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Test 3 Spring 2006

Test 3 Spring 2006 - Physics 2101 Third Exam Spring 2006...

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Unformatted text preview: Physics 2101, Third Exam, Spring 2006 April 18, 2006 Last Name: K E Y First Name: Section: (Circle one) Section 1 (Rupnik, MWF 7:40 AM) Section 2 (Rupnik, MWF 9:40 AM) Section 3 (Rupnik, MWF 11:40 AM) Section 4 (Kirk, MWF 2:40 PM) Section 5 (Kirk, 'I‘uTh 10:40 AM) Section 6 (Gonzalez, 'I‘uTh 1:40 PM) o Please be sure to print your name and circle your section above. Do not write your social security number. - Examine your paper carefully to be sure it is complete. There should be 3 consecutively num- bered problems and 3 questions. The point value of each problem is 23 or 24 and of the question is 10 with total of 100. They are ordered relative to the topics covered. 0 You are not required to show any work on the three questions. You may circle the correct answer and mom on. a You MUST show your work on the three problems. Failure to show your work will result in the loss of credit. :- Present yOur solutions in a neat and logically organized manner. Your graders cannot, and will not, award credit to solutions that are illegible. :- For problems with numerical answers, please carry units throughout the calculation. 0 You may use scientific or graphing calculators, but you must derive your answer and explain your work. 0 Feel free to detach, use, and keep the formula sheet. No other reference material is allowed during the exam. :- GOOD LUCK! Problem 1 (23 points) We At! War MWA. ma 1‘”, are Mafia stream: a w: 9!: eaten. The figure is an overhead view of a thin uniform rod of length D = 0.80m and mass M = 0.12 kg. The rod is rotating in a counterclockwise direction along a horizontal plane, with an angular velocity of magnitude to = 2.8 rad/s, pointing out of the page. A particle of mass m = 0.020 kg and traveling along a straight line, along the same plane, hits the rod and sticks. Just before impact the particle has a velocity 13’ of magnitude 15 m/s at an angle qt = 35" relative to the rod and the particle is at a distance d = 0.30m from the rod’s center. w:2.g>M4/5=WW awagfimww (new (a) (4 pts) What is the magnitude and direction 1&5 451W 5? at? 0f 79-4 mm)A/@T of the angular momentum of the rod before the impact. i406 '1'- - W $%zst :0 “Whole = “'5 I? 2. Particl 2. L: I60 =' “MD to = (MM-96g“) (2'3 Mi) - e—\ l9. l2. Rotation 3X1“ '8’ ..-/ e _ e 2 as ‘\ L = L79): IO Lag-en ( - __.___.____.. 5' h—d-d Z .x. WeeewAw+eeMegW e———D—-——~4 é-f-‘l‘fi (flaw; HW—W-W) gm; rd4_M.$& (h) (6 pts) What is the magnitude and direction ‘ L121 of the angular momentum of the particle before the impact? Path-lial-é 18 W'l'ficf 4.9 Q P0 WW " . 3:5"- Pa ré-h‘alé L: mlfillfilmefigr-mew-me :2) = (0-02 £7)(0'3”l(15§“5—)M& 515:.- 5.16 x (6 fig?" 9 ’8 did-emu: CWor-H wcmflo‘i‘um M -Q (W fiMrW—ade) (c) (8 pte) Find the final anggilar speed of the particle-rod system, after the impact. {)8 Weber-D wagmmm¢wmlgfi (If-“1%: Z: 5 [-41 H ----P ___ 2- w—ftaw Lia — 15%“? and white 1:25? Iliad. +'Z,;hr£t29—-I+Md Ia: -- rad/Matti: = (frat-dz)“; 3. . ~17. 3- w: w "lfiflml 1-79»: figeflsm 1?” =I-4.H’35 .— eneee F flf—rmdl M2 confirm“? A )2— _ /2_ (d) (5 pts) Has the total kinetic energy of the particleerod system increased - or remained the same ? Circle the right answer. Explain! ‘mfimcit‘o-a Ac 4% ¢ Mam MafiaAK<0 (Mmfiorrgfm WE‘W) Problem 2 (24 points) A uniform thin beam has a mass M and a. length L. The beam is connected by a hinge to a vertical wall on the left and is held in its position by a cable attached to the vertical wall on the right. The cable makes an angle of d) = 90.0‘“ with respect to the beam. The beam makes an angle of 6 above the horizontal. (a) (5 pts) Draw a free-body diagram for the beam. 2‘. H -—'~ (b) (3 pts) Relative to the hinge, is the torque of the beam’s weightwinto the page) ‘1: . . 4 __’ Ir' ""“ ' counterclockwise (out of the page) or neither?—(01rclethe right answer. 2" —"-' 4' X M. 95%“. (m awaimd- 40.51) “it“ “‘3 m3. (c)( (6 pts) Find the magnitude of the tension in the cable. Express your answer in terms of M, 6, L and other physical constants as needed. (HINT: Choose the pivot point at the hinge. ) 2:3: MA mo»? 5‘- an? a-r ?=lrllF/ém9,e;-3 3:14:91/mt‘éééw “"9 ' £05 ‘72» /m?m(6w'— 6)+ LTMQOe “'0 l T: figs/349‘ L__.__Z..*_l (d) (5 pts) Find the magnitude and direction .1: down) of the vertical component of the force exerted on the beam by the hinge. Express your answer in terms of only M , 6, L and other physical constants as needed. :0 I? -'F #M?+Tm9=0 29 __ - fim (IH M?" --r i: am} T6079:- “i’j/ ,4“? 2|?!) .14st F m (e) (5 pts) Find the magnitude and [email protected] ur right) of the horizontal fico/mpgfient of the¥ “W force exerted on the beam by the hinge Express your answer in terms of only M 6 L and other physical constants as needed. za=o 4'; +Tm‘k8 == 0 firms: %4m6m16 2: 1334mm) > Oy W 3 at m mg .g Median of if: 1119er Aa(qn’—a)=m9 "up. Question 1 (10 points) Three particles with equal masses m1 :— m2 = m3 = m are positioned along a line, as shown below. Then, you move mg by d toward m3. The initial and final positions of mg are drawn in the figure as dark and open circles, respectively. Circle the correct answer to each. 0 the uestions below. 3: _, _, f 9 _ Wm - «4, wt «43 (a) (3 pts) The magnitude of the net force on m2 4 (1) increased. an; F . m2 4 m3 II I- ........... p. {33; (ii) decreased. F’ . .rernained the same. ”3’" l d d d (iv) Not enough information to answer. ¢_. 0-) He came I v ce are and ‘ w. .5: ’7" . I: ‘ . . “#6; (WM Q P 0819‘) ofi L Fm! 2' " dull} 2’ If: Mjmmdé (b) (4 pts) The potential energy of the ml-mg-mg system (assuming that the zero of gravitational potential energy corresponds to an infinite separation) (i) increased. Aug 3' O ' (ii) decreased. bedmfl 'fiié wit-6.! “FE 1&6 £m€ Md fifpahhfl“ .remafined the same. 61f M?— an; 5 L I \ E# 615% 0- . N h .nf . (a!) an. avenge, fat-"Atlas «rename/arse (1v) ot enoug 1 ormation to answer. 61“ #4 ‘4 Ef‘ E! [ff m :C ?lf-ED'V m4gré£ QIE $«Q 6’) (c) (3 pts) The work done by you on the particle m2, assuming particles are at rest initially and finally, is b D a (i) POSitive. WW 7"" W :— M-k Au + A "H— +A Ml ..- ”may urn—HQ (1) negative. $ WW: AM :15“ 3 O o 3 ® zero. (iv) Not enough information to answer. Question 2 (10 points) A penguin of mass m floats first in a fluid of density pl 2 9.3, then in a fluid of density p2 = 0.95pm and then in a fluid of density p3 = 1.1.00. Circle the correct answer to each of the questions below. (a) (3 pts) Which liquid exerts the largest buoyant force, F5, on the floating penguin? (1)1. Kym? ”W‘WOMWLJ-fl (b) (3 pts) In which liquid is the floating penguin going to displace the most liquid? (5) 1_ "94M ”Tea/M43 - flé/Mdénflf' me Wile (an; .2. fr ”aw? lanai; 3/ (iii) 3. . : “st .- 4W0 W M- . ”‘- i:(i:rl} All three tie. m fie V) M M; EZW'C/ (c) (4 pts) The penguin spots a fish and dives in to catch it. After missing the fish the penguin decides to let the liquid brings him to the surface. Neglect the viscosity of the figuid (drag or trigtjgm). The constant 9 used is the free fall acceleration close to the Earth surface. If F3, is the buoyant force on the penguin during the ascent, which relation represents the correct form of the magnitude of the penguin‘s acceleration, a, during ascent? ..., (i) “:9” 23M Mew-411‘s 129.44?! if“: m“ 1+1, E @“E—g‘ (z 1:; :— M4. s, I» M (111) a=g+;. 1: a. ““3 “5‘5""? 1..__._.—--__.___.._1 (iv) a = Question 3 (10 points) The graph shows the velocity function 11(t) of a. linear simple harmonic oscillator. Assume that the position function 33(t) has the form m(t)— — :nm cos(wt + e). ? (Hwt-wl’ Mw/hnéd-twjzg U-WédtW) Circle the correct answer to each of the questions below. . T ‘5. 1: - : J: * at 1 4- *E ' 4- ' (a) (3 pts) What is the maximum speed, um? (i) 2.0 cm/s._ (ii) 4.0cm/s. (iii 6.0 cm/s. w 7.0 cm/s. (b) (3 pts) What is the period, T? (i) 0-52» T. W W +uro We «mi MJM «(“411- (ii) 1.03. (iii) 3.5s. 6.0 s. (c) (4 pts) What IS the phase constant, 915? Iii-(t) W 71:, Wt) _—_,- .4}; Meat (1) ofd<¢<§md IS'I-mé-lfioot (mm, m 395+ above} (ii) —rad<o‘)<2.7rrad '—"'——“"""" i 4 3; Wfir __....... ...._-. Problem 3 (23'points) Two waves are generated on a string of length 10.0111 to produce a five~loop standing wave with amplitude of 3.0 cm, as shown in the figure below (notice the different units for the distance :1: along the string and vertical displacement y). The wave speed is 65 111/ s. Let the equation for one of the waves be of the form y(a:, t) = ym sinUca: + wt). (a) In the equation for the other wave, what are the numerical values for the following quantities? gramme VIM-WE: ammonia (:T; J38:pl::e giving-M 3606:)" ”7—1“ .3. egg-35 a: (m) E -3.0 figigflgz=2$~m4lfixdmwt (ii) (6 pts) )The wave number k? ”M “.334..." 23,". .b tM fig 3 a; 1.2 ‘5’: 2a.; 351, fiaefif=£fi=i¥fig ”WJ;£;W?4: de—FQAMM-w-eau. .(oiLegWé’zj‘Mf—v Mail-s: = 44.4, (b) For the standing wave on the string drawn above (1) [7 pts) find the maximum displacement of the string element at a position :1: = 1.5m. Wx¢)=fia’(x)+)=(3.0 Mmflaresp] flawl— Yank): ‘0‘!” ”a" MM Ito-3.1a. meat—=1) W: Y{xl)—-fij‘(.t:/.§m)= (Mm) M[(£fii){’5¢tfl= 2' ’2- W ...
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