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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.: $6153 = 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
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(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:“ + «ow30,0w0ses) +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; ‘)(?‘l5k3lmm ,, Lfizsvm 'mw‘ (M75 HOGWAZ T
[6 you (saithFt "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 Uszmng = 519332 for ideal spring
1
UZ x 5193132 — 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 103 kilo K 1 x 103
micro 11 1 x 106 mega M 1 x 106
nano n 1 X 10—9 giga G 1 X 109
pico p 1 x 1012 tera T 1 x 1012 ,. ...
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 Spring '09
 PROG
 Physics

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