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Unformatted text preview: Your Name: M
Your TA: _ l l ’SoLumNS " T&AM 203 Prelim 2
Tuesday March 28, 2000 7:30 — 9:00+ PM Drnﬁ Mnmln 25, 2mm 3 problems, 100 points, and 90+ minutes. Please follow these directions to ease grading and to maximize your score. a) No calculators, books or notes allowed. Six pages of formulas from the front and back of the text are
provided. The back of the test can be used for tentative scrap work. Ask for extra. scrap paper if you need it. 'b) Full credit if
K / —>free body diagrams+~ are drawn whenever linear or angular momentum balance is used; correct vector notation is used, when appropriate; 0
9..
T—> any dimensions, coordinates, variables and base vectors that you add are clearly deﬁned;
i all signs and directions are well deﬁned with sketches and/ or words;
_,I
5‘
U reasonable justiﬁcation, enough to distinguish an informed answer from a guess, is given;
you clearly state any reasonable assumptions if a problem seems warty deﬁned; work iS I. )neat,
II. ) clear, and
III.) well organized; . your answers are TIDILY REDUCED (Don’t leave simpliﬁable algebraic expressions); Ci your answers are boxed in; and >> unless otherwise stated, you will get. full credit for, instead of doing a calculation, presenting Matlab
code that would generate the desired answer. To ease grading and save space, your Matlab code
can use shortcut notation like. “9; = 18” instead of, say, “theta'ldot = 18". 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 1: 3 0 [3O
"7 Problem 2.: 2 [35
I 
M Problem 3: 3) [35 TOTAL: ’00 [100 1)(30 pts) 3wheeled robot. A 3wheeled robot with mass m is being transported on a level ﬂatbed trailer
also with mass m. The trailer is being pushed with a. force F j. The ideal massiess trailer wheels
roll without slip. The ideal massless robot wheels also roll without slip. The robot steering
mechanism has turned the wheels so that wheels at A and C are free to roll in the 3 direction
and the wheel at. B is free to roll in the i direction. The center of mass of the robot at G is b
above the trailer bed and symmetrically above the axle connecting Wheels A and B. The wheels
A and B are a distance b apart. The length of the robot is f. Find the force vector EA of the trailer on the robot at A in terms of some or all of
m,g,E,F,b,h, i, j, and k . [Hints: Use a free bod)r diagram of the cart with robot to ﬁnd thetr acceleration. With reference
to a free body diagram of the robot, use angular momentum balance about axis BC to ﬁnd PAP] ME: Franx ‘ﬁ'ﬁﬁ qhhouﬂce meh+; 2:6 = gov421' : 9.2 The mbo+ docs 00+
move NH!“ FESPCC" to HA: cards.
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ﬂice 0:? N4“ m3 , Jr’ne «Oren—t letbullied 1‘
mt Hoe
cart) FESD Crbbcri) (Continue work for problem 1 here] ' _____........
A gig/041‘s BC : {ZM/c : E/c} 'ABC 1 rﬂj
WWE 35C. = £3: ifacl ’\ b4 k
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are £353ij 3 {EM/CY? gar—=55 chzi,‘ «
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LN 32“
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A2: ”2"— +1 Z>ZZMJQ=HM§ 1: ,_.ﬁ,__ 2){35 pts) Slippery money. A round uniform ﬂat horizontal platform with radius R and mass m is
mounted on frictionless bearings with a. vertical axis at 0. At the moment of interest it is
rotating counter clockwise (looking down) with angular velocity 11:— Tﬁorce in the my
plane with magnitude F 15 applied at the perimeter at an angle of 30° from the radial direction.
The force is applied at a. location that is qi from the ﬁxed positive .1: axis. At the moment of
interest a small coin sits on a. radial line that is an angle 6 from the ﬁxed positive :1: axis (with _ ass much much smaller than an). Gravity presses it down, the platform holds it up, and friction coe‘ men =11 eep51 om511 g.
Find the biggest value of d for which the coin does not slide in terms of _some or all of
Famagaﬂawaﬁaqﬁsand ﬂ. Lg'f “‘7' (0“! was; Support Bearing Coin (at: aura/FM 'u
Wﬁd Iii ﬂPL‘“)
[Voila W 7"”‘(1510 rial/ﬁver, and ac!
m at cﬂ/recﬂon art/Quota W ML "Wmaﬁhw 30 (at (1/) ftgf M 021 MLCWW” {:72 {LEE 1’. rim n 7' “3: '>
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NW9 We, "ma/um miﬂdﬁ a TX = anad Omd Sim rm.<<rm 2 p<1 (Continue work for problem 2 here) 3) 35 pts) Cone on Disk. A disk rotatm with constant ratew about an ﬁxed
axis in the j direction. A right cone held in a ﬁxed bearing at B
rolls at. constant rate so that the point on the corner of the edge of
the cone has the same velocity as the point it touches on the disk, EC = 1.0 Axis AB is in the my plane. Find the velocity and acceleration‘of point C on the cone in terms
of some or all of w,r,,8, 1, j, and k. ﬂ= £1.11 ﬂo= 0031 ("10%
= no K
12c: bl}; (OUSPé'l‘ 9m 6 J x rSMPC'W‘ij
= WWMRM‘PEHMﬁ)
: whampﬁ '
6mm MPH»
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wa=zng=W. a: ' >r+ mxcwxn
: number)
ac: WWW»)
= W» (—MEvEIF 9413) 40),. Cml’g'l W31” Y4“? WP‘E‘MH’]
= m(—MP$+%P§)X raw?
= NORM? Cmﬁj+5“[3%)
: rﬁwkfmfjfgwfﬁ) ...
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