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Test 2 solution

# Test 2 solution - EGM 3400/3401 Exam 2 Name Work any three...

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Unformatted text preview: EGM 3400/3401 Exam 2 Name Work any three of the four problems. Only three problems will be graded. Indicate ch problem you do not want graded. If you do not indicate a problem, you will be graded on the ﬁrst three pro lems. Each problem is North 33 points. 1. A 17.5-lb sphere A of radius 4.5 in. moving with a velocity v0 of magnitude v0 = 6 ft/s strikes a 1.6-1b sphere B of radius 2 in. which was at rest. Both spheres are hanging from identical light ﬂexible cords. Knowing that the coefﬁcient of restitution is 0.8, determine the velocity (magnitude and direction) of sphere A immediately after impact. 21) Draw a diagram to the right of the ﬁgure below for each ball showing all the impulses, and calculate the angle between the normal and x-axes. (10 points) Ab) Write the appropriate equations you need to solve this problem for conservation of momentum and ,, coefﬁcient of restitution. (10 points) 0 CW5 ' IF MM" 1” y- ﬁnch” ma Va ‘l‘ "ﬂy/(i: '- MAVA I 1‘ Mb Uta/Cd? 6 ((0 V I O (“kiwi A: “EMA?!“ VBH/ ‘ VIM. : &( Vm'ﬂB> Q) C) Determine the velocity (magnitude and direction) of sphere A immediately after impact. (13 points) VB,“— VB] VH’ ; W/Caoé VA > VD ) / Fran/t Q7 Van/RVB/1 Vﬁn/+€<Vﬁb’> 3 Vt/me *ev’“ (Al subham (a) ado 0) “AN/0 : MJv,/+ Mg 4,06 < L/A/ng 6 +6,th A EGM 3400/3401 Exam 2 Name 2. The three blocks shown are identical. Blocks B and C are at rest when block B is hit by block A which is moving with a velocity VA of 3 ﬁ/s. After the impact, which is assumed to be perfectly plastic (e = O), the velocity of blocks A and B decreases due to friction, while block C picks up speed until all three blocks are moving with the same velocity v. Know that the coefﬁcient of kinetic friction between all surfaces is ,uk = 0.20, determine the time required for the three blocks to reach the same velocity. ‘8 a) What is the velocity of C just after impact? (7 points) / \/¢’~O b) Find the velocity of A and B just after impact. .(7 points) 0 / / mAv/w MB 3 1 WWW T MINE , / / \ln:\/5 1V”, [mﬁzwlgtmc Mel} C Kilt: “We. At FﬁEClt : M3WAt EGM 3400/3401 Exam 2 Name d) Determine the time required for the three blocks to reach the same velocity. (12 points) A Binds {0+3 M V: 4Mi WW Vcioc-H’g O MAW + Mg ~AWAte3MWAt 1 @+MB§ v P‘OCK C 0 Mﬂ‘!‘ any”: : WV w) gem m tum 4w V MA VA " Li‘uwAt 1 V (33 I’M/(+048 A V: lat/ﬁt: yﬁﬁéiruﬂf QM EGM 3400/3401 Exam 2 Name 3. A 2-kg sphere A strikes the frictionless inclined surface of a 6-kg wedge B at a 90° angle with a velocity of Magnitude 4 m/s. The wedge can roll freely on the ground and is initially at rest. Knowing that the coefﬁcient of restitution between the wedge and the sphere is 0.50 and that the inclined surface of the wedge forms an angle 6 = 40° with the horizontal, determine the velocity of the sphere immediately after impact. a) Draw a diagram to the right of the ﬁgure below for the ball and the block showing all the impulses. (10 points) b) Write the appropriate equations you need to solve this problem for conservation of momentum and coefﬁcient of restitution. (10 points) (“mm-Um is WSQWJL Ea. )(v oetrecitzm o , , , , ”W“ “Va — WVVAw mm m (vii m ACOCQ Jib {€S'i: ‘(uhim 0 VB,“ " VA,“ '- ri<ngy§h3 (Z) c) Determine the velocity of the sphere immediately after impact. (13 points) _ I_ l / . . _ \(AA_\/A) V“ st ’ \1Kn -_ V3 M40 V,W : VAW6,VA/x:\/A’M9 J PW i'i 40') W‘AVA‘EMLQ : MA \lA'sMe + M303 is) vg’me —vi’:e(vA> m 50mm is» W V3,: VA, + 6V4 (fl yina Swish-Mae, [£3 info (3) mi \ln glue = mﬂvﬁ’ma + M (vi/42w} —\ 3M6 EGM 3400/3401 Exam 2 Name MAVAMQ” Maevﬂ 1 WA VA/WQ‘hmBV/t/ Sin/9 3&6 VA W‘ weﬂeﬂ» 1 l( M < " awe v4 M‘%6+ €736 ,; V Mme—e734 VA A< W6 Sine WA W5+ ”15/ 5‘6 we / . \/,f — VA (MAWZQ - ems) M MAWZ‘Q + MB VA] 1 %“/5 <2%&4240°~0,5x(9ﬁ> 7.? 4.940" —» 6 K3 1 Vfg : ’\27L}‘ m/S SO“ EGM 3400/3401 Exam 2 Name 4. A 1.3-lb sphere A is dropped from a height of 1.8 ft onto a 2.6-lb plate B which is supported by a nested set f‘of springs and is initially at rest. Knowing that the coefﬁcient of restitution between the sphere and the plate is e = 0.8, determine the height h reached by the sphere after rebound. a) Find the velocity of sphere A just prior to impact. (Please show your work to the right of the diagram below). (8points) 0 0 e 71 m : 1% 2. My ’~ ii?” 1.8!} -—T K V : ﬁ& 1 \lzx3&:‘—/fjx LS-C'l’ T‘” ”a V: to 77 42% b) Write the appropriate equations you need to ﬁnd the velocity of sphere A just after impact (conservation of Amomentum and coefﬁcient of restitution). (8 points) 0 [WMUA 1’ may; -: MAVAQ MBVg’ " / Vb ‘Vk 3 ECVA’WS 0) Determine the velocity of the sphere immediately after impact. (9 points) Via/l VAI+c1(\/A) MAVA : mkVA/f W15<VAI+€VA3 / MAVA ‘MBCVA : MA VA/ + MB VA MA'l MB EGM 3400/3401 Exam 2 Name (1) Determine the height [1 reached by the sphere after rebound. (8 points) A O O T.+)Z :7:"’V’2, ﬂak: ”‘2va 2. 2 ...
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Test 2 solution - EGM 3400/3401 Exam 2 Name Work any three...

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