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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*1.66e27 ## The mass of the alpha particle in kg
m_gold = 197*1.66e27 ## The mass of the gold nucleus in kg
deltat = (9.107e—21)/100
t = 0 ## start counting time at zero
k = 9e9
q=1.6e19
## objects and intial values
alpha = sphere(pos=(2e—13,b,0), radius=2e15, color=color.cyan)
gold = sphere(pos=(0,0,0), radius=8e15, color=color.yellow)
alpha p = vector(1.458e19,0,0) ## 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
SoldF '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 Mime0* 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 Xwdirecilbht 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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 Spring '09
 PROG
 Physics, Angular Momentum, Force, Mass, Momentum, Rotation

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