This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: I  9° ‘ .
”We (WWW 5‘ g MM
Section day and time: Wf T&AM' 203 Prelim 3
Tuesday Nov 23, 2004 Draft November 23. 2004 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 atithe 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 d1agrarns<—.are drawn whenever force, moment, hnear momentum, or angular mo— mentum balance is used;
__ correct vector notation is used, when appropriate; T—+ any dimensions, coordinates, variables and base vectors that you add are clearly deﬁned;
2!: all signs and directions are well deﬁned with sketches and/ or words; —l reasonable justiﬁcation, enough to distinguish an informed answer from a guess, is given;
you clearly state any reasonable assumptions if a problem seems poorly deﬁned; . o i work is l. ) neat,
II. ) clear, and
III.) well organized; 0 your answers are TIDILY REDUCED (Don’t leave simpliﬁable algebraic expressions); 1] 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 “67 = 18” instead of, say, “theta'r'dot = 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 1: 25 Problem 2: A
Problem 3: __[25__ l 1.) (25 pt) A uniform horizontal bar with mass m and length K falls 3. height h without rotation in grav— \l/S itational ﬁeld 9. The bar is then caught by a stationary hand. The hand does not move, but
imparts an impulse but no torque (it freely allows rotation). Clearly indicate where on the
bar the hand Shauld catch. the bar so that one end of the bar (indicate which end)
does not have any change of velocity at the impact. (Indicate the distance d of the hand from the bar. center in terms of some or all of m,£, g and h.) /( \\
M :_—':__::"'::1 ‘ // ...\\. . ' l ‘l' aﬂ‘
1,.» we», \r ,4» . i W ’
. . t , WM“ M (W l 5mm
““4"“ wildw"
,_._'_.__.____x”
. D «WWMW ’3
4319"” F 1; ,sl 6 c 1 B ,7
A
' ‘ p (7 mS‘AMQ 7? 41+ {‘19 n ‘ ’d(gl+£/Z')
d 1+ 31/1;
‘l‘ — .. ﬂ W 4.
vaW*' V» ‘ V” Pt, c .5 (4119.; m
M I _'. (en‘k‘f 0 'aei'caﬂ’l‘i’m
'3? l/‘J(a(;4i’1«) f, V Thihklhj‘b"! {if :26; 4'
w“ 2+ﬂ 1(2 ‘ L0 ' _
4‘ £3 :ﬁfﬁe ‘7‘ {l :0 {12.8 «A .
L’Q ’ [2— ek‘l {‘4‘ A héj [10 JMMf ‘ 2) (25 pt) A uniform disk of mass m and radius R is released from rat at. t = 0 to rollvwithoutslip down a
slope q) (measured relative to the horizontal) as accelerated by gravity 9. At time if what‘ is
the acceleration of the point on the disk that is then touching the ground? Answer
in terms of some or all of m, R, g, ¢,t and any base vectors that you choose that you clearly e—a'jﬁa +a32x€ﬂm+wzg 4 A , " A
...a>23 maﬁa +w22" 6 M ’\ ‘
egg 3) (25 pt) A small bead with mass m slides on a rigid stationary circular hoop with radius R. Neglect gravity. The bead slides loosely on the. wire (does not pinch it) with coefﬁcient of friction or Theﬁ ‘
initial speed of the bead is '00 (along the circle). What is the bead speed after it has slid I
once around the hoop? Answer in terms of some or all of m, R and u \"x FBD 'f‘ N ," ...
View
Full Document
 Spring '08
 RUINA

Click to edit the document details