F09+Exam+2+Solution - f I Cartesian Coordinates F=xi yj zk...

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Unformatted text preview: f I Cartesian Coordinates F=xi+yj+zk 2i=axi+ayf+azk=E=Xi+yj+2k Normal & Tangential Motion :vxf+vyj+vzk=—~=xf+j§+z'k d? dt d? Work—Energy 2 V 2 UH2 = [13-5194desz —T1 1 i T Conservation of Mechanical Energy 2 Tl + VI + non~conservarive ' : T 2 + V2 1 V 1 1 2 —1- k 6, 6 2 (torsional spring) 2 1 2 2 =—va a) 2 2 G mgy (gravity) ks (Ax) 2 (linear spring) 23:13-17 77 _E out E. m _SOL U‘hom M/VW Polar Coordinates (2-D) a9 : ré+ 2% = rat+ 2m Equivalent Acceleration Expressions dv dv dv dt dx d5 d0) d0) a2”: 0)— dt d0 Uniform Accelerated Motion Expressions 2 x=x0+vot+-at2; v=v0+at; v =v02+2a(x—x0) 2 l 6=Bo+wot+§at2; ammo +051; w2=w02+2a(¢9»00) Relative Position, Velocity, Acceleration Expressions for Planar Motion £8 = 75A + 358/14 173 =17A +17B/A WithGB/A =5)x173/A 673 25A +aB/A WithfiB/A =07xFB/A.“a)2fB/A Impulse-momentum ‘/ 20110,. +2 [fidzzz(ma)f ti 2 particles: [191 ad: = fioz dz]. 0] with [70 = I 17307 pdm*=l7xm\7 1 m y 2 s» RBs: [Modt=10(?)f —IOCT)I- assuming Ois on theiiB 1 IModt=I702 —fi01+1G67)f —IG§)i assumingOnotontheRB Rigid Body Dynamics Zfizmé 2M0 =1007 10 :10 4-de [G = Jrzdm =k2m m where k ~ radius of gyration (units of length) M.\\ H QWD&{Z; EZXMM tiB‘t MttVt/itr: El 1:001 “"4 5 C3 team tits M Name: 1) True/False Questions (2 points each). a. @or False: A force that acts on a particle in a direction perpendicular to the path on which the particle travels does no work on the particle. b. True or ants}: Momentum, like kinetic energy, is a scalar. '0. True or alse. A larger force will always produce a larger impulse on a body than does a smaller force. d. or False: in a perfectly plastic collision between two bodies, the velocities of the bodies immediately after the collision are equal to the velocity of the center of mass of the system. e. True or @ The vector product of force and velocity is power. 10 points 2) A 2000 kg cannon fires a 10 kg projectile horizontally at 600 m/s. It takes 0.007 s for the projectile to pass through the barrel. The cannon has a spring mechanism to absorb the recoil. _ , , _ , _ _ Answers: Find: a) The cannon 8 Initial recorl velomty. b) The force exerted on the recoil spring. VCannc’“: 3 W‘s/:3 “(WW Vcannon = qw K N ‘ «a. Vprojectile = m/s __> (are Z ? Mat. 2000 kg "“ C 0 33$ 6.. t2. WNW (‘3 ts) e?» 37 Me in (it; “rt; m a. «(’7 H J u; 2;» A wt 9 t w,ng my? me» my“? .. _ a it.» . t ' .tfitéww 3 O a enact; «2m retrace} a W Wt/g «w lm “Pvt 3% m Mtgmpmwr'uvm .,,,«b w i' i law» “39/ «.17; S W ‘1‘?" ms Wily}? ta. t“ {jaw WE REE? “ «a 10 points PM “" WWW t, *2“; tetra §" 3) Find the angular momentum of the two 6-kg particies about point 0. v 1712(3z'+2j)-m/S HO "3 {a ")1 m r; taxi “t "t: i2: r: m tr “"7”— M m g K4 Mg: 10 pomts we Wig—gym y: 4) A 10 hp motor is being used to lift supplies to the roof of a building under construction. If the desired lifting velocity is 15 ft/s and the motor has an efficiency of n = 0.8. How much weight can the motor lift? (1 hp = 550 ft-Ib/s) www- .mw {:1 “r: m t/l WE: \N ,, ram»: low(fifgiggiéw‘)(p.zl 73;” - Zrtoo 2:5 « M e i” ‘ ZWE 10 points 5) A mechanical system consists of a block A of weight WA = 194 lb on an inclined plane of angle 30°. Block A is connected by a cord that passes over a frictionless, massless pulley to a second block B of weight WB = 130 lb, which hangs vertically. Find: Assume the blocks start from rest and that block A remains on the plane, Determine the speed of the blocks when B has dropped 5 ft. Answers: 4‘0! 474/3 £390 Vitus “aw/5 i! WA : E‘M C, QM At M”? : m...— “ "x ‘ m my 65‘ 3:, a?” m.” 20 points Q t“ (we? at E “Moss W. mg 6) Tennis balls are usually rejected it they fail to rebound to wist level when dropped from shoulder level. If a ball just passes the test as indicated in the figure below, determine the coefficient or restitution, e, and the percentage of the original energy that is lost during impact. x Answers: , e= o. 8 fit , l «W, \ \f \S 4 % Energy Lost= '55 l Z Hf \ Ill 1 16230 3 l I’ 1100 mlm / 1; mm la: is l l “A Z WWW/r W (to N ‘5 6:8 \l lit-Wm M a ‘ir <7 mm (alga “w w 6: gm 6‘2 6’” xi a ‘ T 1- I [,1 "2y :2??? + \A “t; A. 2. :2. Fl v2, "2 matte 9/1 my“; ft m o 1‘} fl fl v 2- t (4 ’ (fl w. MCWIXLQ w VZ/YVE \iz q M T Ki; fllulmé‘xttg gamer Mk r a M WMNMAWWWMWWNE / \l’l 1“ 12a mam 5r “7:: T m Re 5 T7 “m3 "3“ z c) N m ,Ia s W 1” r::’ ‘3’ >32 m W fim A at? Mam (~53. a; ; 20 points m ¥v ijiijLi 7) A 1.1 kg ball A is falling vertically with a velocity of magnitude vA = 2.5 m/s when it is hit as shown by a 0.7 kg ball B which has a velocity of magnitude VB = 2.0 m/s. Knowing that the coefficient of restitution between the two balls is e = 0.75 and assuming no friction, determine the velocity and direction of each ball immediately after impact. Answers: no rt the {it WEN A»: East'wtwrto M w a, i " \S‘ 3 W I? w a NV fix“. at m £2“ avg“ a; “as > \r ‘ '"’ v W M ' i” '“ 7 w ‘3 ! Em gm t (NSC m W? (it‘ll l t i. E l m r g \YBA m \Tflirk l ‘qggfi ms glee) 36:63? k3¥§z<"‘€"‘lé.;>m at WW3 m, t} «i E {tit t ‘i t“: m » g i A I as E; “W E W l Héiifli’ {we}; its“ M the: g ‘éliw‘étm’a g; t i l 20 points ...
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