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: ES 223 — Rigid Body Dynamics
Final Exam  Spring 2004 Q. Apri127, 2004 ' NM SOHA 1 la! 2 Closed book and closed notes. Show all work and enclose your ﬁnal answer with a box. There is extra blank paper and a stapler at the proctor'5 desk. Ifyou use extra paper, put
your name on it and staple it to the exam. Calculators may not be shared. Problems will be graded for partial credit only if the work is neat and all
intermediate steps are clearly shown and presented in an easy to follow format. 1. (20) The rectilinear motion of a particle is described by v = 4:2 + 31 + 2 m/s
where v is velocity (meters/second) and t is time (seconds). When I = 0,
the position, .9, is 10 m. Find the position and acceleration of the particle
when t = 4 seconds. Find: 3 when t = 4 seconds
a when t = 4 seconds ”U" dS/db 99(19th I 015612“ 5 'b at
d5 : £1Bt+Lcit
nag 5m + 3 ar— t>4=+3>
510: @1333 7.“: at iﬁucseﬁ
.3 7»
5:. Hé+gtﬁat +10 ax (SUNNY2*
73" “2
5: LI 9193+ 399: LWID a: Emu/52
3 2. 5285234 2‘} +5 “D ‘Szlé’JB m! 2. (30) Determine the angular acceleration ofiinkAB and the linear acceleration of
A for 6= 90° if Qog= (ll? and $03 = 4k rad/s2 at that position. Find: £43 and £14 y L; :0
Because L803 J Relalwe. mallow, H’cmslalmra ates.
6) QM?» +QLR/B D
9.01:}: 921: wﬁuﬁmw it: 042: M was» A MW Subs‘lrlwle mic.) CD A
ant“: _I.b’a\— 0.30f333—0u4 dag A @ gm“; ’2‘“ memew‘l57 Death0.30M» [EM/‘
_' a
089%: _$_'33 :7.) (3:33 533 .5 subs4.m+ m+°@* (1,92pr (4‘33) 2 29:3*l32 m/S'L 3. (15) The assembly consists of a disk having a mass of 6 kg, slender rodAB
which has a mass of 2.6 kg, and slender rod CD which has a mass of 1.5
kg. Determine the mass moment of inertia about an axis perpendicular to the page and passing through point 0. Find: 1.9
Note: The disk can be treated as a
cll'cular cylinder
170.8mA——]~0_5m_40
Dls Ci
‘ *4 2 6“ at? renaminyg’; ,0 ,1
DISK: I0: IA—mQ, :sz +m *2 1’ .
.— 1. 1 . 1 :" ' 25
Pool : Io=I+m [1;— {ELM m4:léflablll3)+(:b){a.;5)1'0 Ll
.— "" '1. l 7" I 0,751 I l— : I
R0421 JozImcl .: 3M mat ff'SX +0 M9 5] 0W5 To" blilOHIEl DANS In: bqq ha. ML 4. (5) StateinwordsNewton’sFirstlaw. a Pdf+ide TCWQMS 61+ {951‘
or Covd‘mues “+0 m't‘Nﬂ erA \vaonrrm Vernal7
“0 Jr'bere \S m. unbalanced 4:0ch aolmc‘t.
0“ 1+. 4 . S. (30) The 3 1b uniform slender rod BD 15 connected to crank AB and to a 0011a:
of negligible weight at D. CrankAB rotates with an angular velocity2 0f
12 rad/sec counterclockwise and an angular acceleration of 80 rad/sec2
clockwise at the instant shown. Neglecting the effect of motion, determine
the force in the pin at D. For rod BD: 8.3 Find: Force in pin at D ‘1» F = 0.00539 Slug  02 _
13:0.0216 Slugt12 .ﬁ
X New’ in Compuie 0Q”, ,bw} LU!”
new to” also Use. IC. +2, 1Cmd = —aq‘4‘t+!8: +0557ng +0.50%};
5‘45 mic @i 0b“ Deli 3531303: 1W1} HR 3+0 wanna; ”SumW
Equcvte" 4, *. o .= 4.04th +0 Sofas § 9’50: 88 Mal/f Back 42 CD @434 W‘" @0042: bDQIQ(€E’N+(%~3 “M M’QD’Ep3hajcng
(0.913474% ~I0h =~ W42 0.145st +4 42’}! 0.504: 3 ESL! —> [Bx =7.\\ 0: 9‘
5 . 6. (25) A 3 kg uniform slender bar rotates in a vertical plane about a pivot at B. A
spring of constant k = 300 Mum and of unstretched length of 120 mm is
attached to the rod as shown. Knowing that in the position shown the rod
has an angular velocity of 4 rad/s clockwise, determine the angular velocity
of the rod aﬁer it has rotated through 90 degrees (in other words when rod
AC is vertical) The radius of gyration of rod AC about an axis through B (k3) is 312 mm. Find: arm when AC has rotated 90 degrees clockwise to the vertical
position ‘ 1 G T, was \Je, kafTvaVQz. The“ SubeiL‘i'uitm‘ back
Mi0 0) Q‘3Q+o+lo
‘1.
0,]lew7j': SAL} =5 U311: 37.15 101,1 (M0 card/6 D 6 as: = owe. ohmume 7. (25) The double pulley consists of two wheels which are attached to one
another and turn at the same angular velocity. The pulley has a mass of 30
kg and a radius of gymtion k0 = 250 mm. Iftwo menA and B grab the
suspended ropes and step off the ledges at the same time, determine their
speeds and directions (up or down) after 4 seconds starting ﬁ'om rest. The
mass of man A is 60 kg and the mass of man B is 70 kg. Assume they do
not move relative to the rope during the motion. Neglect the mass of the
rope. Be sure to determine the speeds and directions of both men. Find: Speed and direction of man A ...
View
Full Document
 Spring '07
 MORRISON

Click to edit the document details