Exam1 - EM311M - Dynamics Exam 1 Monday, Sep 25, 2006, WEL...

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Unformatted text preview: EM311M - Dynamics Exam 1 Monday, Sep 25, 2006, WEL 3.502 33’!” £145" “715? (4.4% a—l" w. ¥.-w4wrfmx".* P‘V‘V- 1. A particle is moving in a straight line with a constant acceleration a. At some time to > 0, the corresponding position and velocity are $0 and 00, respectively. Derive the formulas for position m(t) and velocity v(t) at any time t (5 points) Va 5 a : 1/ O ,‘0 If 1/ D "5 ’ V ‘ Mb“ ) + “Va / fair" f {-o‘ , " 1" X40 4 CE“ 7‘ '4 *1/59 x-Ko w J '1' x .53; .- 4: (1‘ "7‘ £450 {’4‘ W f a {- ix :3, a 7",.» ., if! 2,15," 1 7,... X0 3‘ 3 x e W“ ‘mmlflmvfli-flm‘l 2. The large and small hands of a clock meet at noon. What time will they meet next again? Give the answer in terms of a fraction (no decimal round off, please...) (5 points) v ./ ’ " ’ -' e -"' w. 3"” _ Q? n- .5 .3 .j‘ if" . \f‘ 4/“ ‘ “mi *1 r‘ ‘ ’5“ A 5"? Van" a.» a; if It. .... "I m... . - i (_ .f fl 3» _ A K .9 “a. 6. “$- r * 3 ,2 ‘2'": ’ I, x: I , " w A} a :2 ‘ dd; (h “ I I“ ~ 1—81-. 13: x a f {.1- ; -J‘ _ i , 1 N " 4 Q) @ 3. Give examples of motions in which: a/ at 76 0, an 2 0, b/ at = 0, an # 0. (5 points) a) fliafi‘ou .c 'at J ft ‘ ,r‘ f“ _ L? :3: ,4 {a as c" 6.: (3&0.ch - A ) flan-16.1.?“ «1!. u 4. £761.45; t d ML" 4' C h 5'" é ‘ V I (CM: 4/; my {(4 / #6619736) :2" I ” f 4. Derive the formula for acceleration vector components or and (L9 in the polar system of coordi— nates (5 points) 0(3" cf: IMF-h“, 2 c 5‘ ~— I’" r" a “(’6' ‘ 6" / £6 r— ,V m. !" O A“ e a v .i- (.1 y; P'fSr 1L. it"‘gf : r 5,, 1‘ {€3,559 t5; '5' (J a a . ’- 0 46f" ' * ‘37 n .. wiwwfgg. ’ g .- r 5?," «f I Egg-v c9 1 I” {a 4 r555, ,4 r fig» 5: v ‘ ; 3&7 "gr 0" ‘° <2 i “’ I i m...” —'“~;"" -- MM“, 3 MM ’ a. r a 9' 5. A particle moves along a parabola y2 = a: with a constant speed 1). Determine the Cartesian components of the velocity vector as a function of coordinate 1:. (5 points) C’oaafim heal" rid-0790a 5 raw «'3 l“ 5‘ X Z n s“ 2; ‘2 i? L W g“; L,» a w V a... )6 £3: V 1/ I, I N as (a? z ¢ x J 7' ’ ~ 9" V l/ v + ~~~~ «- 4‘ W, _ .3 was,” _-r .—. ,~- “7 f7 "' f If 7 3+ 1 f i’éxw 1/ :r f .2, X 6. A projectile is launched at 100 ft/s at 600 above the horizontal. The surface on which it lands is described by the equation shown. Determine the :1: coordinate of the point of impact. (25 points) /00 0635001 1‘ 2’ 50¢" X .127 ... ’ I o z y _._. .. 52.1,» :49? + Ioo 5.3m 56’ wt.- : ——/6,/z‘ 74 596605 142:" fiv/WC Zf‘ Mag, W‘ac ‘fd'o/Jtcfii/C [a f: “fat? jroamyf (5) y I: 'fllflait x / Z. X = 5753's? iii] 6‘; r « lo/.‘i’/ 3 64.1524 ; :r w a i x ~ m 5% 53 8,6? «mm 7. The car increases its speed at a constant rate from 40 mi/ h at A to 60 mi /h at B. What is the magnitude of its acceleration 2 s after it passes point A ?? (25 points) ' 7 #- y as+o%~g stew [T] l 120a ‘ if; '— fi I ‘ B w A ‘ o go‘ft_._I—x 041.3%“; 151,9“, x4 +0 3 a 3’0 S r; «S’sz + Jfi’hgfi'rwa r3“? ~2F'/00 35:0 x 150 +£2.93 r52.3é=r.27-52,z)4~4/ ~_u ‘ a 5:357 W, m? r Q :5“ "2': "‘ «pl/.26 3' 59.57 H— . 4f :- 7g/[ [3—] @ M 2 V 5 4k i 0 ,__ ‘fl V—— 51? 67«—- 736/54, ~==> V5 7"“ 30 Z J] @ %41fioa (bf/6t. 3° 3 QtL =r 247/6 8. A point P moves along the spiral path 7‘ = (0.1)6 ft, where 0 is in radians. The angular position 0 = 2t rad, where t is in seconds, and r = 0 at t : 0. Determine the magnitudes of the velocity and acceleration vectors of P at t = 1 s. (25 points) P A r: 0/ 6 :7 <94" [7‘47 0 Q r .1.“ J 69 r 0'1 [if F: m a = o u- “-mwumm m— MW"? m V:- 02:“"+ m“ “' 0””? 5‘2"?” WWW-” M, if“ m s n z «~27 ...
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This note was uploaded on 11/03/2009 for the course EM 311 M taught by Professor N/a during the Spring '08 term at University of Texas at Austin.

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Exam1 - EM311M - Dynamics Exam 1 Monday, Sep 25, 2006, WEL...

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