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
Exam I February 18, 2009 NAME :39 Mi] 071/ Closed book and closed notes. Show all work and enclose your ﬁnal answer with a
box. Problems will be raded for artial credit on] if the work is neat and all
intermediate steps are clearly shown and presented in an easy to follow format. If
you apply Newton '5 Second Law or Imgulse in a solution: you must show a FBD. All solutions must Show a coordinate system. Equations:
Uniformly accelerated rectilinear motion: Acceleration due to gravity:
_ 2
v=vo+at g—9.81m/s 2
1 g = 32.2 ﬁ/sec
s = so + v0! +—art2
2 Conversion: v2 = v02 + 2a(s — SD) in:
hr = ﬂ
Normal/tangential g path} coordinates: 3  6 s A K : ver 2 ' ' miley ) = ﬁ‘
g = v— é” + 13.63, (for circular motion) ( hour xl.47 see p v = r9 2 v ~  1 . .
an=—=pﬁz=vﬂ an=L=r92=v6 P r
ar=13=§ al=ﬁ=rt§
a = on2 + of
Polar coordinates: Quadratic eguation: A ' A 2 __
y=fer+r993 ax +bx+c—0
g=(r_ra'2)é, +(r9'+2w‘)é5 x:—bi\/b24ac 2a
(for circular motion)
Vr = 0 Power
v9 = r6 P =E'2
' 2
or = —rt9 pomp“ a9 = r6). m P. Workenergy:
T: + U192 = T2
T1 + V3] + V9! + U11): = j?"2 + V32 + Vt,2 U: Ii'dﬁ T=—mv2
142 U = —%k(x§ — x12) (Spring) =mgh V = k):2 i
‘ 2 S' F = kx (Spring) Imgulsemomentum:
fz! g1+ jzgdz = g Q = my fig + Imam: 11:02 ﬂo=r><m£ E=QX£ Coefﬁcient of restitution: e = (van —(v:),, (V1 )n “ (V2 )n Selected integrals: I dx =lin(a+bx)
a+bx b Isinm + bx)dx = —% cos(a + bx)
Icos(a + bx)dx = ésinm + bx) Friction force F:
Fmax=us N (static. friction) F=uk N (kinetic friction) 1. (30) If the coefﬁcients of static and kinetic friction between the 20 kg block A and
the 100 kg cart'B are both the same value of 0.40, determine the acceleration of each part if P = 60 N. Ignore the mass of the pulley and assume the pulley and cart
wheels are frictionless. Hkﬂps=0.40 P=60N Find: tip. and a3 Fm“: 14st = 0.4 (1%.2) —..—.> Fm“: 75mg N
ajSume sipping occurs: For" H l iiFKimnmﬁ at) mesa r 30 up. @i a“: 2.07s urn/6.. a. I weapon—amt elmgwrzas mg» l 2. (30) The rotation of the 0.9 m arm 0A about 0 is deﬁned by the relation t9= 0.15t2, where 6is expressed in radians and t in seconds. Collar B slides along the arm in
such a way that its distance from 0 is r = 0.90.12:2, where r is expressed in meters and I in seconds. ©o\ar Cod‘fc‘l‘ 3’10;th .5 After the arm has rotated through 30" (0.524 rad), determine A (a) The velocity of the collar in vector form. er (b) The acceleration of the collar in vector form e= 0.514 > 0.156% 1,: Law 5 
r g; 0.31: @f [.8515 , 6: 05M {Wad/5 er 0.3 ' {‘2 0.9042+? @télquJ l1“ 0.‘l8\ m (1:. 03.th “ r —OLl‘/Cl "Y;
F: ~0'7Ll I A.
are: ta + was. = — aweé‘wtrDWlwwl Ea _. 0"le 5r 4— 0.170 go “/5 Inna—W '—nl~r"w)v'r w... .7”, t. q. A. 935% §:_{~é"jé‘r + (fe'+g\r9 ea
4. 0.1L; ~(0.u3:)(o.%1)j {1+[0.qar)(o.s)+a.eo.wo(0.5bﬁ Ea a3: “ 03Q Er “0359 @e mgr, 3. (35) A 2.5 lb block B 13 moving with a veiocity v0 of magnitude vo= 6 ﬁ/sec as it
hits the 1 5 1b sphere A which 18 at rest and hanging from a cord attached at 0
Knowing that ,uk— 0. 6 between the block and the horizontai surface and e= 0. 8
between the block and sphere, determine after Impact the following. (a) The maximum height I: reached by the Ephere. “t
(b) The distance x traveled by the block. .
”61‘er \W‘Pa‘ri pw‘GiQM do ~Fm& 2L6*“J_ .. ag ”If“ 0W5} ’Ué, : m AVA * M6735 ; m M" 1+ m 6 1%! _
* ~— . —4
END) 1%? 742’“) 32 L if”); (7357* m) 15;: 104671119 CocH 01F rashH441“. e: We VA $an ’63:, (:0— M77173) Uﬁ' 'm 0 _.. 6 153‘. 1.95 {AL/Sec ) my; 1.410—lu'lo7095) :3 131;; (.15 $7M V w Wom Enerﬁn‘a’? 0 7,: 2° /F:r A: T +\/%’.+\/2+ :‘u‘riu. Ta VWVT—ij
“5 " ‘5 3L} : : Dr O i 31.2.. (6‘75) ' (3'25L ( )(A) BLm aslb
For E) I 2111. mayo >~TJS+N 0 => N= 3515 #:TN F3144”: (0.6)(35) => F: i5 lb ~ 0 a +—
:. 32.30%) zcrx o em 4. (3) State in words Newton’s second law. )NQ, accemmiww 3'? 0% (qu‘l‘lole LS
Plpov+wﬂal 4o 44x6; T‘ESuH’Ihﬂ pa{‘ce.,« 515‘
alarm m H“ and {ﬁx/n +he dweohow ~H‘\ if3 1ofce... 5. (2) According to your textbook, what term is used to describe an imaginary set of
rectangular axes assumed to have no translation or rotation in space? (Bewitd or as4rovxowumt {e4erance #mwre, (,9 L71) ...
View
Full Document
 Spring '07
 MORRISON

Click to edit the document details