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Unformatted text preview: Final Exam
5 problems, 20 points each 1. (20 points) A ball of mass m is shot through a tube of length Z that is elevated
by an angle 0 as shown. The ball has initial speed 210 at the bottom of the tube. The tube is aimed at a target a distance d away from the end of the tube. How far below
the target will the ball hit the wall? 2. (20 points) Two blocks with masses m1 and me are being pushed by an external
horizontal force acting on m1 as shown below. The coefﬁcient of static friction between
the blocks is p. There is no friction between the ground and m2. What is the minimum acceleration that the external force must give the system so that m1 does not slide
downwards? *‘Y 3. (20 points) A rod of mass m and length 6 is initially at rest in outer space. A
point mass m moving with speed v0 collides with one end of the rod. The rod initially
makes an angle 0 with respect to the direction of motion of the point mass. The point
mass sticks to the rod after the collision. How long does it take the combined system
to make one complete rotation after the collision? gyg=¢0ol +l0qll 4. An astronaut of mass m is at the center of a space platform of mass 2m, radius R.
and moment of inertia mR'z. The platform is initially rotating about its center with
rotational velocity we. The astronaut then carefully walks to the edge of the space
platform. (The astronaut. is able to walk on the platform in the absence of gravity
with the aid of magnetic boots.) Analyze this problem in an inertial reference frame
where the center of the space platform is initially at rest. Treat the astronaut as a
point mass. (a) (5 points) Is kinetic energy conserved in this process? Explain. (b) (5 points) Does the center of mass of the system move during this process?
Explain. (c) (10 points) What is the ﬁnal rotational velocity of the combined system about its
center of mass? Hint: Use the parallel axis theorem for the moment of inertia I of an object rotating about a point other than its center of mass: I = 1m +1i'f‘r3m, where [cm is the moment of inertia about the center of mass, and ram is the distance between the axis of rotation
and the center of mass. Ca3l$01atedi 5Y5) lom‘t as€vovxotul7 expechs clnevviicC—tl
emexrcml =3 \<;?‘ K1”
...3 A a
003 [Solutcol sys =5 —_ {)4 =3 Va“); ammo; = O 25 cm AQ‘CS VicL move Cc.) 5‘. AllY ‘9‘ +x Mgﬁvonu at at camear of plut‘FwM) cm at C(StVOV‘c‘Mt at 343:,“
ovCal“ o? platfwm ) 0’" 5 ‘ at 0V; (‘n l_  L; LISOlai’CA W5) 5 L = (E‘a‘hﬁ +1 ,6
J; v “'0 w‘c Cogent w)
1 V1” " QKMD m“) = *3{2 Ir‘a’Gu’G = WW4?— + Um} K‘a‘LY = L‘ mﬂz
G1 2 2
IaS‘EVoJ'E = m __ :Iwaz =3 LP: (Eclijk guwﬂz= "(gWK?" EVYZNW = %¢>\1®o —'}_
QJ‘F— €0.30 5. (20 points) Two point masses with mass m are attached to a rod of total length
3é’ as shown below. The rod has a pivot attached a distance 6 from one of the masses.
Find the frequency of small oscillations of the system about equilibrium. Neglect friction and the mass of the rod. Use the small angle approximation sin 9 z 0,
cos 0 2 1. ...
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 Fall '10
 MarkusLuty
 Physics

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