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Practice_Exam2_handwritten_solution

# Practice_Exam2_handwritten_solution - Mark your recitation...

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Unformatted text preview: Mark your recitation time PHYS 172 - Spring 2009 With an X Hand-Graded part of Exam 2: 1 Tu W Th F 8.30 9:30 Name (Print): 10:30 11:30 y 12:30 Signature: ’ 1 :30 2:30 PUID: 3:30 — \ 4:30 Problem 1 The ﬁgure below shows the elliptical orbit of a comet around a star. When closest to the star (point A), the comet is 5 ><1010 m from the star and the comet’s speed is 9.4 ><104 m/s. at AA 8 f” '- A [V2 pt for each arrow. Must have correct direction and roughly correct magnitude] a) [4 points] At each of the points A, B, C and D on the comet’s orbit, draw vectors representing the net force exerted on the comet and the comet’s momentum. Take care to represent the directions and the relative magnitudes of these vectors. b) [3 points] Consider the comet’s speed at each of the locations A, B, C and D and liSt them in order from the location with the greatest speed to the location with the lowest speed. A B D C [1 pt off for each incorrect slot] c) [10 points] What is the speed of the comet when it is 2 x101‘m from the star. Show your work, and explain brieﬂy how you determined your answer using fundamental physics principles and deﬁnitions. System: Star + Comet [1 pt] Surroundings: no signiﬁcant interactions with surroundings AEW = Wm + Q energy principle [1 pt] AEM = 0 3 E f = E, applied to the system using the fact that the [2 pts] system doesn’t interact signiﬁcantly with surroundings For this system E, : mcc2 + KC, + msc2 + K3,. + U. 2 2 Ef =mcc +ch+msc +pr +Uf Since my << m6 AKY E K 5/ — K“, z 0 (approximation) [1 pt] So, Ef=E, :> ch.+Uf=Km.+Ui :> imcvff — G mm“ = lmcvfi — G moms (fundamental deﬁnitions) [2 pts] 2 r/ 2 r,- . 2 l l . Finally, Va 2 Va — 2Gms —— — — (solve) [_1 pt] . ri rf = (9.464)2 —2(6.7e —11)(2e30) 1 — 1 m/s 2 6.964 m/s [2 pts] 5e10 2611 [minus 1 pt if units are missing] d) [3 points] Circle the graph which best represents the kinetic and potential energies of the comet—star system. [3 pts for correct pick] , C Problem 2 [10 points] Astronauts are working to transfer equipment from a transport ship to a new space station. One holds an instrument package as she drifts at a speed of 4 m/sec parallel to the side of the transport ship. At the right moment she pushes the package in a direction perpendicular to her initial velocity so that the package then drifts toward a waiting coworker on the station. Suppose that by pushing with her arms the astronaut exerts a force of 150 N on the package for 0.4 second. What are the new velocities of the package and the astronaut? The mass of the package is 30 kg. The mass of the astronaut and her spacesuit is 120 kg. Show your work. Explain brieﬂy how you determined your answer using fundamental physics principles and definitions. System: package [1 pt] Surroundings: astronaut interacts signiﬁcantly with system F0npbya =< 0,150,0 > N (deﬁne coordinate system) [1 pt] A13 p = Enpbyam (momentum principle applied to this system) [1 pt] Use the deﬁnition of momentum in terms of velocity to conclude that a a 1 ~ va2vpl+—FonpbyaAt mp a 0.4 So, vpf =<4,0,0>+E<0,150,0> m/s=<4,2,0> m/s [1 pt] System: astronaut [1 pt] Surroundings: package interacts signiﬁcantly with system 131wa =< 0, —150,0 > N (reciprocity) [1 pt] Aﬁa = 13;)“ abypAt (momentum principle applied to this system) [1 pt] Use deﬁnition of momentum in terms of velocity to conclude that vaf = aw. + iﬁmbypm [1 pt] a 0.4 So, vpf =<4,0,0>+ﬁ<0,—150,0> m/s=<4,—0.5,0> m/s [1 pt] [minus 1 pt for incorrect or inconsistent vector notation] ...
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