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PHy317K Lang-Ritchie Spring01

PHy317K Lang-Ritchie Spring01 - n4" I KO r P" PHY...

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Unformatted text preview: n4"? I KO r P" PHY 317K October 2, 2001 Name:.J§»§si}..&1llmfefi: ...... .. Exam 1 —— Unique number 57820 Instructions: '- Take alternate seats if possible. 0 No notes, textbooks, calculators or similar aids are permitted.- 0 Use the scantron answer sheet to provide the answers. Follow exactly the directions how to mark it. Write your name, SSN, course number, unique number. Sign and date it. . Mark solutions for all problems. Mark your answer sheet using #2 pencil. Any errors in filling in your scantron sheet could result in your exam being discarded. N0 PARTIAL . CREDIT will be given! 0 Assume g = 10 rn/s2 only where it is explicitly stated so! 0 Unless you are ready to leave at least 5 minutes before 12:15 pm, please, stay in your seats until all answer sheets are collected exactly at 12:15 am. 0 Any questions you may have about the test have to be directed to the instructor —~ no conversations and/ or collaborative work are permitted. 0 The next page contains some equations and other information that may be useful on this exam. You may not ask questions about this sheet, however. 0 Use blank sides of the exam pages for notes and calculations. Some Equations for Exam 1 sin30° = 1/2; cos 30° = fl/2; sin60° = VIE/2; cos 60° = 1/2. For any function of the form x(t) = at", where n is an integer, $11;- : mum—1. ' The antiderivative of (t) = at” is 3:71:73“. The definite integral of f(t) from t1 to rig is j}? f(t)dt = F02) — F(t1), where F(t) is an antiderivative of f ' A A B = A333, + AyBy + Asz 2 AB cos 6. If a particle’s position is represented by r = r(t), _dr _d ' a"d_v_d2r V‘EE 3“ "dt‘dfl' For a constant acceleration a, 1 r(t) = ['0 + vot + Eat2 and v(t) = v0 + at where re and v0 are the position and velocity at time t = 0, respectively. Freely falling objects accelerate dewnwards with g =: 9.8 m/s2 = 32 ft/sz. Centripetal acceleration for uniform circular motion: a = 112/1“. Newton‘s Second Law: F = ma. Static friction: fs 5 lnaN; kinetic friction: fk = [MN (N = normal force). Answer the following questions: 1. A dart is thrown horizontally aimed toward the center point X of a target with initial (horizontal) velocity 10 m/s. After 0.2 s it hits the target at a point directly below the point X. How far from the point X does the dart strike the target? (Ignore any effect of air resistance and assume 9 2 10 III/S2.) a . 3: —Fag+34 vch + Bo - m (c) 0.1m E): "'li‘C|0)L0«35a+o+o e . m 2. A car traveling at 3'6 k‘m/ hour begins breaking and stops after 2 3. Assuming a constant deceleration (negative acceleration) during the breaking, how far-does the car travel during breaking? Recall 1 km = 1000 m and 1 hour = 60 min = 3600 s. (a) 5 m (I W x; x61» Vol: + it :Lta‘ m; 1000‘ no x l'bf @ 101” I ' M" “to 3:553 ' (c) 20 m _ v4: V0 + out . (d) 80 m — gsabwm' : "3 W5 (6) 160 m 'o: m + Lcha) Beer’s 3.: "5 m/SE “:43 003(3) + @05fo = so -10 : Io Refer to the following statement in each of the next three problems. The position in one dimension of an object is given as a. function of time by x(t) = 20 In — (2 m/s)t + (1 m/sz)t?. 3. The position of the object at t = 10 s is: (a) 22m 100).: 30 -— 200) #- FUOGJ (b) 210m : 20—30 Hod (c) 200m : 130 (d) ~100m ‘100 m 4. The acceleration of the _object at t = 10 s is: @2‘11/52 _ V4145): —?_+ 2+. (b) 3 m/s2 ’ (c) 4 m/s2 Mt) p E (d) -2 rn/s2 (e) 2t 5. . The scalar (or- “dot”) product A - B is equal to: The velocity of the object at t = 10 s is: (a) 0 m/s (b) 21 Ill/S . @18 m/S Vet):~a+ at (d) —1 m/s v00) 3 "8+ 20°) (6) 99 m/s : 20"2 ': r3 Refer to the following two vectors A,B in the next two questions: A =5i—3j; B=2i+3j. The symbols i and j denote the'unit vectors in the positive a; and y directions, reSpec- tively, of the rectangular (Cartesian) coordinate system. {53'33 ' (a) 15i (h) 0 (e) none of these : @1 (d) 54 IO ‘9 . The magnitude of the Vector A is: : l (b) 14 (e) none of these (a) «1—5 ' (c) 8 m Illgiifishea)? 5 \g: Q . A 2500 kg airplane moves in a straight flight at a constant speed speed of 500 kin/hr. The force of air friction is 2500 N. The net force from all sources on the plane is: (ED zero (b) 3000 N (c) 2500 N (d) 1000 N (e) 500 N . Two blocks are connected by a. string passing over a pulley. Masses of the blocks are 90 grams and 110 grams. Assuming that the string and pulley are massless, the magnitude of the acceleration of each block is: (a) 0.049 m/s2 (b) 0.020 m/s2 (c) 0.0093 m/s2 (d) 0.54 m/s2 .98 m/s2 I'oflN : {makgjcon QC; 3.3,; 0.: lmxsa : -cmN : 6-3 N outs 'FNET LIN I . fiwu i, 0,532}; {0.9 a; .95 5’ t *2; l. L, f I /_,_-- E E73 \{Boc} Refer to the following'situation in the next two prob e c's. A cannon, which is sitting on the ground in a region where the ground is perfectly flat and horizontal, fires a cannon ball into the air at an angle of 60 degrees with respect to the horizontal direction. Ignore air resistance. The initial speed of the cannon ball is 200 m/s. In your calculations take g = 10 m/sz. (Hint: \/§ = 1.73.) 10. What is approximately the time of flight of the ball (i.e., how long' is the cannon ball in the air before hitting the ground)? (a) 8.6 5 wt 2 I73 l: = 17-3 5 v.1: 200 since" @173 s (3:113 ~ next) is room's - D ' —- aooc ‘51} (c) 34.6 s or = Bocce.865) '(d) 12.5 s “fr-Y" + ‘9‘ _ : IT? "Us (8) 10.0 s (c 11. What horizontal distance approximately will the cannon ball travel before hitting the ground? 6 Vex : COS (a) 17.3 m _ l 34 6 m — .2006 5' 10011-315 d 3460m V 1730m 96'3U00X17.3j 3 [730 m 12. Two masses, m1 and 1712 are connected by a string as shown below. The leading mass ' is being tugged by a force F pointed along the direction of motion. Both masSes have a coefficient of kinetic fiiction WC with the table they are being dragged along. What is the acceleration of this system? Take m1 = 15 kg, 1112 = 5 kg, ,uk 2 0.25, g = 10 111/32. ,. a) 10 ni/s2 4 ‘ “N 2.5 111/52 k (C) 4 III/s2 N : (Boy-16) : 200 N (d) 5 III/s2 I 3 (e) 7.5 m/s2 rx: 90.253300 . : m N . M “at N r" 1‘ L P I t in F - : (BOBCO-D 136-50: 2063.) .8011QE‘A S 1 a: '1. mfg 5 <53 6 - ‘ ‘ H600 |L6 13. A crane operator Ioifiers a 4000—lb steel ball with a downward acceleration of 8 ft /52 The tension in the cable is: as s: s95 ' (a) 40001b (b) 1000 lb @30001b (d) 5000113 (e) dependent on the velocity of the ball 14. An object with mass 10 kg is dropped from a. height of 80 in. What is its speed upon impact with the ground? Take g = 10 m/s2. #33: — léttext‘?) £2; ’6 t: ‘45 (a) 10 m/s (b) 20 m/s (c) 30 m/s 40 m/s (e) 80 m/s xi: 0 - new) : ’LlO mg; 15. A 1,500 kg car moving on a flat road negotiates a curve whose radius is 80111. If the ' c0efiicient of static friction between tires and the dry pavement is 0.5, find the maximum ‘ speed the car can have without skidding. Take g = 10 m/s2? (a) m m/s 5+m+ic ¥p§c+icm :: can’tflileAGe‘ (“C3 (b) 5 m/s' . is= Ln,S)Ll500>UOJ 10 m/S : 7500 N a Va 6‘ 20 m/s - 7506 = new )L 55") 5 2 :96 (e) 40 131/3 16. A forward horizontal force of 5 N is used to pull a sled of mass 1 kg at a constant velocity on a frozen pond. The coefficient of kinetic friction is (take 9 = 10 Ill/S2): sh : FA {if #19,” (a) 0.05 0.5 (c) 0.1 (d) 1.0 (e) 0.2 5- 41: 5: man 17. An object is kicked with speed 20 m/s at t = 0 upward along an inclined plane, with 5 : (DUGXM) inclination of 30° with respect to horizontal. There is friction between the surface of the plane and the object with pk = 1 /\/3. Measured from its position at t = 0, how far will M: Q '5 the object move along the inclined plane before stepping? (Take g_ = 10 111/32.) (a) 0.5 m ' lk ; (XfflMJCiOKgo/s‘fi) 1 ' - Vox :: . " ' i f . (b) 1 m 33 x a": : Tsihscf = lair i. ‘ . l A x i J i : (C) 5 m W5 I .1" i ' i l i g a ,4“ I, j ax ax V04: BQfInSO :\Q/m(5 I its- act-£4. “3ch I 0 _ if, . \ t: QE— '3 26 , of m T’ a: 1!“ 7,5(‘0’ t mise' - y 10 18. A airplane is flying in a circle with a constant speed. If the radius of the circle is 600 m - 036 a and the-centripetal acceleration is 6 m/s2, approximately how long does it take the tc airplane to gocompletely around the circle one time? (Recall 11' z: 3.14.) .2133 (a)13.ls‘~ 3V ' _ ’- Jc (b) 93.3 s M C ‘ (2“ X600) c me; = 600 l (C) s — IBOO 1T UL __ “W‘VL—x _ %OQ ‘ “ g a 00 gm am? @ 62.8 s I ' 6e ms ‘3 e e O .30 r r} - I —\ A 0 / ' _ . . s: '7 O “" 3‘ 3:0, m 1 ‘ 6‘20? 5- \l0 ’10 Z L“ n O 4; : 5 = Cl; ; 1‘ 2m '3 E. g: a; k . I“ a r. 1.10 2: 04-20(3) + epdéléll ‘3‘: —5m/S 0= 2-.0' 45* 3510 {figs W 19. A ball of mass m is being twirled around in a horizontal plane by a young child. The ball is at the end of a string of length R and is moving with constant speed 1:. At the point indicated by AA, the string breaks, and the ball goes flying ofi‘ in some direction. The figure below shows 4 possible trajectories the now-unfettered ball could take the instant after the string breaks. Which of these trajectories does the ball follow? (a) A @ B (C) C (d) D (e) depends upon the Speed 1; 20. A block of m1 = 3 kg is resting on a table. The block is connected by a light, flexible string over a light, frictionless pulley to a mass m2 = 1.5 kg that can fall freely. If the 1.5 kg mass is falling at constant velocity and if there is a coefficient of kinetic friction ,uk between m1 and the table, compute the coefficient pk from the information given. Use 9 = 9.8 III/82 in any calculations. (a) 0 1 ‘Fk: FA (1)) 10 (c) -10 gamma-w) (d) 2'0 (a s) FA: (LS) ‘ L151 2) : $3131») AL: (3.5 21. Which version of this exam are you working on? (a) white pages photocopy @ colored pages photoc0py Test?) 7 Answer the 20 questions: 1. Density is: a 333.13? (b) a vector (:2) a measure of the weight of a fluid (d) always larger fer a'solid than a liquid (3) none of these '2. A Ill-tube initially contains a liquid of density 4g/cm3. A diflerent liquid of density ' 1 g/cm3 is then peured into one arm of the Untu‘be. The two liquiliS do not mix. If the second liquid fills a. column of height 8 cm in the arm Of the Uétube into which it was poured, how far does the first liquid rise in the Other arm of the U-tube with respect to its initial “light? The yrescw‘e at A M B (8 05cm Mus-t in. flu: {Au-‘- 2: gm 1‘ i. 9 = 4'9‘ “1) (a) 4cm ‘1: i a»- {e)‘ none of these 3. A toy boat floating in pure wate; (fiensity llngem3) a. volumeof 1 liter of water. Ifthe same toy boatis to a. tank filled with a liquid of density 2.0g/cm3, what will be the weight of the liquid displaced by the toy boat? {Hint recall 1 liter = 1000cm3and1kg=10003,andofoouraeW=mg.) ‘ Mtg ' (a) 1 N weight. of glaring-X, “Q1434 * MW: Log/4.2 1.0km; lrfi/las b 5N @ON does M dingo... l iii-mu- = M3 on; = (0’3 w“: d-)20N WM“ = w, , (eJ40N 9 in V 3L _ l = la’xlo"aa elou \ 4. Water flows through a square pipe of varying ewes-section. The pipe runs horizontally, so the water remains at constant height. The velocity of flow is 8 m/s at a point where the pipe’s side-dimensions are 1 At a point where the pipe’s side are 2 cm, the velocity is: 4F” _ . ‘M The coo-tumult fling-clan ; 5; _ (a) 16 “1/3 I 7 my Av “are (b fwflffl‘. 1 ' ? = faulth 2;: I”. 2 m/s «1r: 2 w/s‘ ( 0.5 m/s _——__. '(e) 0.25 m/s 9. The maxinium velocity of the masssis: (a) 0-1 m/s Finn The musevw-L‘wn u'l «away 10. After the mess is released, how much time will have elapsed when the mass first reaches . the positibn of zero displacement {i.e., Where the is (a) {3.255 The Pas-non ‘11:) ',g aw.“ la)! (b) 3E 5 . z: = L a (c) % 3 arm at», w: (Lu-t) (Lo) m,( if) Hm: 1 in = % (d) %S TH} 54495113: 0 {~31 who“ it 2 7L ' Es ‘t=‘£: a 11. A mass attached to a spring oscillates at a particular fi-equency. Which of the following changes would result in a. higher fi'equenLy of oscillation? _ ' s k a Use a. larger mass. .[. = _ E @ Use a smaller mass. c) Use a spring which has a smaller spring constant. (:1) Increase the amplitude of the oscillation. (e) noue of the above 12. What is the wavelength of a transverse travelling wave with a. velocity of 50 m/s and a frequency of 5 Hz? _ tn ar- mzso-Dm ‘U’=+A='> A*T9T: 1a.?- (b) 50.0m 910.011; 5.0111 (e) 29m 50.0 m 17. When fistening to tuningforks offrequenda 4401-12 and 448 Hz, one hears the following number of beats per second: (a) 444 41‘ of beats/m «a Hui] : 4H- 479.: e (W333 @3 d)4 (e) 2 18. An ideal gas occupies a. IG-fiter container. At temperature T = 27 °C, the pressure inside this container is 3 mm. lithe gas is heated by 100 °C, the new pressure is: ’4etm get (an; '. 19V: VIE—r (mam w“- (c) Satin T : 273947: hakfi €509 Kw (d)12'atm z ‘5 9:": (8) 20am: P 3 a“ a h 3” z 4a“ . -——_.._ 19. The specific heat of an object is: (a) the amount of heat energy to. melt one gram of the substance (1)) the amount of heat energ- per unit m emitted by burning the substance (c) the amount of heat energy per unit mass needed to raise its temperature from its freezing point to its boiling point (d the temperature of the object divided by its mass _ me °f these The amt a") hat energy [ma- umit Mac: u was its tenure-M are by IK. 20. A heat engine operates between reservoirs which have temperatures of 300 K and 500 K. What is the maximum efficiency of this engine? T... 3,. I Maxim-M eff-(tau? -= L 75::- [--;—:. =_ Egg a? (c) 0.6 (d) 0.8 (e) none ofth‘es'e PHY 317K November 6, 2001 Name:.§l._m..€7iillman ............ .. Exam 2 — Unique number 57820 Instructions: 0 Take alternate seats if possible. a N 0 notes, textbooks, calculators or similar aids are permitted. 0 Use the scantron answer sheet to provide the answers. Follow exactly the directions how to mark it. Write your name, SSN, course number, unique number. Sign and date it. Mark solutions for all problems. Mark your answer sheet using #2 pencil. NO PARTIAL CREDIT will be given! 0 Assume g = 10 m/s2 only where it is explicitly stated so! - Unless you are ready to leave at least 15 minutes before 12:15 pm, please, stay in your seats until all answer sheets are collected exactly at 12:15 pm. a Any questions you may have about the test have to be directed to the instructor — no conversations and / or collaborative work are permitted. a The next page contains some equations and other information that may be useful on this exam. You may not ask questions about this sheet, however. 0 Use blank sides of the exam pages for notes and calculations. Some Equations for Exam 2 , sin 30° 2 1/2; cos 30° = fi/2; sin 60° = «32; cos 60° 2 1/2. The work W done by a force F: W = [if F 1 ds, where z' and f represent the initial and final positions, respectively, of the particle. The instantaneous power: P = d—dvg. - - . m l 2 The kinetic energy. K M imv . The work—energy theorem: Wnet 2 AK. The change in potential energy U and the work W done by a conservative force are related by: AU 2 —W. The potential energy U of a system is AU = Uf — U,- = —W = — if F($)d:c. Gravitational potential energy AU 2 mg(yf — ya) = mgAy. 2 2 . Force due to a spring: F5 = «km. Elastic potential energy AU = ékx} — éka: Momentum: p = mv. In an isolated system where the forces are conservative, U + K = E’ = constant. When the net external force acting on a system is zero P = const. Position of the center of mass: ram 2 fiflmiri, Where M =: 2mg. . For a solid object of mass M, ram = fi frdm. The impulse J of a force F acting on a particle during a time interval from t1 to 152 is J = f? th. The impulse is equal to the change in the momentum of the particle: J = pfinal "‘ pinitial : Ap- For a one—dimensional elastic collision: _m . _2“12_ . _ 2_im_ . _m_2"_m.i. . Ulf _ mi+mzvlt + mi+m2 v21 vzf _ mfl—mzljl2 + m1+m2 02“ For one-dimensional motion and completely inelastic collision of two bodies: mlvl + m2U2 = (m1 + m2)V. Angular velocity: in 2 d3? Angular acceleration: a = fi—‘g’. For a constant angular acceleration, -— w = we + at, where mg is the angular velocity at t m 0, — 915 = qfig + wot + éatz, where 450 is the angular displacement at t = 0. For circular motion, tangential acceleration: GT 2 or. Radial acceler.: a3 = 122/?" m w2r. Rotational inertia, or moment of inertia: I 2 f rzdm. — for a solid sphere about any diameter: I = §MR2 — for a solid cylinder about the cylinder axis: I = éM’R2 — for a hoop (a cylindrical shell) about the cylinder axis: I = M R2 0 Torque: 7'" I r x F, so 7' = TFSiDG. For a rigid body7 ‘7' = Id. 0 Angular momentum: L = r x p. L = va sinqfi = rpi : 1"va = up : 71mm In special cases L : Iclr'. For an external torque, 7" = %. o For rota-ting bodies is AK = %Iw% w 51w? Answer the following questions: 1. A man pushes an SO-N crate a distance of 5.0 m upward along a frictionless slope that makes an angle of 30° with the horizontal. The force he exerts is parallel to the Slope. If the speed of the crate is constant7 the work done by the man is: (a) 61 J (b) 140 J @200 J (d) 240 J (e) 400 J 5m h h= 55:11.90" 0 2 L50, Us: CgGNJ(£.SmJ-_ 2. A mass m at the end of a string moves in a vertical circle; that is7 the circle lies in a plane which is vertical. The bottom of the circle is at y r 0. At the bottom of the circle the kinetic energy of the mass is just barely enough to get it up over the top of the are i that is, the mass just barely has enough KE to do a “loop-the—loop”. What is the tension in the string when the mass is at the bottom of the circle? Hint: Use conservation of energy. Also, what provides the centripetal acceleration? U=? , K=? (a) mg g, -n _ NR / \ (b) 2mg m .- "iv—a my} (c) 3mg ,' I‘ T_ 9' r. T‘mg 3 V2 d) 4mg T J i} a _ if? 5mg rub/Ti}. // lémv : "Scar 3 \ i , Tami}: gm? \i“\uzo,jK=? ‘/' l’a 9W2 = Ewgr “ "” r0 1 T: s I‘ A r: :33- m9 "3 3. A particle of 1 kg mass is moving with constant velocity in the positive direction along the sis—axis and has kinetic energy of 8 J. Another particle of 2 kg mass is moving with constant velocity in the negative direction along the .r—axis and has kinetic energy of 4 J. What is the total momentum of this system of two particles? (a) l kg-m/S 3‘: (,3 g: $2.20? = (2,) Va (b) 2 kg-m/s a“: Z © q (c) —2 kg-m/s 5c 2 v: “‘2 mfg ' u‘ —1 kg-m/s if: V: Li (M g, (be) r t‘ZJCZ Refer to the following description in the following two problems: A student with mass 80 kg is standing on an initially stationary cart of mass 10 kg. The instructor, who weighs 75 kg, throws a medicine bali, whose mass is 10 kg, with velocity of 5 m/s. The student on the cart catches the ball. There is no friction. 4. Suppose the instructor is standing rigidly planted to the floor. With what speed will the student1 the ball, and the cart be moving after catching the ball ? ((1: mjs “6303) +6: C Io + 90 Ho) Vf - 111 S @0'5 “1/5 - 5o : Isaac (d) 1.0 m/s ‘ (e) 0.0 m/s VF Bus {fl/S V: 2. 7. A golf ball of mass m is hit by a golf club so that the ball leaves he tee with speed v. The club is in contact with the ball for time T. The average force on the club on the ball during the time T is: (($771va 3:. 4-,- : mo ((3) (l/2)mv2T F' AT = “W -0 (d) Wig/(2T) F 2 .0221 (e) mTZ/(2U) T _ ’33 ) @191 in 8. Sand is dropped straight down onto a moving conveyor belt at the rate of 3.0 kg/s. If friction in the bearings can be ignored, the power that must be expended to keep the belt moving at 2.0 m/s is a)l.5W b)3.0W @nw d)9.0W e)12W 9. If a wheel1 turning at a constant rate, completes 100 revolutions in 10 5, its angular velocity is about: (a) 0.17? rad/s use ray 2” [mg :- fl—KZOOH ma; ZOfl fold/S (b) 0.27: rad/s {as HQV MS (c) 317T rad/s (d) 10w rad/s 207T rad/s 10. The angular velocity of a rotating wheel increases 2 revolutions per second every minute. The angular acceleration, in rad/s2, of this wheel is: (a) 4%? A c 3% 2 ra/Wl as? 2 arm rad/S (b) 271' ‘9 1 5 wet! (c) 1/30 rm mils ‘ 21r/30 pi : 2;):— (e) 471' = 32%,; 11. Three identical objects of mass m are fastened to a massless rod of length L as shown. The rotational inertia about one end of the rod of this array is: a) mfg/4 ‘0' b) ml?2 H) c) 3mL2/2 ®5mL2/4 L/Z L/2 e) 3mL2 i _... P. I: (ME) 1‘ mate a = mct) + L3 : fim LE 12. A disk rotates initially with angular vel...
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