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Unformatted text preview: MECH 310 , First Heurly Examination Fl : KEV
4Mar 05’ ! v . CLOSED BOOKANDNOTES NAME
4 ‘ ' ‘ LET THE GAMES BEGIN!!! ‘ , 1. I In the course of ‘your reading you no doubt noticed the following problem,
which turns out to be quite interesting [30 pts]: 4 A damper b and spring K are used to move a mass M. Two possible conﬁgurations are considered below  [A] and [B]. In each case, however,
the input is NOT a force, but a DISPLACEMENT Y(t). The force which ' produces Y(t) is not given and is not relevant. For each conﬁguration, ﬁnd the displacement X(t) of the mass M.
In one case the mass M begins to move as soon as Y(t) is applied;
in the other case M starts to move much more gradually. Identify
which is which from your solutions for X(t). Take: zero ICS; 1 Mel; b = 6; K: 9; Y(t)‘= 1 (step input) L Page 2 of 3 pages
2) [40pm]  a) ‘ Identify the massSpring systeni that’s represented by. the following
' block diagram: (20 pts) 'fAPfL 4" , An empty barrel, massM, rolls back—and—forth ‘ . f” Without slipping on a circular track. The track 3 ' ' radius is L andthe barrel radius is a. The track P“
exerts dry friction on the barrel. _  L 1 a '
Find the period of oscillation. [20 pts] 45—“ V‘ . ’ " ‘ law«3%: — aéaﬁe ' r
.458va M ['3 A rum muff; L>7m , . i ‘ Page 3 of 3 pages 3. [30 pts] ’ ' a). Use dynamics arguments to explain just Why a cylindrical rod prefers to
roll ‘without slip”, rather than sliding, ' along a slightlyrough surface.
Take the translational motion dX/dt to be given. 1 (Be complete! There are two parts to the answer. Start with dG/dt = 0
@ t = 0.) Franny—mma; "+ .1 Ache, Lm‘l'm‘l' 93W l $301le twp»! M” will 5 é;— a E'Ltn‘i'lva VEchﬂy 1’7" F 312039.! 73
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b) Use the ideas you’ve developed in part (a) to draw a block diagram
showing how the output dG/dt relates to the input dX/dt. Assume “dry” ﬁiction which depends only on relative velocity. We. chmN Mama WWW WWW“
“rm. buzzer/ant a; Fae/mm. Tm“; DLﬂszm/Vé—M/ W.th u ‘ a? 4 Rﬁ. e:— 514 67mm M ‘ Dlﬁ‘mmwm/ 55L ,, ...
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 Spring '09
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