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Unformatted text preview: Physics 171 101 Final Exam Answers
May 7', 2007
Prof“ Barnett Take g =2 10 nit/sec? 0°C: 273°K, R = 8 Joule/(mole—“IQ
Use a pen. You may use material written on four 3” x 5” index cards. Write the foliowing two sentences onto the front cover of your blue book and sign it. I agree to complete this exam without receiving unauthorized assistance from any person or
device, I will not reveal the contents of this exam to any unauthorized persons. 1. 30 Two vectors are given by F} = (21+ 31 + 4k) and 172 = (51— 61') A.) (10 pts) If the ﬁrst vector, F1: (21—: 31' +411) N, is one of two forces acting on a 5 kg
mass and the second vector is the mass 5 acceleration E1'— — (51— 61') 111/secg, what' 18 the second force, F2, acting on the mass? Fg—  1115' w F1: (231' m 331' w dih)1 N B) (10 pts) If instead the ﬁrst vector is the total force, meg m (21 + 31 + 41th N, acting
on an object and the second vector is the distance d: (51— 61') meters moved by
the object what is the work, 11V, done by F1010; during this motion? XV: F (1’: 8 J C) (10 pts) Suppose instead that the first vector is the location, F: (21+31' +411) meters,
of a 5 kg mass relative to an origin and the second vector is a force, F— (51 — 61')N applied to the mass what torque, T, is being applied relative to the origin?
T= Rx Fm (241+201~27k) N111. D) (10 pts) Suppose, ﬁnally, that the two vectors represent the velocities of an object as
measured in two different inertiai coordinate systems i e. V; — (21 ~i~ 31 + 4k) )1n/sec
and V2 m (51' ~ 61') 111/ see, What' IS the velocity of inertial coordinate system number
1 as measured in inertial coordinate system number 2? (31— 91' —— 4A) iii/sec. George Washington throws a 1 0 gr am doliar coin to his wife Martha, who is a distance
(1' «~— (251 —~ 251' ~— 6011') meters from George wher‘e ‘up’ is in the 1' direction and 1' and k
are 1101 izontal Martha catches the coin 5 seconds after George throws it. A) (10 pts) What is the coin’s velocity, 17(0), when George teleases it?
17(0) m (51' 1— 201—1211) 111/3
B) (10 pts) What is the coin’s minimum speed during its ﬂight? 13 111/ sec. C) (10 pts) What 15 the coin ’s veiocity, 21(5), when Martha catches it?
(5 )m (51 — 301' — 12k) 1n/sec D) (10 pts) If Martha catches the coin in a time peiiod of 0.01 seconds, is if it takes
0. 01 seconds from when the coin first touches \‘Iartha’s hand until it is stationary,
what is the average force F’cnm, that the coin exerts upon Martha’ 3 hand during the catch? Fave m w.(0 51— 31' — 1 211) N E) (10 pts) If the temperature is 72" F during this event, what entropy change occurs
when Martha catches the coin? AS m 9% m 951%; m +181 x 10“”3 J/“K. TURN PAGE OVER. 3 . Two identicai 2 meter iong wires are used to suspend two 3 At t = 0 a pulse on a string has a shape given by the equation
ili(rc,0) = (0 03) (2‘m')171.. Both :1; and a“) are measured in
meters. The pulse has a speed of 2 211/8 in the —i direction A) (10 pts) Sketch I'll/(.73, 0) in the region from
—5m < :i: < 5171 Label the axes. B) (10 pts) Draw a sketch of the pulse 1 second later, i.e. n4 free;
1,!)(rr, 1), from w5m < :E < SW. C) (10 pts) Write down the function describing the pulse at
t=° seconds, i.e. #203,?) 21201:, 2) = (0.03) (2”(1+“)”)m. D) (10 pts) Write down the function describing the pulse at
an arbitrary time, i.e. 11bit, t)
were) m (0.03) (seer”rm. it mares: / f r ' / /;’
. . . in
10 kg masses from the ceding. Each ware has a. mass of 0.10 grams and is 2 meters long when the temperature is 27 ”(V 27 06'. The wires have a thermal coefﬁcient of expansion of
2.4 X 10““ ”If"? a
10 itg A) (10 pts) When its temperature is 27 ”C the left wire is caused to vibrate transversely.
What is the speed of the wave along the wire? 11 2 g m 1414 111/ sec B) (15 pts) What are the wavelength and frequency of the fundamental standing wave on
this wire? A = 4 m, f m 3535 Hertz C) (15 pts) The second (right) wire is cooled to a temperature of 0 ”C. What are the
wavelength and frequency of the fundamental standing wave on this second wire?
A = 3.974 771,)” = 354.7 Hertz. D) (10 pts) If both wires Vibrate at their fundamental frequency what beat itequency
would be heard? often; m A f m 1.2 Hertz Space stations have been proposed to accommodate extra.
population of the Earth. A design is tor a hollow, uniform,
cylindrical station of diameter 3.00 km, length 10 00 ion, and
total mass of 1.20 X 1010 metric tons The space station spins
about the symmetry axis of the cylinder. A) (10 pts) What angular speed, w, is required to si1111.iiate
the acceieration of gravity (g = 10 m/sg) for individuais
at the enter perimeter of the station? or = 0.08165 sec’1 B) (10 pts) What is the rotational kinetic energy of the station? $10412 = 9 X 1016 J
C) (10 pts) What is the magnitude of the angular momentum of the station?
L = In} 2 ‘11:.ng = 2.205 x 20” he mg/sec. D) (15 pts) The space station is set spinning by attaching thrusting rockets tangentially
to the outer surface. Each rocket exerts a force of 1000 N. It takes 100 years (365
days) to get the station up to its design rotation speed starting from rest. How many
rockets are reqnired? % = 7 X 10m N r m = NronE racket ”4116600 rockets. 6 A horizontal 111assless spring is attached to a 5 kg mass on a frictioniess surface A 10 kg mass slides horizontally
into the 5 kg mass and they stick togethei, causing both
to oscillate on the spring, The speed of the 10 kg mass
just prior to the collision is 1.5 {11/ sec A) (10 pts) ‘What is the speed of the combined system of the two masses immediately
after the collision? Momentum conservation —+ em“; = 10 rn/seo B) (15 pts) How does the mechanical energy of the system of two masses change during
the collision? Ilemmaz m 11.25 J, rleﬁm = 7.5 J, AME = —3,.75 J C) (10 pts) The osciilation arnpiituc‘te of the spring with the two masses after the collision
is 15 cm. What is the spring constant of the spring? glint? = 7.5 J ——> A: x 667 N / 111 D) (10 pts) How much time passes between the instant of the coliision and when the two
masses ﬁrst come to rest? T 2 Eng ——> T/4 = 0 236 sec
I .r'l Two moles of an idea} inonatoniic gas (6’ m 25R, and ill" 1‘1an His? iﬁUf'llt‘l‘lual
CV = 1511?) are taken around the adjacent cycle, The B
achahatrﬁ initiai pressure is 105 Pascale and the initial volume is
20.0 liters. The tlnee processes are 1) A ~—> B isothermal
until the volume doubles, 2) B —> 0 1300110110, and then i C“
3) C > A adiabatic Use R m 8 Jonie/(mole—C’K), l A) (10 pts) What are the pressures for the three states A, B, C'?
PA = 105 Pascale, PB 2 (15 X" 105 Pascais, Pg = 0315 x 105 Pascale. B) (10 pts) W hat are the temperatures for the three states A, B, C"?
TA 2 1250K, T3 = 1250K, TC 2 78.701117 (3) (10 pts) During the ﬁrst piecess, going from A to B, what is the heat coming into the gas, the work done by the gas and the change in the internal energy of the gas?
AT = 0 1,1 AU = 0,, W = nRTlM—l—gf) m 1386 J, Q = 1386 J D) (it) pts) During the second process, going from B to 0, what is the heat coming into the gas, the work clone by the gas and the change in the internal energy of the gas?
W = PAV = 0, AU = 11.01;le m ~1111 J, Q = AU =2 wiill J E) (15 pts) During the third process, going from C to A, what is the heat coming into
the gas, the work done by the gas and the change in the internal energy of the gas?
Q 2 0, AU = nC‘VAT = +1111 J W m ~AU = —1111 J F) (10 pts) What IS the efficiency of this engine?e— _ 7211:— : éfﬁ~  19 8% G) (16 pts) What is the entropy change of the gas during one complete cycle? AS— — 0
H) (10 pts) )What would the efﬁciency of a. Carnot engine be if it operated between the highest and lowest temperatures expei‘iencecli 3y this engine? 13— — 1 — ﬂ — —37% ...
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