EGM3400_Test_2_solution

# EGM3400_Test_2_solution - EGM 3400/3401 Spring 2010 Exam 2...

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Unformatted text preview: EGM 3400/3401 Spring 2010 Exam 2 ' Name Please draw a box around all your ﬁnal answers on all problems. BE SURE TO SHOWMA GNI T UDE AND DIRECTION FOR ALL VECTOR QUANTITIES. When complete, sign the honor pledge. On my honor, I have neither given nor received unauthorized aid on this test. Signature 1. (30 points) An 8-lb block is attached to a cable and to a spring as shown. The constant of the , spring is k = 10 lb/in, and the tension in the cable is 2 1b. 1a) Draw a free body diagram of the system showing all forces/on block prior to the cable being cut. (6 points) T 1b) How much does the block displace the spring from its undeformed position prior to cutting the cable? Indicate if the spring is stretched or under compression. (displacement 4 points, stretch or compression 2 points) all“: *TeEt—U) 1«O EGM 3400/3401 Spring 2010 Exam 2 Name ( 1c) Draw a free body diagram of the system showing all forces on the block after: the cable is cut. (6 points) tr \U ld) After the cable is cut, what is the maximum displacement of the block from its original position as shown in the diagram? (6 points) _‘ T,+V\ ‘l A Mamimm itspmcwm J “FL-.0 3 swank-m3 ﬁrm rchr/ lbxl u ; Ll \_ 5L} _ 2. V| ‘ — WX‘ V‘k’ :KVLA“WXQ X1-X\: lwt'WQI" 'kiKKlk‘ WK 1 iiixj" ’WXL ‘KZ‘K: O'Ll m >4 {‘4 l QQ X ‘0 + w 5‘ u 0 EGM 3400/3401 Spring 2010 Exam 2 I Name 16) What is the maximum speed of the block? (6 points) 0 1 Ir “5-71 1 (7‘ 0 X )c §71<><A2g + 40202; = :mv‘ x, A. VKX’L I: EGM 3400/3401 Spring 2010 Exam 2 Name 2. (35 points) Collar/I weighs 15 lb and is attached to a spring of constant 75 lb/ft and of undeformed length equal to 18 in. The system is set in motion with r = 13 in., V9 = 16 ft/s, and v, = 0. Neglecting the mass of the rod and the effect of friction. ta. : WWW. *4 '15t’lwt3/x'éﬁ 31“ 7' s [1/ 2b) What is the initial kinetic energy of the collar? (6 points) I \ 2, ‘ I, 'L .- (. ‘- :mv\ ~ 5 \5 mm (was) - (£12019ng 5 2‘1 20) What is the initial potential energy of the spring? (6 points) 1, l '2. 2 VJ» :H- — %*‘§i(tw—w.x3 Eff) V"- 651 1916+ : 73425 um EGM 3400/3401 Spring 2010 Exam 2 Name 2d) What is the potential energy of the spring when r = 21 in? (6 points) ., .J.~ ‘1 1 J” 7513“ p- 4 '2’ {4; 1 Va‘ 2K5“. 1" 114:” ((544) 15;“ [ELL 2,31% 1519+ : 221251 [L .‘n 26) What is the kinetic energy of the collar r = 21 in? (6 points) ‘1: +V\ : T1 ‘1’" .m (1‘ T. *‘vl "VL 1 é ~ Yr 32--,1_1}{M9¥ r 63,5, a“ Z'qul‘af (’9 I: \$3.733) 11H 21) What is the radial component of the velocity when r = 21 in? (5 points) :w- = :w if to (L n.“ \) z 2. ('L ZKS’Z.2 (141/?- 4 a w s K3713JKH12750‘ ﬂog/Z Eva: F EGM 3400/3401 Spring 2010 Exam 2 Name 3. (35 points) Three small identical spheres A, B, and C of 1 kg each, which can slide on a horizontal, frictionless surface, are attached to three 300-mm-long strings; which are tied to a ring G. Initially the spheres rotate clockwise about the ring with a relative velocity of 1.0 m/s and the ring m0ves along the x axis with a velocity v0 = (0.4 m/s) i. Suddenly the ring breaks and the three spheres move freely in the xy plane with A and B following paths parallel to the y axis at a distance 400 mm from each other and C following a path parallel to the x axis. Determine (a) the velocity of each sphere, (b) the distance d. 3a) What is the linear momentum of the system? (magnitude 4 points, direction 1 point) - ' 0 A 3094004». = Want a - (Ell/14V: ’ ._._.___5_____. 3b) What is the angular momentum of the system? (magnitude 4 points, direction 1 point) 3c) What is the kinetic energy of the system? (5 points) : moi-2i» tiara“«%(’%>‘~0<'?ll /7. T: _’L 3 '3MV + ZMLVL Z 4} I EGM 3400/3401 Spring 2010 Exam 2 V Narn'e 3d) AfEr the ring breaks, what is the velocity of QTmagnitude 4 points, direction 1 point) A A LI :LL LIL ; A’) "— \$21: ’5‘ 2ch vtwkavg 2:2» i r J VA=VB 3e) After the ring breaks, what is the velocity of (magnitude 4 points, direction 1 point) {1" ‘0. NW 'am‘xt 01%“)1' r %*%<v33* “‘4” '7. .o x. - 'L i 251- Vﬁ VA = 10/ “A in = Am? J’ 3f) After the ring breaks, what is the veIOCity ofg? (magnitude 4 points, direction 1 point) i‘ F . ii); 2- (,0; 01/55 t-“ 3g) After the ring breaks, what is the distance d? (5 points) [ flax/1} +~ x<vﬂ 3>+¥é<rgx2 + T5 a3\>¢(‘/3J3+%( Ext-i j>X Vc A /\ /\ 1, q ) ...
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EGM3400_Test_2_solution - EGM 3400/3401 Spring 2010 Exam 2...

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