Physics 218 Exam 1 with Solutions Spring 2011, Sections ,526,528

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1 Physics 18 Exam 1 wih Soluions Sprin 11, Secions ,56,58 Fill ou he informaion below bu do no open he exam unil insruced o do so Name Sinaure Suden ID E- mail Secion # Rules of he exam: 1. You have he full class period o complee he exam.. Formulae are provided on he las pae. You may NOT use any oher formula shee. 3. When calculain numerical values, be sure o keep rack of unis. 4. You may use his exam or come up fron for scrach paper. 5. Be sure o pu a box around your final answers and clearly indicae your work o your rader. 6. Clearly erase any unwaned marks. No credi will be iven if we can fiure ou which answer you are choosin, or which answer you wan us o consider. 7. Parial credi can be iven only if your work is clearly explained and labeled. 8. All work mus be shown o e credi for he answer marked. If he answer marked does no obviously follow from he shown work, even if he answer is correc, you will no e credi for he answer. Pu your iniials here afer readin he above insrucions: 1

2 Par 1: Basic ideas of unis, conversions, and vecors. Problem 1.1: (p) Wha sysem of unis is used in his course? Wha are he basic unis of mass, lenh, and ime of ha sysem? Inernaional Sysem (SI), Kiloram, meer, seconds. Problem 1.: Pascal, Bar and psi are unis of pressure defined as: 1 Pa (Pascal) = 1-5 bar 1 Bar (bar) = psi Table o be filled by raders only Par Score Par 1 (15) Par () Par 3 () Par 4 () Bonus (5) (Acually 6 poins) Exam Toal Quesion 1..1: (4p) Express 9 psi in unis of Pascals. 9 "# = 9 "# "# " = "# " "# " " = 1 " Problem 1.3: The followin plo shows he posiion x as a funcion of ime Quesion 1.3.1: (7p) For each ime rane A,B,C I, fill he able below wriin in each cell wheher he velociy and acceleraion are <, >, or =. x[cm] A B C D E F G Reion Velociy Acceleraion A > > B > = C > < D < < E < = F < > G = = [s] Quesion 1.3.: (p) Is he maniude of he velociy reaer in reion B han i is in E? Why? The maniude of he velociy a a iven ime is he maniude of he slope of he anen line in he above raph a ha iven ime. The slope a ime rane B is abou + squares/ squares, wih a maniude of +1. The slope a ime rane E is abou -4 squares/ squares wih a maniude of -. Hence, he answer is NO; he maniude of he velociy a reion B is smaller han ha a reion E.

3 Par : Tennis sho. Problem.1: (p) You are a a disance of d meers from your friend s car which is drivin away from you wih a velociy of Vc and some acceleraion. In an effor o pass a ennis ball o your friend before he is oo far away you hrow he ennis ball a an anle of 45 derees up wih a horizonal componen of Vxb. Graviy is presen and nelec he size of he car as well as yours Quesion.1.1: (4p) In he space below draw a schemaic diaram of he problem and wrie any associaed imes. In addiion choose and draw a coordinae sysem and clearly indicae is oriin. = C Oriin d Quesion.1.: (6p) Wrie he equaions of moion of he accelerain car and ennis ball accordin o your coordinae sysem. Indicae which known parameers are zero. X c () = d +V c + a c X b () = V xb Y b () = V yb = V xb Quesion.1.3: (4p) Find he ime he ennis ball will be in he air. Y b ( L ) = V xb L L = " L = V xb Quesion.1.4: (6p) Find he acceleraion he car needs o have such ha he ennis ball will land on he car. X c ( L ) = X b ( L ) d +V c L + a c L = V xb L a c L = V xb L " d "V c L a c = ( V xb L " d "V c L ) L 3

4 Par 3: Parkin he rocke. Problem 3.1: (p) A spaceship is approachin is dockin saion locaed on he side of a buildin and 5m above round. When he spaceship is a a horizonal disance d=m from he dockin saion is horizonal velociy is 5m/s owards he dockin saion and 1m/s owards he round. The enine of he spaceship is inied producin acceleraion in he verical direcion. The followin quesions mus be answered in he form of a number wih proper unis. Quesion 3.1.1: (3p) Choose and draw your coordinae sysem on he fiure h=5 m Y Dockin saion above and associae imes o he relevan evens. X d= m L=5 m Quesion 3.1.: (5p) Wrie he equaion of moion of he spaceship as a funcion of ime X() = 5 m s Y () = h 1 m s + 1 a y Quesion 3.1.3: (5p) Find he ime a which he spacecraf reaches he buildin. X( L ) = 5 m s L = m L = 5 s = 4s Quesion 3.1.4: (7p) Find he acceleraion of he spacecraf in he verical direcion such ha i lands exacly a he dockin saion. Y ( L ) = 5m 5 1 m s L + 1 a y L = 5m " 1 a y L = m +1 m s 4s = +m " a y = 4m 16s =.5 m s 4

5 Par 4: A more complex problem. Problem 4.1: (p) Two balls are ied up o a rod of lenh L and conneced o a moor ha makes i spin in he verical plane wih a circular uniform moion. Ball #1 is a a radius L and movin wih velociy V1 and ball # is a a radius L. The cener of roaion is locaed a heih h above he round as shown in he picure below. All answers mus be expressed in erms of known parameers. Quesion 4.1.1: (p) Which ball moves faser he one farher o he round or he closer one? why? h L 1 L Y V 1 = L T,V L = V = T V 1 The ball closer o he round moves faser as i has larer radius. Quesion 4.1.: (5p) When he rod is a he minimum posiion (as shown in he diaram) boh balls break loose wih a X horizonal velociy and evenually fall o he round due o raviy. Indicae a coordinae sysem and wrie he equaions of moion of each ball in he verical and horizonal componens. X 1 () = V 1 Y 1 () = h L X () = V = V 1 Y () = h L Quesion 4.1.3: (5p)Find he ime i would ake each ball o fall o he round. Which ball ouches he round firs? Y 1 ( 1L ) = h L 1L = " 1L = Y ( L ) = h L L = " L = (h L) (h L) Ball # ouches he round faser. Quesion 4.1.4: (8p) Assumin ha he heih h is exacly 3L, which ball has a larer rane? (Hin: calculae he rane of each and ake he raio) X 1 ( 1L ) = V 1 1L = V 1 (h L) X ( L ) = V L = V 1 L = V 1 " X ( L ) X 1 ( 1L ) = V 1 V 1 = V = Ball # has a larer rane. = 5

6 Formula shee: Vecors: A = A xˆ i + A yˆ j + Azˆ k A = A x + A y + A z an (") = A y,where " = anle beween x ˆ axis and projecion of vecor A o he (ˆ x y ˆ ) plane. A x Mahemaical Formulae: The followin equaions are always rue: The followin apply for consan acceleraion: Oher Equaions: In - D, " = anle beween x ˆ axis and vecor A. a + b + c = " = -b ± b # 4ac a If x = a n " dx d = na n -1. a If x = a n " $ x( ) d = n +1 n +1 n +1 ( # 1 ) v = d r d a = d v d r ( ) = r + v ( ) = v + " v x = dx d " a x = dv x d # v ( ) d " x # a ( ) d " v x ( ) = x + v x ( ) v av -x = (x - x ) 1 ( - 1 ), a = (v - v ) x 1x av -x ( - 1 ) r = r + v o + 1 v = v + a " v x v x ( ) = v x + a x #x ( ) #x = v x + v x a rad = v R = 4" R T v P/A = v P/B + v B/A # d ( ) = v x + a x ( ) # d a " x = x + v x + 1 a x ( ) = v x + a x 6