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Unformatted text preview: f ,. Your Name: Mam/3‘4 A .3er Section time: T&Al\/l 203 Prelim 1
Tuesday September 26, 2006 Draft September 25, 2006 3 problems, 25Jr 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, linear momentum, or angular mo— mentum balance are used; 0 correct vector notation is used, when appropriate; T any dimensions, coordinates, variables and base vectors that you add are clearly deﬁned;
all signs and directions are well deﬁned with sketches and/ or words; .___)
:t
——+ reasonable justiﬁcation, enough to distinguish an informed answer from a guess, is given;
a}; you clearly state any reasonable assumptions if a problem seems Willy Wail;
. . work is I. )neat, II. ) clear, and
III.) well organized; . your answers are TIDILY REDUCED (Don’t leave simpliﬁable algebraic expressions);
E] 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 “07 = 18” instead of, say, “thet a7dot = 18”. You will be penalized,
but not heavily, for minor syntax errors. 0) 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 toga clearly deﬁned
set of equations to solve. Problem 1: z 25
Problem 2: [25 Problem 3: [25 CD 1) (25 pt) Pulleys. In the problems below you are asked “What is the relation” between this and that.
This means you should write the simplest possible equation in which this and that are the only
unknowns.) a) (1 point) Please read all the rules and hints at the front of the exam. Write here: “I read
the cover page”: ' b) (3 points) The ideal pulley system (make the usual assumptions) in (b,c) below shown is
part of a larger mechanism. What is the relation between TA and TB? Clearly justify your
work from ﬁrst principles. c) (10 points) For the same pulley system what is the relation between (1A and a3? Clearly
justify your work from ﬁrst principles. I [Part (d) will only be graded if (b) and (c) above are correct] cl) (11 points) The two pulley systems below (d) are treated as having all ideal components.
What is the relation between ac and am? You may use the results from parts (b) and (0)
above without rederiving them again and again. When comparing the systems use m = m and T=T. Cop/‘fﬂﬂt _ y, ._ J ‘ ’ A;»,..;na 7’74" ,1) f Hf"? '\ {I any “if..” q ~ ‘ \
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evant to this course. It runs without error; (This code is no good outside a test, obviously, because the variable names are not suggestive, intermediate variables aren’t used, and there is
no commenting.) a) (10 points) Write a mechanics question (with values, units, basic assumptions etc.) that
the output of this code answers. Your question should make no reference to matlab or
computers but should be in the language of mechanics. [Grading of parts (b) and (0) below depend on the answer to (a) above being correct. So be conﬁdent before moving on.] is added just below the b) (10 points) Assume that the command command plot(t,z(: ,2))
t(end). Draw, as accurately as you can, the resulting plot. Label (give numerical values) key points and asymptotes which you ﬁnd using your own pencil—and
paper analysis. Label the axes (even though the code does not do this). 0) (5 points) Get as far as you can towards ﬁnding a numerical value for 1: (end) without using
the computer. Ultimately you Will be stuck without a calculator. But get to a point where
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 Spring '08
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