{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Test 3 Fall 2009 - Problem 1(25 Points In a recent lab you...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 8
This is the end of the preview. Sign up to access the rest of the document.

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 = 6.7e-11 #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 Wit-M cmCfim/mg(aemnm++)”z * the} 4* E3: ~GMEML$ l‘FI‘ _. craft-w 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—MH-m /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 spacecraft-Earth 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 carbon-12 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 carbon-12 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 oxygen-16 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 ‘ Evil-x (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) wu-k {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 ...
View Full Document

{[ snackBarMessage ]}