Exam 3
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Georgia Institute Of Technology *
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2211
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Mathematics
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Apr 3, 2024
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PHYS 2211 Test 3 October 29th, 2009 Name (print)__Zma_f /D//Y/ Qa/ Instructions e Read all problems carefully before attempting to solve them. ¢ Your work must be legible, and the organization must be clear. You must show all work, including correct vector notation. Correct answers without adequate explanation will be counted wrong. Incorrect work or explanations mixed in with correct work will be counted wrong. Cross out anything you don’t want us to read! e Make explanations correct but brief. Don’t write a lot of prose. ¢ Include diagrams! . ) ) . ab _ (8x10-3)(5x108) __ 4 o Show what goes into a calculation, not just the final number, €8 od = (ax10-5)(ax10%) = 0 X 10 o 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.” S S Sign your name on the line above
PHYS 2211 Do not write on this page! Problem Score Grader Problem 1 (3§ pts) 2 2@ FHF Problem 2 (25 pts) & X/ Problem 3 (25 pts) s Tl Problem 4 (25 pts) =1 e
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 * #CONSTANTS G = 6.7e-11 #Gravitational Constant #0BJECTS 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 = 15e3 #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 / r_Earthcraft = C(‘Ocu'.(,og = Eo.r‘ux\.(—'og cMaq T Mag (r,\{,f“m(r mfi) / #Force on craft due to Earth /+ Force_Earthcraft = = C-,.% E(JH« -"‘\\‘f U"“QL . W‘/(‘ K Ec\,r {-\/\ (_rtku X - G* Eacth.m™ cro\H.m/ rm“f)** 2 F - Earrheradt #Update Momentum of spacecraft o * craft.p = coad et Forcc,to\r L\'\Lfikmr &&HC«.—L v #Update Position of spacecraft Ny * craft.pos = C(K‘C# , Pg,g L CM\’L\“() /c(°3\\— » A d&’+ml program source code continues on the next page
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#Update Kinetic energy of the spacecraft K_craft = Mm%(c(ajr- \H(Q/(Q trall '\/\) . #Update Craft + Earth potential energy U_craft_Earth = — G ¥ C(kc‘("M* EHL(‘H’\-M /(_MD) #Update Total Energy = 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. EA & K won't be zerc ot any point en ellipse. D Uf/”“fi (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. EA &i Ky~ - v % ,
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 p toward the alpha particle. The speeds are non-relativistic. (a 6pts) For this process, as a function of the separation r between the alpha particle and the carbon-12 nucleus, plot K + K» (the sum of the kinetic energies of the two nuclei), plot the potential energy, and plot the sum of the kinetic enfz{g%{ffid the p?&eq‘t@ energy. Label each of the three plots clearly. 4 - . X -5 ’ N 7 e Con 'wv"/w/\ 2 ergy (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 R, and the radius of the carbon-12 nucleus is R,. Your answer should be symbolic, — Ue(a‘:é/ilf_{ S k [¢)
(c 9pts) There is a head-on collision of the alpha particle (R, = 2.06210~'® m) and the carbon-12 nucleus (Re = 2.9871075 m) 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 = 1.6022210712 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? LW W=0 AE-0 £ F / [ ~ K p Qf\-ffravv\\/ 2 g C X b + ™M 7
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= Problem 3 (25 Points) ’[T) - A spring with stiffness k and relaxed length Ly 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. ~ M i} k AF W . 3 Ty P - e /I( " ey My oL Lf&n»\,o 4 (b 10pts) 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. A |‘? = ()\) gy
- (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 given above. 4
Problem 4 (25 Points) M 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 AFiermal in the water. Show how you calculated this number. IS TN m (AT A€ (2000 o7 Vst )33 - 2231) AF - (.72 x 10° Heema) (b 10pts) Determine the thermal transfer of energy Q into the water from the surroundings. Show how you calculated this number. (c 5pts) What was the change A FEgurroundings in the rest of the Universe (the surroundings, including the stove and the beater)? T -AE, AE l n;;f'é.:» SUrcouna ings ) (17 1S
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_This page is for extra work, if needed. .