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Unformatted text preview: Problem 1 (25 Points) In a recent lab you wrote a program to predict the motion of a spacecraft interacting with the Earth and
Moon. The initial lines of your code were similar to the program below except that we are no longer
including the effects of the Moon. (a 16pts) Add the missing statements needed to update the momentum and position of the spacecraft and
compute the kinetic and potential energy of the spacecraft—Earth system. from visual import * #CDNSTANTS G = 6.7e11 #Gravitational Constant #OBJECTS AND INITIAL VALUES Earth = sphere(pos=vector(0,0,0), radius=6.4e6, color=color.cyan) craft = sphere(pos=vector(10*Earth.radius, 0,0), radius = 3e6, color=color.yellow)
craft.p = mass’craft*vector(0,7100,0) #Initial spacecraft momentum Earth.m = 6e24 #Mass of the Earth craft.m = 15e8 #Mass of the spacecraft distance_EC = 2*radius_Earth #Two Earth diameters away craft_trail = curve(color=craft.color) #The trail for the spacecraft
U_graph = gcurve(color=color.blue) #A plot of the Potential energy
K_graph = gcurve(color=color.yellow) #A plot of the Kinetic energy Energy_graph = gcurve(color=color.green) #A plot of the Total energy
#CALCULATIONS
t = 0
deltat = 10
while t < 60*365*24*60*60:
#Relative position vector % .9 d
r_Earthcraft = CPAHHPOS ‘ Eqr'Ha.PoS it P t robs“ CNMK A rkm‘: r. Ear’rkcmti/ may (r Earh‘cr‘“) 1“? V]: a r/[Fl #Force on craft due to Earth orce ar cra = ” ¥ ~ * —
F —E “1 ft G WitM cmCﬁm/mg(aemnm++)”z * the}
4* E3: ~GMEML$
l‘FI‘ _.
craftw me? + smearmmemm’r tr set; + FmtAt #Update Position of spacecraft craft.pos = CMH.?0\ + QmQ'LP /Qr0\‘i+v\~. * oiell‘ai' 1k FC ’3 I: ’5 \"/ At #Update Momentum of spacecraft program source code continues on the next page #Update Kinetic energy of the spacecraft '  ‘ c i ‘2
K—Craft = "“3 (cra§~93**2 /('Z*cmH.I~\ 1" K “‘ £ ov K 2 “MI
W cM—Lm " w«g(“‘*""9/<:ea€¥.u§ )“2 /z 2““ #Update Craft + Earth potential energy U_craft_Earth = ' 6* ERPW‘W‘J‘C—MHm /y\.a3(r'. ENk‘CNetl') ‘4’ U3 i " GME'WN. #Update Total Energy l '7': l
E = K_craft + U_craft_Earth #Update Plots & Time craft_trail.append(pos=craft.pos) #Plot new position of the spacecraft t = t + deltat U_graph.plot(pos=(t,U_craft_Earth)) K_graph.plot(pos=(t,K_craft)) Energy_graph.plot(pos=(t,E)) (b 7pts) Draw the kinetic, potential and total energy of the spacecraftEarth system as a function of
separation, if the spacecraft has a velocity below the escape velocity and moves in an elliptical orbit. (c 7pts) Draw the kinetic, potential and total energy of the spacecraft—Earth system as a function of
separation, if the spacecraft velocity is above the escape velocity. Problem 2 (25 Points) An alpha particle (two protons and two neutrons) moving with momentum p is shot toward a carbon12
nucleus (containing six protons and six neutrons) that is moving with the same momentum 13 toward the
alpha particle. The speeds are non—relativistic. (a 6pts) For this process, as a function of the separation 7" between the alpha particle and the carbon—12
nucleus, plot K1 + K2 (the sum of the kinetic energies of the two nuclei), plot the potential energy, and
plot the sum of the kinetic energies and the potential energy. Label each of the three plots clearly. E7. k+U= Cong (AM { Energy U (b 10pts) What is the minimum momentum p necessary, so that the alpha particle and carbon—12 nucleus come in contact? The radius of the alpha particle is Ra and the radius of the carbon12 nucleus is RC.
Your answer should be symbolic. SyS+“M = Guyana; 4 o< ~pw+icle P m
AE=O —9 E“:E€ (1.9—4 N =1) ®9MK (c 9pts) There is a head—on collision of the alpha particle (Ra = 2.061310‘15 m) and the carbon—12 nucleus
(RC = 2.983710—15 In) creating an oxygen16 nucleus (containing eight protons and eight neutrons) and a
photon. The kinetic energy of the photon after the nuclear reaction is 10.352 MeV (1 MeV = 106 eV =
1.60225610_13 J). The oxygen nucleus recoils with negligible kinetic energy. Assuming the momentum of
the alpha particle and the momentum of the carbon—12 nucleus are identical right before the reaction, what
is the minimum (non—relativistic) momentum that the alpha particle must have in order for this process
to occur? AE=O ~9 E‘:EF
P [WWW
“P
(9‘3 é[email protected] =9 . «o my > 1. 1, 'L 7. a
mac +ch. + L 4' ”IL... 2 M061 + by
2W9 2MK :: 1 ‘ '
02%” +0!ch 4r}: + i = (Mm. )c"
ZMc 2W!“ P + E) ﬁes } M455 6 g Problem 3 (25 Points) A spring with stiffness k and relaxed length
L0 stands vertically on a table. A mass M
sits on the spring in static equilibrium. (a 5pts) What is the compressed length of the spring L in terms of the variables given above and any
known constants. 9,5 : M455 0%: ’1?wa a Fwt=° Fm = —\<(\M"Lo3 “M3 = o
8) —‘<lLl +kLo ”W3=O ‘K Nola: For L50 ‘ 334 L
K (b lOpts) Using your hand, you compress the spring so that the spring now has a length of L / 2 and you
hold the spring motionless at this position. Calculate how much work your hand did? Explain if the sign
you obtained for this work is reasonable using a different argument from the one you employed to calculate the work. SyS.‘ Lax. sfrhj ‘ Evilx (m —l=~wl L ll: 1= I ‘ I —
iii.) WW) ' W
AUJI‘IV U r'
Expandakj odl‘ A ””5
= 7% gamim.
Flu ‘ \ 1
””9 "‘ L=L°~M9
?
k): ”aim Lo + .L (M3? 1 I ‘1 zkaEt 0
H3 8 T + "kL. :Ek(2l(LO~W‘_3))'2 K23) wuk {S ”5‘14“ Lccwm applnd ﬁance. f: in “\L alt'rw‘oh
O; m mhkbh. (c 10pts) You let go of the block and watch it shoot straight up into the air. How high does the block go
before it starts to fall back towards the ground? Be sure to express your answers in terms of the variables Sysi lobc‘t.5pr:\«fl Earn. given above. Problem 4 (25 Points) You put a thin metal pot containing 2 liters (2000 grams) of room—temperature (20°C) water on a hot
electric stove. You also continuously stir the water with an electric beater. You observe that after 5
minutes the water starts to boil (temperature 100°C). Over this ﬁve minute interval the electric beater did
30,000 J of work on the water. When answering the following questions, you can assume that the change
in kinetic energy of the water is negligible. (a 10pts) Determine the change AEthermal in the water. Show how you calculated this number. 6‘1“ the 05:15am» = chT
= (‘ll 7/3 “0(20 005) 000°C 40°C} = é‘tz.oooT = éFIleosj (b 10pts) Determine the thermal transfer of energy Q into the water from the surroundings. Show how
you calculated this number. 375: Hyb AE—zw'fa
9 OzAE’w7AEMn~W
2 632x116)” , 3xloqj (c 5pts) What was the change AEsurroundings in the rest of the Universe (the surroundings, including the
stove and the beater)? 6Y5: UMJWR Ag: AEHLO *AES‘ut‘mandi‘BS :1 O Liv) AEJuN‘m/mdi’ys '2 J AEHZO ...
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 Spring '09
 PROG
 Physics

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