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Unformatted text preview: l Your Name: 14 5%] é ﬂwédL Section time: T&AM 203 Prelim 2
Tuesday October 24, 2006 Draft October 24. 2006 3 problems, 25+ points each, and 90+ minutes. Please, follow these directions to ease grading and to maximize your score. a) No calculators, books or notes allowed. A blank page for tentative scrap work is provided at the back.
Ask for extra scrap paper if you need it. If you want to hand in extra sheets, put your name on each
sheet and refer to that sheet in the problem book for the relevant problems. b) Full credit if '\ / . ' .
o —>free body d1agrams<— are drawn whenever force, moment, llnear momentum, or angular m0— mentum balance are used; 3 correct vector notation is used, when appropriate; T—) any dimensions, coordinates, variables and base vectors that you add are clearly defined;
:1: all signs and directions are well deﬁned with sketches and / or words; «4 reasonable justiﬁcation, enough to distinguish an informed answer from a guess, is given;
3; you clearly state any reasonable assumptions if a problem seems warmly Wed; 0 work is I. ) neat,
II. ) clear, and
III.) well organized; . your answers are TIDILY REDUCED (Don’t leave simpliﬁable algebraic expressions); D your answers are boxed in; and >> Matlab code, if asked for, is clear and correct. To ease grading and save space, your Matlab code
can use shortcut notation like “(97 = 18” instead of, say, “theta7dot = 18”. You will be penalized,
but not heavily, for minor syntax errors. c) Substantial partial credit if your answer is in terms of well deﬁned variables and you have not substi
tuted in the numerical values. Substantial partial credit if you reduce the problem to a clearly deﬁned
set of equations to solve. Problem 4: ' [25
Problem 5: z 25
Problem 6: z 25 4) (25 pt) Particle sliding in circles in a parabolic bowl. As if in a
James Bond adventure (in a big slippery Cornell—managed radio
telescope bowl in Puerto Rico), a particle—like human with mass m
is sliding with negligible friction around in level circles at speed 1).
The equation describing the bowl is z = CR2 2 C(zv2 + 312)
a) (20 points) Find 1) in terms of any or all of R, g, and C. b) (5 points) Now say you are given w, 0 and 9. Find 1: and R
if you can. Explain any oddities. /\
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to their common tangent plane at contact is 11 = egg i + sin 0 j. In terms of some or all of
v, m, e, 0, i and j, ﬁnd the velocity of particle 2 after the‘ collision.
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The person walks continuously and repeatedly, over and over and over again, moving relative to
the boat sinusoidally in'time, with period T. The length of the boat is L and the drag force on
the boat from the water is F 2 cm. After a while the boat just moves back and forth also. How
far does the boat go back and forth? (That is, the bow of the boat goes back and forth between
two points, what is the distance between those two points?) Answer in terms of some or all of
mp, mb, L and T. 777079027 of péo’SOW and“ wax? X fl}, "5 a2 o FED _  L_
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 Spring '08
 RUINA

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