Prelim1_F07_Solutions

An Introduction To Mechanics

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

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

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

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

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

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

View Full DocumentRight Arrow Icon
Background image of page 10
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Plzys 116 Prelim 1 ' Fall 2007 Your Name: SD\ 0‘45 Section Number: ______________ Section Instructor: Problem Points Your Score 1 25 2 30 3 20 4 25 TOTAL 1 00 Instructions: o Please write your name, section number and sectlon instructor at the top. - There are 4 problems in this exam. The total number of points is 100. - Make sure that your capy is complete (11 numbered pages) before starting. - The exam is closed book. No graphing calculators are allowed! The last numberedpage of the exam contains formulae that you may find useful. - You must show your work to receive full credit. Correct answers without justification will only receive partial credit. "- Two blank pages are attached at the end of the exam. They may he used for scratch paper, but will not be graded unless you clearly refer us to some Clearly Indicated item there. - You may remove the equation sheet. You do not need to hand it in Witl‘ the rest of the exam. Phys 116 Prelim 1 Fall 2007 1. [25 points] A block with mass m on a horizontal frictionless table is attached to a central pivot by a massless rope of length L The block twirls about the pivot with a constant speed v. (a) a) [2 points] Draw the force diagram for the block in this initial configuration, which is shown as viewed from above in Figure (a). Clearly label each force. In the diagram, you do NOT need to calculate the magnitudes of the forces, nor break them into components. OAR (are, :5 {k8 Jr'efivsCow CA. (Le 10(36— ’l’ke. ’% M b) [7 points] Find the tension in the rope in terms of m, vand L (as in Figure (a)). use Pakox wor'A‘x w/ Sue: W 5% agave. A ‘2.» (“A er»? '3? alrfime“) r (CFCuWn—j‘bfi W/ ‘0“3‘u'd sped ::> r) ’ V '2. ‘- 2 co=\’(: \so 't’>-W~L(T-3 " "3.....V L. Phys 116 Prelim 1 Fall 2007 The string is cut, and a second block, also with mass m, is installed at the middle of the rope and both blocks twirl as shown in Figure (b). Again, the outer block has speed v. c) [4 points] . Draw the force diagram for each block in this new configuration, shown in Figure (b). Clearly label each force. In the diagram, you do NOT need to calculate the magnitudes of the forces, nor break them into components. 7r“. U.- :rou ‘51— \Al‘ "PW d) [12 pOints] Find the tensions in the inner and outer sections of the rope in terms of m, v and L (as in Figure (a)). u/ M W Care‘— 59—“' “"i "5 L Phys 116 Prelim 1 Fall 2007 2. [30 points] Having watched (too?) many episodes of This Old House, you decide that you could SUpply your dormitory’s bathroom with a much nicer sink and vanity than Cornell provides. You buy some sheets of plywood and a new sink and load them into your friend ’s truck as shown. You’ve secured the plywood, but have simply rested the sink on tap of the plywood, as shown in the figure below. - The plywood rests at an angle 9 with respect to horizontal, the length of the plywood is L, and the highest end of the plywood is a distance h above the road. The mass of the sink is M, and the coefficient of friction between the sink and the plywood is it When leaving Home Depot, in your enthusiasm you rapidly accelerate forward from rest with acceleration of magnitude a, as indicated. The sink begins to slide up the plywood. Y \ a) '[4 points] Draw a diagram showing all the forces acting on the sink, clearly labeling each forces. In the diagram, you do NOT need to calculate the magnitudes of the forces, nor break them into components. Phys 116 Prelim 1 Fall 2007 b) [6 points] Using the coordinate system shown in the system, write the equations for the acceleration of the sink in the horizontal (x) and vertical (y) directions in terms of 6, L, h, M, p, a, and constants of nature. You may introduce alternate coordinates if convenient, but their relationship to x and y must be explicit and clear. Your results should incorporate any constraints in the problem. ) A p) ':=' “stat? ~2- -'«- “059 g ' VJ ‘ '- M3: 2 ’ Q .— 5:¢\Gg F? ,PIJ as} r” \s Lat- w... (mil—0w a ,3 D4 5,, gallon. N .-.- same. (was r W . . a U. a §=k9”“°’9:“'“ L .9 x: KP:- tA-LDS. i g = astfie F 3 = ws “9 . . — fiézicose Err/~7- q : “(5'49T/‘50593 RbMG’L . 0 ) I ‘ I ,_ LA. 5 A“ g U (40569 —» 5MB» A" M c) [10 points] Find the maximum acceleration amax of the truck for which the sink would have remained at rest at the bottom of the plywood. Express your results in terms of 6, L, h, M, p, and constants of nature. W M? AWN. ) $~"‘~\" ((+‘j feadnéé {*3 MAK:W"~>' “gagi- Lo stcla, So FF 'b-NU 9 Q 5 Phys 116 ' Prelim 1 Fall 2007 d) [1 0 points] Find the time- ttop it takes the sink to reach the top of the plywood. At that time, what \o' is the sink’s horizontal velocity relative to the (i) the ground and (ii) the truck? You \V may take 6 = 30° (see formula sheet) and p = 1h/3, but otherwise express your J results in terms of L, h, M, a, and constants of nature. QC“ 6‘: 30° ) l)“; VJ: 3 CL) ECM" (:0 I; ~ - ( if} a \C ‘7 \j A ( \ .L : N - M a“- 2. J \ I K.’ N i 1 o . w 0-. r A “fl-3 — a!" ) '- N, .. + 2"." M g ‘3 N('; 2&3 ’ A)"; " M05 7’) jogié a A? - '53 " 3’ ‘ w 0' =5 a —- ’- V‘ "" "r3 3 «P 2’ w ’ J? ‘ a.“ $35 :: J73 0’ «h 3“ .. , 3: <5 (9” w ‘3 AG. ’3 J __\_ ,_ J— 1"} (LL—a)» tA 4.) AM: LEE—1'. a :lfgj abasz A3 .. 2—. ’ 3: ‘ 2.6 t a . rcé/c c TD Mama (1741:25- D-‘N (’QSNAAS MA ~11 ~( vag . kk Lshda + \3 we} 7- V“ 5 Q ‘3'5 ' z . . 4.7- 2 ‘ - L I. s A. w s A9 f '2- —'-> Ls‘Aa " ‘1- ‘3 2’ or ~ 3r? 1. zl... 2J— // -—- >- V" "‘ ’5’?) ' Phys 116 Prelim 1 3. [20 points] The two blocks shown at right are connected by a heavy uniform rope with mass Mn. An upward force of magnitude F is applied. a) [6 points] Draw three diagrams depicting the forces acting on each of the three objects, the upper block with mass Mu, the lower block with mass Md, and the rope. Upper 50% i .3 LL" Wu. Tu? 1’1,P {2.0 P6 J % Wr A, a A ,. \rr Lowe/lac x V' 5" T _, /\ “a b) [4 points] Determine the acceleration of the system. Fall 2007 Z c Mr ? é / Z g o. . Phys 116 Prelim 1 a Fall 2007 c) [10 points] Determine the tensionsat the top and the bottom of the heavy rope. Note: you do NOT need to determine the tension as a function of height . "’ L 4L2. accake/bukovx 0‘ M C > g .3 -' ,_.. A ‘3 - M a“: (TD/’3 FT‘L ‘7 ‘A‘P r ‘ WA 33 3? U’y/fit’fl“: MA; —-M MW+MA¥Mr T 3 A.“ C "‘ a ._ A W '5 “My; :> F -'T' -- 7. M Gk = M“ F —- “P “‘3 “‘ 3 M“ M +M-r T '= C "" 3 ":. A, F d) [BONUS 5 points] Determine the tension at the heavy rope’s midpoint. Note: you still) do NOT need to determine the tension as a function of height. Tr“: A, Car-3w W~ LA? 0" r‘W J _. mill/T— , k A A .3 Mr A TWA-.- no», wig: ":7; 6‘" Mr F 1» TM‘% - N F 3 EP“‘: " Mw¥AJrN Mun-Mrt-MJ / W4 T& r M‘s/fMF/L lM : F Mud-M,- i-MA Prelim 1 Fall 2007 Phys 116 4. [25 points] Snoopy stands on a flat boat so that he is a distance d from shore} He walks a length L on the boat toward shore and then halts. Sn00py’s mass is ms, the mass of the boat is MB, and one can assume that there is no friction between the boat and the water, or drag from the air. SHORE r,» (J 1 fawn:- 3; waitmz'amzzt'af a) [5 points] \— \~r ~ What is the total buoyant force that the water must exert on the boat? You MUST justify your result - simPly quoting a correct result will not earn full credit.g t- _, . Or ‘3 BOW = stn 9A A ‘) km ‘ 1: \F3M$\ “ - 5(- FB7A$ 5' 5945’ 0A 5394’; 3 ' ' , _ 3" 0 ’> $145 = “:3 Q6 N0 VV‘t-CésL Nari , $0 Ffiw‘s M53 [4,“ ROW-“35” Same =0 {Lad- . t' b) [2 points] F8 1:: (Mg-+- MI‘ 1' wa‘wa 5 (.0433 What is the total horizontal force and the total vertical force acting on the system of Snoopy + boat? Phys 116 Prelim 1 Fall 2007 c) [18 points] How far is Snoopy from the shore when he halts (you may ignore the accelerations as he starts and stops). Express your results in terms of d, L, ms, Ma and any constants of nature; 3 Gib/ML gig/ca; arc to"? ’50 it - a; O g V$ 7. —- W V; “to SWOOP3\J V2} ) f¢Wu¢ ‘r-O &_ ) I I M “l “5 " “5“”: 3 VJ” 1’0 walk. $3“ L- DA ‘RML t; \ :L t .. 1::- -— J- L OJ>J> use a l "' V “l V: ‘ (H- “S/Me) M was saw.“ or» share rs M9": . - ' ’ ' ' ‘ L— Me. -Q :: —-- """"'""""" —- .. $3,?» “st A o + film ’ ‘3 L- NW riWr‘\ l W LL‘. ...
View Full Document

This note was uploaded on 09/09/2008 for the course PHYS 1116 taught by Professor Elser, v during the Spring '05 term at Cornell.

Page1 / 10

Prelim1_F07_Solutions - Plzys 116 Prelim 1 ' Fall 2007 Your...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online