Mi «.2 at; at, : <05§mvl o>At 2hm is given by the expression t = _. . IF gravl determine the mass of the Moon. my: Gamma,“ «a MM (c)(8pts) On Earth, one of the astronauts weighed 777 N. How much does the astronaut weigh on the Moon? If you were unable to determine the mass of the Moon from part (b) you should use the variable mmmm in your calculations. 'W‘ mm a Wv “tail/3 ’5 iW/Mw :- 773543 6—“ a ‘ a ' “2 (ammo L13 w; ‘)(?‘l-5k3lmm ,, Lfizsvm 'mw‘ (M75 HOGWAZ T [6 you (saith-Ft "J: get Pew} t Eigle C CWA MM : Rt? Things you must know: Definition of average velocity The Momentum Principle Definition of momentum The Energy Principle Definitions of particle energy, kinetic energy, and work The Angular Momentum Principle Vector Products: -+ XB=&&+%%+&& A’ x E =< Asz — Asz, [lsz — AmBz, 14sz — 14sz > Multiparticle systems: _, m1F1+m2F2+... ~ _, rem : Ptot '3 Mtitvcm (71 << C) Ktot = Ktrlms + Krel Krel = Krot ‘l‘ Kmfib Kt'rans % EMtotvgm (’0 << 6) I = mlrfl + "1270;. + ' ' ' L2 1 4 a 4 Ifrot = 237‘ = 5101i :A = TA X F a a # Ltrans,A = Tcm,A X IDtot L'rot = I‘D LA = Ltrans,A 'l‘ L'rot Other physical quantities: 1 2 2 ’Y E a 2 E2 — (pc) 2 (mc2) 1 - (1') c -‘ m1m2 A m1m2 F = —G U = —G gra’u IFl2 gra’v [Fl ngm, 2 mg near Earth’s surface AUgmv % mgAy near Earth’s surface -' 1 41% A 1 (1142 = __ U = __ elec 47r€0 IFIZ 7" elec 47r€0 _. 1 spring = kss opposite to the stretch Uszm-ng = 519332 for ideal spring 1 UZ- x 51931-32 — EM approx. interatomic pot. energy AEthermal = mCAT 13.6eV EN = — Where N = 1,2,3... (Hydrogen atom energy levels) N2 k . EN = N hwo + E0 Where N = 0, 1, 2 . . . and we = ‘ / 77:1 (Quantized oscillator energy levels) d5 dlfil A A 6113 * dlfil -* 0115 I17 A - - . - - — = — —— h = —- A : A — z —— dt dt 1) + |p| dt W ere F” dt p and Fl |p| dt R n and R 18 the radius of the klssmg ClI‘Cle 2 w=—7: $=Acoswt w: E T m _ F/A ksi . ks’i Y — m (macro) Y — -d— (micro) speed of sound '0 — d m—a f = (cos 0x, cos 9,,, cos 0:) unit vector from angles Moment of intertia for rotation about indicated axis _. l =(q+N 1)' 35191119 1 9 ql(N—1)! f III €113; AS = % (small Q) prob(E) cc 9 (E) {W Constant Symbol Approximate Value Speed of light c 3 x 103 m/s Gravitational constant G 6.7 X 10"11 N - mz/kg2 Approx. grav field near Earth’s surface 9 9.8 N/kg Electron mass me 9 X 10’31 kg Proton mass mp 1.7 x 10'27 kg Neutron mass 'rnn 1.7 X 10"27 kg Electric constant —4736 9 X 109 N - mZ/C2 0 Proton charge 6 1.6 X 10—19 C Electron volt 1 eV 1.6 X 10—19 J Avogadro’s number N A 6.02 X 1023 atoms/11101 Plank’s constant h 6.6 X 10—34 joule - second hbar = % h 1.05 X 10—34 joule - second specific heat capacity of water 0 4.2 J/kg Boltzmann constant k 1.38 X 10—23 J /K milli m 1 x 10-3 kilo K 1 x 103 micro 11 1 x 10-6 mega M 1 x 106 nano n 1 X 10—9 giga G 1 X 109 pico p 1 x 10-12 tera T 1 x 1012 ,. ...
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T1 - PHYS 2211 Test 1 September 17th, 2009 Name (print)......

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