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Unformatted text preview: Problem 1 (30 Points) In an amusement park ride called The
Roundup, passengers stand inside a
rotating ring with a diameter of 16 m.
After the ring has acquired sufﬁcient
speed, it tilts into a vertical plane as
shown in the diagram. The ring takes
4.5 s to make one complete revolution
while in the vertical plane. Rotation
axis (a lOpts) What is the contact force on the rider when she is at the bottom of the ride? Your answer should be numeric and include a direction. : :1: '1 a (un mfg)" "g
F M R + aj m[_..___...<m mam/$13
:2 25qu [kl/kg“: (093 (b lOpts) What is the minimum angular speed of the wheel, such that the riders do not fall off at the top? 7.
Fnet$L= ls: +mg ‘1 .: mwlP‘“ Fe 1'” “1(a): R“ (j) > O Jco 5mg \ri cantacit (MR 93 ‘> O
to > «WI/R = Magma/(m =~ mm rad/e ners: We didn‘t Consider“ OJ (“PAIR because, 0) >0 . (c 10pts) Now the ring returns to a horizontal plane but continues to rotate. You notice that, if pick your
feet up off the ﬂoor, you do not slide down the inside surface of the ring. The coefﬁcient of static friction
between your back and the inside of the wheel is 0.4. What is the minimum angular speed of the wheel,
such that you will remain suspended, motionless, on the inside surface of the ring? (mt
L911 ‘7
+7“ L Makaom Static, Friction can he. is [L5 FM =/u_,5 Fe _
Fne'tALJ‘ Fe m a)?“ To 043+ slide clown) F; may 3 F3 jag, (miss?) 2, mg
as Z xiii/gusto = «(rewrite/(emerqu = lms‘ rail/31 Problem 2 (25 Points) Consider a ball of mass m hanging
from the ceiling by a spring with rest
length L0. The ball is a vertical dis—
tance h from the ceiling and travels in
a circle of radius R at a constant speed
as shown in the ﬁgure. (a 5pts) Using the momentum principle, determine the spring stiffness ks. Hint: consider the net force in
the y—direction. No Moldova “m {j‘dirscé’ioﬂ ’39 53%;: a “'3? Rake: O z? Fsprinq {mg a Q R m “’2
kSCLLD 5M6) = mg and L 3 005(9) 3”" “WWW.
ma (Pl/caste) ' L53 s’mCe‘) .
(b 10pts) Determine the speed of the ball. Your answer should only depend on the variables given in the
problem statement and or ﬁgure. k.st = ._= my:
Fruit! 'L E‘Primﬁ‘ l J... R
Ks (L— La) cos(e) = “Lsz
mg L .3 “1V1
iﬁL'LQslMSB (L D» mace) R (c 5pts) Now, consider the case where air resistance is not negligible and the ball slows down and eventually
comes to rest. What is the work done by the spring during this process? L 2 , ;
Nap!an = ' Auapr‘ma = 2ks<5i "‘ 5;“) ) where. S; mnci 35: are the Anibal aﬁé ﬁnal; sﬁraﬁhgg 0»? line, spring: a a t a ' Fill‘m“
Nee \ m ' $4; * V i
d Mo+xonle$5 =39 Fﬁpraﬁs == 131%
F3 mg \«Ss; =m35 => 5+: — 5
And 4mm 3:) k5: m— _/ Ssinieb
Then 8; == 5L" 5§n(9). l l
‘Wsprmq "‘ ‘2‘ k5 (5&2 “ ngsénzéeﬂ = ‘i2‘ kSSE (lsinXCaﬂ = E ks S? £05203) '1 1?. W5 6; 5051(93/s‘mCG3 = (d 5pts) How much work was done by the air during this process? §%s+e.m ; Morass; ﬁpr‘mg“ Earth ﬁercﬂumﬁlm a} A“
AEsﬂs 3“ WED”. : Nair é waif 7': + AU$9rZﬂg +~ ﬂ : <0 w + NSPYRUSB + It
Part b‘) Patric, :3) 'AB: (“ L3; —' 2: ll ’ L3;
m3 = h— (Lac—L93 — Lo
Wm.) ‘
amassing Euarawma ‘2 _ 5; a 5: 5N9) ‘C‘Qm shew... w . =7— — ~——....E‘,W., ,2, ‘ __ Qgﬁﬁv‘g {a m ‘
WM m3 [HO“(9‘) + 2 (armaim ' LA m3: +Kca5£§9fL35m<63+ Lo“ ii} We exegesis New < O g‘mce, it‘s holding emergg moi: 3—? like; saga‘l'ﬁm, Problem 3 (25 Points) You blast off from Mars, and you turn off the rockets when you are 3500 km (3.5 x 106 m) from the center
of Mars, well above its thin atmosphere and headed away from the planet. You intend to leave Mars for
good, and by the time you get very far away you want to be coasting at a speed of 1800 m/s. Mars has a
mass of 6.4 x 1023 kg. (a 18pts) Calculate the speed you must have when you are 3500 km (3.5 x 106 In) from the center of Mars
in order that your speed when you are very far from Mars is 1800 m/s. Explain carefully and completely,
starting from a fundamental principle. égs—tem ' Me. “' Mo‘s Surroundin3§1 Nol‘n‘ma r 0
Ma: E,‘ "z E;
x 2 GM'WL _ I 2
5: V1” r_ " 7.ng
l.
,: 2 ZGM ‘ 7. Max “‘Nm2 2 GA 23k
Vt. Vt“? r = (t8oornls)1+ —————————————3————————( ‘0 /k MO 33 L (3.5:: lo" m3 (b 5pts) Which of the following energy graphs best describes the Mars—spacecraft system? Circle the
number next to the correct graph. K+U / K‘= 1.38xlo'nz K K+U (c 2pts) On the graph you chose for part (b) label the kinetic energy at one point on the graph, by giving
its value. KR: émvg = é—m (52¢;ng "‘le = 138"IO7’”1 [J‘s] L Problem 4 (20 Points) Three potatoes are dropped into a pot of water to make potato soup. Initially, the potatoes are at room
temperature (25 degrees Celsius) and the 3 Liter pot of water is boiling (100 degrees Celsius). Each potato
has a mass of 2.2 kg and 1 liter of water has a mass of 1 kg. The speciﬁc heat of a potato is 3.43 x 103 J
kg“1 0—1. (a 10pts) If the water and potatoes are well insulated from their surroundings, what is the ﬁnal equilibrium
temperature of the water + potato system? You can ignore the change in thermal energy of the pot. §g$temi Water + ijt‘m‘l‘ﬁ Surround‘an§‘ Negiig‘x‘olﬁ o O
AESSszmr «argﬂ»; 1:0 :3; AEﬂuo mw‘ﬂ'ir Cwn‘i‘er (T4 “uniwa+ar\) + mpa‘kﬁn Cpa+cx+o ("TF” .rl‘mnfwiux : 0 (Shawn maﬁa.) (T1..— iooecﬁ) + (mega) (my 103 $5393 (T4  25:30 a Q 5.52Lixio“ [~35] 1; ~ Lszcxio‘” [:1 = o a, ,
T :W/‘mwm “c =‘ 51.82°C {
‘ 5.524xio“ (b 10pts) The pot containing the water and potatoes is now placed on an electric burner. If the electric
burner has a power rating of 1000 W, how long does it take before the water and potatoes reach 100 degrees
Celsius (i. e. boiling)? Again, you can assume that the change in thermal energy of the pot is negligible. /_\ Eqrh == (3%» (4.2X103 €75.Xioo“c— 51.322) + (c. to k3)(3.u3x :03 ﬁa‘ximz « 51.s32°c§ = League": _, "lei; __’l_‘f—_. =_l,;<_03__8_>:in‘f.l .5
Power w at => A”: " pcwir looow ‘ 8WD ...
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 Spring '07
 JUNGH.CHOI

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