practice+2a+solutions - 544mg Physics 140 Winter 2010...

Unformatted text preview: 544mg Physics 140, Winter 2010 Second Midterm Exam: March 11,2010 Physics Department, University of Michigan FORM 1 Please print your name: Your DISCUSSION SECTION or INSTRUCTOR: INSTRUCTIONS AND INFORMATION 1. Fill in YOUR NAME, SECTION NUMBER and EXAM FORM NUMBER on the scantron. 2. RECORD YOUR ANSWERS ON THE SCANTRON USING A #2 PENCIL. Prof. Len Sander l2 14, 15 Mr- Tim Cohen 3. Turn in this exam copy with your scantron answer sheet. 4. This is a 90-minute, closed book exam. You may use two 3” x 5” cards on which you have your favorite equations. You also may use a calculator but please do not share calculators. 5. All cell phones and other communication devices must be shut off and out of sight. 6 There are altogether 20 multiple choice questions. All questions are of equal value. 7. Equations that you may find useful: Sf = s + vot + 1/2 a t2 0f = 9m + wt + 1/2 0c t2 Rod, axis through one end I =l/3ML2 Vf = v0 + at cof= (00 + 0L t Rod, axis through center: I = 1/ 12ML2 arad = vz/r = r0)2 vt = r 0), at = r on Solid sphere: I = 2/5 MR2 F= ma 1' = r x F = dL/dt=1a Hollow sphere: I = 2/3 MR2 p = mv L = r x p =10) Solid cylinder: I = 1/2 MR2 w = F.s w = 'c (92 — 91) K Hollow cylinder I = 1/2M(R.2+R22) F = —VU Fk = MN Hoop: I = MR2 Frad = mVZ/r Uspring = 1/2 kx2 Impulse E J = lF.dt = Ap w = AK 1 2,10,n + MR2 P = AW/At = F.v AK + AU = Wm Krm = 1/. Icoz v1,f = m1 —m2 vlin + 2m2 Vzm V2] 2 2m] V1 + m2 —M, V2.11: . .' , ,in ml+m2 m1+m2 m,+m2 m1+m2 Problem 1: The angular momentum of a system is constant when: A. the total kinetic energy is constant. B. no net external force acts on the system. C. the linear momentum and the energy are constant. no external torque acts on the system. E. the moment of inertia is constant. Problem 2: An electric fan is turned off, and its angular velocity decreases uniformly from 500 rev/min to 200 rev/min in 4.0 3. How many revolutions has the fan made during those 4.0 s? A. 11.7 revs C. 43.6 revs D. 75.0 revs E. 116.5 revs (a. — $790M”— W Q1/2260 ~011- 270Z: ’24sz M :7005’04/3; I1: 9 a n g- 54311-1;411 : 53253.9 - {dig/é: /4é.éra/ fa 6 0 7' Problem 3: A graph in figure shows potential energy versus position for a particle moving in a straight line (along the X-axis). From this curve and for the region displayed, we deduce that: U(X) A. This could not represent an actual physical situation since the drawing shows the potential energy going negative, which is not physically realizable. B. There are three positions of stable equilibrium. F: - ‘14-} «VIZ/flu" 0/X ,/ 194m 15 XL @The force on the particle would be strongest when the particle is near the origin. 1&4» [fizz D. The force on the particle would be greatest when the particle is near point P. /‘. 7 N06: /jz‘ ., ,1, . E. For a given value of x, the particle can have a total energy that lies either above or below the value given by the curve at that point. Problem 4: A 7.0-kg stone is subject to a variable force given by the equation F(x) = 6.0N—(2.ON/m)x+(6.ON/m2 )xz. If the stone is initially at rest at the origin, find its speed when it has moved 9.0 m. A. 11.6 m/s B. 20.2 m/s C. 36.7 m/s D. 42.3 m/s E. 51.5 m/s Cl ' 2 . W: AK => jaw. ._ gmpo 9 (7 ”z, . - J . f/é‘v—zx¢éf)dx : 51/ ~J/+/¢$”3’:/43/ ’5 z X; 2’” 0 7;: gut/37 = JO'QW/S €33 /’___——_-J Problem 5: A ball of mass m is suspended from a string of length R. The ball is set into freely swinging circular motion in a vertical plane. The centripetal acceleration of the ball at the top of the circle is 8g. What is the centripetal acceleration of the ball at the bottom of the circle? A. 24g B. 16g C.14g E.10g R L ” é/Mli/aaejmgg :Zl—mzép/A» Z L :djp'l‘l/C’p g/Z R WM“.— 62/ +177? J 1 d a" a .2 fl _ /2’ 1,5414% 72 r ii Problem 6: A long, thin bar of length L and cross-sectional area A has its long axis parallel to the x-axis as shown. If the density varies along the length of the rod as p(x) = orxn where 0L is a positive constant and n is an integer, where along the x-axis is the center of mass of the rod? 4x Problem 7: A 58 kg runner is standing on the outer edge of a horizontal turntable mounted on a frictionless axis through its center. The turntable has a radius of 2.9 m and moment of inertia 500.0 kgm2 and is currently at rest. The runner starts his run along the outer edge and is observed to run with a speed, relative to the earth, of 5.6 m/s. If he runs for 60 see, how many revolutions does the turntable make? A. 18.0 revs B. 15.4 revs C. 12.6 revs D. 9.2 revs E. 7.8 revs ,1} =7 O: meg-+1; :7 CC) __, ,_ HRU' : .. b—d’x 2'915—-é : __ /r37<lnfl’~(/5 I 500 he; 42/2” I744 mad; drflcjméfi oé’raC/{m / w/M/M 5): Cut = I.izf4x60=HI/3m/( [/3 rap! 2 . —/apreu§ :77- // Problem 8: The force on a particle 13 given as F: 2 x j where j is a unit vector along the y- direction. The particle travels on a square“loop in a clockwise direction starting from the origin. How much work 1S done on the particle by the force Eduring one complete trip around the square? (5,5) ‘ . g L A ‘ ‘ jflru IS Vawglé au/ pZN'éaZl/é/ a5?) / 7 4W5 I‘l/Qré I11 mi .102 ”111/ IX 5’ x= = 0 I w. = Imp? =0 +7 a) 0 Z s N /) . Wm _. F (1 = 2 ’4 [[X L = O buéfi I :L (0,0) (5,0) x .4 /~ / j "A N ,9 h, A. —250J B. -l80J C. OJ D. 180.] E. 250.] 5’ f Physics 140, Winter 2010, Midterm 2 Problem 9: A 12.0-kg block is sliding on a rough, horizontal surface at 6 m/s and eventually stops due to friction. The coefficient of kinetic friction between the rock and the surface is 0.3. What average power is produced by friction as the rock stops? A. 47W B. 62W C. 84W D.lO6W E.216W w 4A? => UALMJA:0-Z*ML:7 d,;j:gL/7 WC "’P—Zfi pg.— wznn aJWM‘Z/ 5L0" rx’ X’- x 2: (44‘ ft: fa div-:07 - (73 /Z h? 3 Wm]; mafl/i‘flg‘m/‘a <9 gawzfiZafiuzmllw 6‘) 0 I] m v 6: 4:04.- 1471—55-1” /:m1.a .=/2y2.(7)l/: 35“ ZfN :2) M]: :2fo 6‘IZSZ/é‘j ' I) jt’ 4- w: 24 _ MVr/OéJ ' z? ‘ - m 6 Problem 10: (Zufilzwjfl7/fiuw: 4 Block A with mass mA = 2.0 kg and block B with mass m; = 3.0 kg are forced together, compressing a spring between them. The system is released from rest on a level, frictionless surface. The spring, which has the spring constant k = 250 N/m and negligible mass, is not fastened to either block and drops to the surface after it has expanded. If block B acquires a speed of 2.0 m/s, by how much was the spring compressed from its equilibrium position? )4.» mmfizm %- 0,390" Physics 140, Winter 2010, Midterm 2 Problem 11: Two identical masses are released from rest in a smooth hemispherical bowl of radius R = 1.2 m, from the positions shown in figure. You can ignore friction between the masses and the surface of the bowl. If they stick together when they collide, how high above the bottom of the bowl will the masses go after colliding? Problem 12: A ball with mass M moving horizontally at 5 m/s, collides elastically with a block with mass 3M that is initially hanging at rest from the ceiling on the end of a 0.5 m- long thin wire of negligible mass. Find the maximum angle 0 through which the block swings after it is hit. _ wan . 20.12/67 W “”7311 V... * yea 2'" / Problem 13: A box is sliding with a speed of 4.0 m/s on a horizontal surface when, at point P, it encounters a rough section. On the rough section, the coefficient of friction is not constant, but starts with uk = 0.0 at P and increases linearly with distance past P, reaching a value of uk = 0.30 at 6 meters past point P. How far past point P does the box slide before stopping? A 2.8m B. 3.6m C48m U’ r2” im fl>fl _____ ifiifi U ng= Al< “P at a Z. 0 Wife???” 1 V a Z a 1 ”/r l MVZ :7 0495/33” ; X, o 0g ,9; = ._ «it—‘— = 5 7/07; "‘ ' 7 a7 Problem 14: W i In figure, the pulley (a uniform solid disk) has radius R = 0.2 m and mass M = 0.8 kg. The rope does not slip over the pulley and the pulley spins on a frictionless axle. Block A has mass mA = 2 kg and block B has mass m; = 5 kg. The tabletop is frictionless. With what acceleration is block B descending? Physics 140, Winter 2010, Midterm 2 Problem 15: A hollow, thin- walled sphere of mass 12 kg and radius 0.5 m is rotating about an axle through its center. The angle (in radians) through which it turns as a function of time (in seconds) 1s given by 0(t) — 1 5t2 + 0. St“. At the time of 3.0 5, what IS its angular momentum? A. 94.5kgm/s B. 126 kgm/s C. 148 kng/s D. 172 kng/s E. 189 kng/s 2 J1. L:I,(,J ”90891.1 7L1”. "T“2 EHQifflZxQfi) _ 02’3”“L ’ W” d5 MHZ +4105,§3_3£;‘2; 1 w/f-35):3x3111w271: 7+.:§‘9 53 “(/5 L: ij; 92% 6,3; 416 fim/S :23 W Problem 16: A mass m= 50 kg IS attached to a light string which Is wrapped around a cylindrical spool of radius R — 0.1 m and moment of inertia I — 4 0 kg.2.m The spool is suspended from the ceiling and the mass is released from rest a distance h— — 5 m above the floor. How long does it take for the mass to hit the floor? h " Tin mg—mq="2 mew”? A 14s B175 C22s D26s @ W O .8 L _. 3. 451-10% I)“ _P:L O+LOJVV _L ‘1 7 If: 23‘ , “2"? = 303424, Xi: Z—a‘é 2‘ a [:04 \ Problem 17: A 5 kg package slides down a long ramp that is inclined at 120 below the horizontal. The coefficient of kinetic friction between the package and the ramp is uk=0.31. If the package has a speed of 2.20 m/s at the top of the ramp, what is its speed after sliding 1.50 m down the ramp? A. 4.46 m/s N B. 2.46 m/s C. 2.03 m/s D. 1.43 m/s E. Stops before / covering 1.5 m . 7;. _ 3 on the incline \AJWC‘ b 14* 43 L; L L Z k —- L/M mev«A:émlé"£/W‘/IL+O- 07, W’/ I J g ‘ é L/f L 5”, — '5 “L szr mu+2jAme—kag/Mme Problem 18: A block of mass m = 2 kg travels on a horizontal surface. There‘is a coefficient of kinetic friction pk = 0.25 between the block and the surface. The block has a speed v = 4 m/s when it reaches x = 0 where it encounters a horizontal spring. The block compresses the spring, momentarily stops, and then recoils and travels in the opposite direction. When it reaches x = 0 on its return trip, it stops. What is the spring constant k of the spring? ( A. 6.0 N/m ) B. 10.6 N/m C. 18.2 N/m D. 26.4 N/rn E. 34.5 N/m W ,:A14+AUS x) “/1ng (2x) = O~Zimvl+O-O 414’ 92x {:5 M [4A1 0194/1”th M ééég ’7Lrtoi/cfg Zyéi . f 0 ””1 {X m. [A h/ 5 fling’W fl: 3 n? J C “70 ? {Abba/v fam’m M X m /4« W; A“! 14/4?” flu ,3 /4 WA‘W ' 9ng 9x 0-25‘x 7-9 ’ 497V/Jvf/V/ % 60”}? 7 = 5 . /l/91J et/céfixzf % 420/4? /A‘({‘m ZZQK AZOOZ ”hated/41L“ X 0 X 4“,.ij = 0— gay. #520 ® L- m‘f— 21%; :2x42 _ 2wmwt 60%. X Problem 19: A meter stick with mass M = 0.2 kg is pivoted at its end. Neglect the friction at the pivot. If the meter stick is released from rest in a horizontal position, what is its angular velocity when it passes the vertical position? M,L m [Wryfjéu mecjéuic'z/ aha/fl H [i 01 71/ K ' Mam 4/ A i: ,L. t 14 Ce «UV 2 :: z , 2 II N) A. : a l .TCJ (,H H 1’ j a + O L 7‘ 2. __~ 1 z :i Ame/wk! fit/Otpz / [/1 611% [44 J: 3 flL 'I H /‘1 A =1 1 ”L260; :3 9 J 2 iii?) Co : t§€ ; V 317; ., 5;9rl{7; A. 2.5 rad/s B. 5.4 rad/s C. 7.7 rad/s D. 8.9 rad/s E. 10.8 rad/s Problem 20: The object shown in figure is pivoted at 0 about an axis perpendicular to the plane of the page. Five forces act on it in the directions shown: FA = 10N at point A that is 8.0 m from 0; FB = 16N at point B that is 4.0 m from 0; PC = 19N at point C that is 3.0 m from 0; Pp = 12 N at point D that is 5.0 rn from O; and FE = 15N at point 0. What is the net torque about 0. Take the direction of the torque as positive if it is pointing out of the page towards you. a T ’ 3% 493+» 95’ = Jae/v». ”JV/730‘;- F. : ZI‘x/é 092. 700: 6400”,. mt /fl/Dagg 7 .— 3.19.-.200:/a5?2€’1//>afie C 0 (D: 5x /2 Who at 0 Z =0xKaO E A. —22.4 Nm B. -7.4 Nm C. 5.8 Nm E. 22.4 Nm 3.1: Z? r 5w +(—e9 H915: mm. 1.3/4, 3, C ' z. a; W/ /9“ W‘zfid/ow e. @ / 7“ ...
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