{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# Exam1 - EM311M Dynamics Exam 1 Monday WEL 3.502 33’!”...

This preview shows pages 1–5. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 5

Exam1 - EM311M Dynamics Exam 1 Monday WEL 3.502 33’!”...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online