Test 4 Spring 2009

Test 4 Spring 2009 - Problem 1 (25 Points) A portion of the...

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Unformatted text preview: Problem 1 (25 Points) A portion of the Rutherford scattering VPython code from lab is shown below. Fill in the missing lines of the code indicated below. from __future__ import division from visual import * from visual.graph import * scene.width=524 scene.height=524 scene.x=1 scene.y=1 ## constants and data b = 0 ## Impact parameter m_alpha = 4*1.66e-27 ## The mass of the alpha particle in kg m_gold = 197*1.66e-27 ## The mass of the gold nucleus in kg deltat = (9.107e—21)/100 t = 0 ## start counting time at zero k = 9e9 q=1.6e-19 ## objects and intial values alpha = sphere(pos=(-2e—13,b,0), radius=2e-15, color=color.cyan) gold = sphere(pos=(0,0,0), radius=8e-15, color=color.yellow) alpha p = vector(1.458e-19,0,0) ## The initial momentum of the alpha particle gold p = vector(0,0,0) ## calculation loop while t < 200*deltat: t = t + deltat (a 6pts) Calculate the force on the alpha particle (2 protons) by gold nucleus (79 protons) r = aipha.Po-‘S a fioidaFOS that: r‘ /w\ag (r) FM‘PM = kKQWlTWEVwafflwz *‘rhqi (b 6pts) Calculate the force on the gold nucleus by the alpha particle F” gold 1' "' F- fiiPl’Wx (c 4pts) Update the momentum of both the alpha particle and the gold nucleus 1'3 “t Equal/m *de Sold-F '2 joldlp “ri— *aiei‘ha'i' (d 4pts) Update the position of both the alpha particle and the gold nucleus 6‘ 'PL‘" F03 f a‘ it‘hm F“? "F 4PM“ P /m,al}>l\o\ 3“ deltat- 30W“ (303 1* gulch Ms: 1— gulch P/ Wer 2k file [la—f (e 5pts) Calculate the “scattering angle” of the alpha particle am mawz www Mime-0* 18O/ri Problem 2 (25 Points) View frnm slams A stick of mass M and length L is lying on ice. A small mass m traveling at high speed vi strikes the stick a distance d from the center and bounces off with speed vf as shown in the diagram, which is a top view of the situation. The magnitudes of the initial and final angles to the x axis of the small mass’s velocity are 0i and 0f. All of the symbols in the diagram represent positive numbers. (a 9pts) Calculate the center—of—mass velocity of the stick (um and vy) after the collision. System: gia‘ck «r «MISS Afi¢ficfiét (:0 we (Para 0 Xw-direcilbht WW1 C575 9: ‘2 MVX as mVp COS a! (b 9pts) After the eollision, what is the magnitude of the angular velocity w of the stick. grsffiflni “1. mass «A __. «A __> A L t ’6 LL : ._‘3 a 0 [4+ 1? s3 LWE Ln “W XP any 7; , f\_/\\\ M—fi HK—i? a ,3 ' W\V:&c;<>s€.£ : +meOICoSQ£Z + W W '1 gamma.) gunman W (c 7pts) What is the increase in thermal energy of the objects? You can leave your expression in terms of the initial quantities and 'Um'Uy and w. §y§+emi s HCE +WMI‘ AE: g+gl a A AEW’W‘ : "AKi‘musPAKmi- Problem 3 (20 Points) As shown in the diagram below, seven forces all with magnitude = 32 N are applied to an irregularly shaped ob— ject. Each force is applied at a different location on the object, indicated by the tail of the arrow; the directions of the forces differ. The distances shown in the diagram have these values: 11) = 12 m,h=18m,andd=17m. Inthe figure x is to the right, y is up and z is out of the page. w—h Tim = — UHF) (e 2pts) Calculate the 2 component of the torque due to force (5) relative to location A. (g Zpts) Calculate the 2 component of the torque due to force (7) relative to location A. (h 6pts) Consider the object under the action of a net torque due to all forces acting on it. If its moment of inertia (with respect to a rotation axis passing through A) is I = 137.5 kg ~ m2 and is initially rotating with angular velocity c231- =< 0,0,18 > radians/s. After a short time At = 0.001 3, what is the new angular velocity of the object Q}? Your answer should be a vector. ¢ «g ALrtAt ~> fg=fi+fzyc 034,: (0,0,l8mls"> ‘4’ {010"“K68MHM3 ((lebOls‘r) Problem 4 (30 Points) ’j unkf "satellite, i {2: out Of page) A spherical satellite of radius R and mass M is originally moving with velocity vsati =< va, 0, 0 >, and is originally rotating with an angular speed wl, in the direction shown in the diagram. A small piece of space junk of mass m is initially moving toward the satellite with velocity vjunki =< ~vb, 0, 0 >. The space junk hits the edge of the satellite at location C as shown in the diagram, and moves off with a new velocity 'Ujunkf =< —'vc, 0,1, 0 > Both before and after the collision, the rotation of the space junk is negligible. The quantities: va, 125, '06, W are all greater than zero. (a 5pts) After the collision, what is the final momentum of the satellite? Your answer ghouldbe a vector. fillsaahemq‘ *jumk ‘3 it: 0) may P: 2 u‘ a k E flat; N W 7‘3 1 1' Raw : {Mvmm (WW9) , v- WWA , o (b 2pts) Assuming the density of the satelli “V troot, t se f the satellite? -2 ’1 I~§MR «TEL (c 5pts) What is the initial rotational angular momentum of the satellite, around location D (its center of mass)? Your answer should be a vector. .._A ,5 f. . “2, Ly‘lizi I“); D 0’ aw“) (d 6pts) An instant before the collision, when the space junk is almost at location C, what is the transla— tional angular momentum of the space junk about location D? Your answer should be a vector. (e 6pts) An instant after the collision, when the space junk is just slightly beyond location C, what is the translational angular momentum of the space junk about location D? Your answer should be a vector. '4 Lika = r‘xfiwk" : <0,P\,O» >4<~WV¢I mV5110> (f 6pts) At the same instant after the collision, what is the new angular velocity of the satellite? Your answer should be a vector. Syjlemx 5:. kn“? + juflk ~43 AT, T/gAtto F») If: “2 “z «4 (“MP (W + A _ ,Z ’1 A " \S/l—VZJ {:35 ” 5M2 W3 “““ WVbR’L‘ L+FnflS“,€ a) ...
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Test 4 Spring 2009 - Problem 1 (25 Points) A portion of the...

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