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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. The
initial lines of your code were similar to the program on the following page. (a 7pts) Add the missing statements needed to compute the kinetic and potential energy of the spacecraft
Earth system. from __future__ import division from visual import * from visual.graph import * #CDNSTANTS a G = 6.7e11 mEarth = 6e24 mcraft = 15e3 deltat = 10 #DBJECTS 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)
vcraft * vector(0,3.3e3,0) pcraft = mcraft*vcraft trail = curve(color=craft.color) ## craft trail: starts with no points
t = 0 scene.autoscale = O ## do not allow camera to zoom in or out pscale = 100000 #CALCULATIONS Kgraph = gcurve(color=color.yellow)## create a gcurve for kinetic energy
Ugraph = gcurve(color=color.red)## create a gcurve for potential energy
KplusUgraph = gcurve(color=color.cyan)## create a gcurve for the sum of K+U
while t < 60*365*24*60*60: rate(8000) r=craft.pos—Earth.pos rmag = mag(r) rhat = r/rmag F_earth = —G*(mcraft*mEarth)*rhat/(rmag)**2 pcraft = pcraft + F_earth*deltat craft.pos = craft.pos + (pcraft/mcraft)*deltat trail.append(pos=craft.pos) ## (a) complete the following two statements K “0‘3 (PCMHYKZ /(2¥wicmc+\ 11: K: lawn)” :
“ Gymcmt‘i’thvﬂ/rmo‘j Kgraph.plot(pos=(t,K)) r‘
Ugraph.plot(pos=(t,U)) KplusUgraph.plot(pos=(t,K+U)) t = t+deltat U I! (b 6pts) 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 6pts) Draw the kinetic, potential and total energy of the spacecraftEarth system as a function of
separation, if the spacecraft velocity is above the escape velocity. (d 6pts) Replace the Earth and the spacecraft by two equally charged objects interacting only through an
electric force. Assume that the two—particle system has zero kinetic energy when they are close to each
other and draw the kinetic, potential and total energy of this system as a function of separation. Problem 2 (25 Points) A box contains machinery that can rotate. The total
mass of the box plus the machinery is M. A string
wound around the machinery comes out through a small hole in the top of the box. Initially the box d2,
sits on the ground, and the machinery inside is not rotating (left diagram). Then you pull upwards on +
the string with a force of constant magnitude F. At dli an instant when you have pulled a length of string d2
out of the box, the box has risen a distance d1, and
the machinery inside is rotating. (a 10pts) Using the (CM) Point Particle System ﬁnd the speed of the box at the instant shown in the right
diagram. Slgkm: Pom? Mb“ AE t Wed =) (ZLMV2—03 I: +E>. : FOL 'Mjorl
“m
=AERP. (b 5pts) Why is it not possible to ﬁnd the rotational kinetic energy of the machinery inside the box by
considering only the (CM) Point Particle System? A Poial’ has no s.‘%Q,SL‘qulcr ,‘A‘lernel qu'H 50 only i‘l‘f ‘H‘qhslai‘l‘onal la'nefl‘c CHE/:57 C‘xh Le CalCulOIiYOi. (c lOpts) Using the Real System ﬁnd the rotational kinetic energy of the machinery inside the box.
SyS‘l‘Q‘M‘ box to] IMQCIM‘AU)’ d Ear“ (>5:th (éMvz— o» + AEmr + (MgohOl 3 (Ci+692)?
W W AKfrmS A U;
grab a
f 0 €le quol" + Fat + Foh A Eial’ :tm‘l.“ “0 = Problem 3 (25 Points) A spring with stiffness k and relaxed length L stands vertically on a table (which is on the surface of the .
Earth). . l (a 9pts) You hold a mass m above the spring and very slowly, Without releasing it, you bring the mass
down compressing the spring a certain distance. At this point, you release the mass and you observe it
does not move. How much work did you do? Al' N A$=o "> ‘Fpef' = kS'le . O i s) 3': W3
‘ T
SyS‘ieM % C'N’Ha‘ sprhjl W453 1L4 AE 1' (In/n3 (L—s} ~M3L) + (ngJ—03 : (My;
// AU: AU! (b 7pts) Now you hold the mass just barely touching the top of the spring, and then let go. What is the
maximum compression of the spring? (Neglect air resistance) Systwt Emit, sprig, was (c 9pts) Next you push the mass down on the spring so that the spring is compressed an amount 3, and
then let go. The mass starts moving upwards, leaves the spring, and goes quite high. When the mass is a
height 2L above the table, what is its speed? " SyﬁtMi Earl“ ,sph'“), «a!
A E; Wax)” 7' O V .
L E? EL. Problem 4 (25 Points) You put a thin metal pot containing 2 kg of room—temperature (20 °C) water on a hot electric stove. You
also stir the water vigorously with an electric beater, which does 100 J of work on the water every second.
You observe that after 5 minutes the water starts to boil (100°C). The speciﬁc heat capacity of water is
4.2 J (gC)_1. (a lOpts) What was the change AEthermal in the water? 46M»! = «Mc AT : (20003)(q23/3/°C> (100°C 40°C) = (b lOpts) What was the thermal transfer of energy Q into the water from the surroundings? A5 :AEMM= Q+Mx+ : Q + PA’c r) QT’AEMM "PAt V IN : 6.?2xlorj ~ (/00 [4) (SW, , 60$ )
= aqzno‘: (c 5pts) What was the change AEsurmundZngs? 7A Esydgm ‘1‘ A EJuNovno/ninys : o s) A tforrouadtnjj : ~ A ...
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 Fall '10
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