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WB_Solution_Ch07 - Dynamics 111 Motion in a Circle 7.1...

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Unformatted text preview: Dynamics 111: Motion in a Circle 7.1 Uniform Circular Motion 7.2 Velocity and Acceleration in Uniform Circular Motion 1. a. The crankshaft in your car rotates at 3000 rpm. What is the frequency in revolutions per second? 3000 rev X in?“ : 5-0 1-5:! [min 605 5 b. A record turntable rotates at 33.3 rpm. What is the period in seconds? 33.?2‘: x ‘62: g 05.5-5- red 2. The figure shows three points on a steadily rotating wheel. a. Draw the velocity vectors at each of the three points. b. Rank in order, from largest to smallest, the angular velocities (01, (02, and (03 of these points. Order: outage); Explanation: Eu)“ Psmfi- ”traverses 'HM. Soc-NW. 0M5”. "" ‘H‘t ”W'- ‘tTWL . All pom-h 0A the dual reel-wk ”Kl-k the Same ?£T-'O&- c. Rank in order, from largest to smallest, the speeds v1, v2, and V3 of these points. Order: - V3 § 0, r. 0:. Explanation: UL“ \" w ‘ c9613 '5 is JPN-HM”— cw! any ‘PTDM *Hu. .- CMCis o-R‘ he‘l‘a'fioa QMQ So Mots 0k firm-rec 3922:? film» posit: l anti 2-! “Jud-x our-L rat ((-kt Some. 1" gig each o'HnfiJ“ 7_1 7-2 CHAPTER 7 - Dynamics III: Motion in aCirclc 3. Below are two angular position-versus—time graphs. For each, draw the corresponding angular velocity-versus-time graph directly below it. 9 A, a: a. a b. ON: a w L_*———"‘. 0 . I u—__ 3 . . .' 4. Below are two angular velocity-versus-time graphs. For each, draw the corresponding angular position-versus—time graph directly below it. Assume 60 = 0 rad. a. co b. ca 1 l Q: Cb 5. A particle in circular motion rotates clockwise at 4 radr’s for 2 s, then counterclockwise at 2 radfs for 4 s. The time required to change direction is negligible. Graph the angular velocity and the angular position, assuming 60 = 0 rad. 6. A particle rotates in a circle with or = 8 mfsz. What is a, if a. The radius is doubled without changing the angular velocity? : ”’1 3' b. The radius is doubled without changing the particle’s speed? Misl— c. The angular velocity is doubled without changing the particle’s radius? M Dynamics III: Motion in aCircle - CHAPTER 7 7-3 7.3 Dynamics of Uniform Circular Motion 7. The figure shows a top view of a plastic tube that is fixed on a horizontal table top. A marble is shot into the tube at A. Sketch the marble’s trajectory after it leaves the tube at B. 'Tl‘" mwhla {pn'l'lvlmes in ax sfia'fiék l" (in: Top View of horizontal tube one revolution, a very sharp knife is used to cut the string at the instant when the ball is at its lowest point. Sketch the subsequent trajectory of the ball until it hits the ground. Film- ngc'l'oh is '{JNo-lbol‘s c. , lilac. fine-'1‘ oi“ at Horia—onl'allY lauackeaL produ‘hie. 8. A ball swings in a vertical circle on a string. During / 9. The figures are a bird’s-eye view of particles moving in horizontal circles on a table top. All are moving at the same speed. Rank in order. from largest to smallest, the tensions T] to T4. v v v m v 2m ®m gm Order: T3>Tl5Tfi7 ‘1 Explanation: '2. r Smiler P. Case "l is He. same at: Case. l inseam \oo'l’la HA9. Mas: omfl Hm magma. we— afloat-rude 7-4 CHAPTER 7 . Dynamics 111: Motion inaCircle 10. A ball on a string moves in a vertical circle. When the ball is at its lowest ‘\ point, is the tension in the string greater than, less than, or equal to the ball’s weight? Explain. (You may want to include a free-body diagram as part of your explanation.) R'l din lowes'l‘ poi-‘4’, 'H-I— aceelerd'han [r MParsr& . .5 Tina—s, 'HAQ +£ASI'OA magi" lat fil‘fia‘i‘r 'HAAIA ‘H'uL wthbh‘l' $ar+lu and {-ora. in lat use-«Hui. 8L 1 1. A marble rolls around the inside of a cone. Draw a free-body diagram of the marble when it is on the left side of the cone and a free-body diagram of the marble when it is on the right side of the cone. ~—-) \ r“: {- w \- On left side On right side 12. A jet airplane is flying on a level course at constant velocity. a. What is the net force on the plane? Fuel-3 0 b. Draw a picture and identify all of the forces acting on the plane. Fi-H iii-Hi : ml F'Harufi iF—Hnr-Asfl : \ F’“‘$l (A “33 '63 c. Airplanes bank when they turn. Explain why, in terms of forces and physical laws. Hint: What would a free—body diagram look like to an observer behind the plane? When HM. {pl-4M» banks, in“, 'Mcludes as homes “hi Componed‘. The. Moriwinl Componen'i' OJ" EH- ?row‘m a. rqu'tauv viva-aural For“. “teal-2A +0 cams; “Hm. flea-u. +0 Jrurn. Fromloehfral 'l‘LLPl,&n¢'- Iu'l'kis Cast, ‘Ipltgpi > lwi ,W- _: 'H'tt “liar-m K: in OK “0““ “fil -—> F'W‘ dtrufiOA 6* w Dynamics III: Motion in a Circle - CHA PTER 7 7'5 7.4 Circular Orbits 13. The earth has seasons because the axis of the earth’s M'Wbml PM" rotation is tilted 23° away from a line perpendicular \ to the plane of the earth’s orbit. You can see this in f- - - - - ----- 3:93 ad- Find- the figure, which shows the edge of the earth’s orbit around the sun. For both positions of the earth, Nonhem winter Northem slimmer draw a force vector to show the net force acting on 5°”th mm“ 8mm“ mm the earth or, if appropriate, write F = 0. 14. A small projectile is launched parallel to the ground at height h = 1 m with sufficient speed to orbit a completely smooth, airless planet. A bug rides in a small hole inside the projectile. Is the bug weightless? Explain. Tim: gang is Wfilslfd—lfisx‘ Fm the range 'ikm‘fi'l‘i's lvx 'Pv‘eeizaii -wi‘iirti‘n Proéec'itile , The leaf)" Sfitl bug‘s: weiak'i' 9'? U5: Muflfl. 7.5 Fictitious Forces and Apparent Weight 15. A stunt plane does a series of vertical loop-the-loops. At what point in the circle does the pilot feel the heaviest? Explain. Include a free-body diagram with your explanation. ’TL‘L P'Ito‘k h‘XS iAtAUiQSQ' R‘i— 'Hm-L bO'H'DM cyp- +L~¢L MCI-.1 (Oi-0‘9 . M 'HMST Po'm‘i' “at normal Rafa. on 'HNL PiiOT I5 aorta-“ST, AS is TLn. +941: ’11". " h . OtFrqren 5 Amy .F"“T “+09. E“ ‘00 M' .5 4- w W Tilus din-$756 063wa 4.4»). ?"\o't' a moving) «4' compfltalt. 8?},ch ‘fixrowakflvdi- 16. A roller-coaster car goes around the inside of a loop-the-loOp. Check the statement that is true when the car is at the highest point and at the lowest point in the loop. Highest Lowest The apparent weight wapp is always less than w The apparent weight wapp is always equal to w The apparent weight wapp is always greater than w — L wan, could be less than, equal to, or greater than w L [At-{kn intakes‘i' 93-“, +1qu answer-Ache-afis' mph flagged oi-Hu Cal”. 7-6 CHAPTER 7 - Dynamics 111: Motion in a Circle 17. You can swing a ball on a string in a vertical circle if you swing it fast enough. a. Draw two free-body diagrams of the ball at the top of the circle. On the left, show the ball when it is going around the circle very fast. On the tight, show the ball as it goes around the circle more slowly. J 3,1“ .e.‘ Us ”1' Very fast Slower b. As you continue slowing the swing, there comes a frequency at which the string goes slack and the ball doesn’t make it to the top of the circle. What condition must be satisfied for the ball to be able to complete the full circle? T? +1 WU}: :- Muir . Tin. Minimum clown WN'D( fart—n. 'LS H"- WLSMI “1 r '1. '1- __ , _._. i ’0 ma 1': mt.“ LJMIA 0(— “Min '— S/r— ”Jam" 9/!— 0. Suppose the ball has the smallest possible frequency that allows it to go all the way around the circle. What is the tension in the string when the ball is at the highest point? Explain. :12: O . PH" H». SMaiiESf‘Fflme-«cyf HAIL Ouhr (-Aagiatliir “A Mr‘fi PDFGQ {5 +Lu. #Dr‘u 0‘? Elf-“J“fi ’ m ”grab“: 18. It’s been proposed that future space stations create “artificial gravity” by rotating around an axis. (The space station would have to be much larger than the present space station for this to be feasible.) a. How would this work? Explain. (Mir? T11; om'l'sloaa. wall 9'? HA1 Shfioq menial frog/141.. ‘HM. 'i‘loot‘ Walk ‘Hru. ncr Mai “Fart; F('\V\:Mo( *1) We? Ha... OCCMPAA'h- simian-lead; poi-’3‘“) “NJ" ‘0; ‘i‘LLaHJAr'en'i “Rigid-oi.- 'HmL okjglc‘hr Tm «Nu mt‘fifiu‘d (adehf' b. Would the artificial gravity be equally effective throughout the space station? If not, where in the space station would the residents want to live and work? Tia. apps-amt MCBK+WLA beak-u. iv an trim-m9 normal kcLPmm-M bY Maud-51M mu. As any; mod-es "mum—321m urn-{lull thumb! . n. J 1 Micah-9g bacon-Ac manor- Amt-+0 kid—Smile!— NoQtM-d. Y1: MUN) r. .n h :t M . a ' fiver Dynamics III: Motion in aCircle - CHAPTER 7 7-7 7.6 Nonuniform Circular Motion 19. For each, figure determine the signs (+ or —~) of a) and a,. Speeding up Slowing down Slowing down Speeding up a1+ to" co+ (0'- a, 4' a,_+_ a, "‘ a, _ 20. The figures below show the radial acceleration vector ('1', at four sequential points on the trajectory of a particle moving in a counterclockwise circle. a. For each, draw the tangential acceleration vector 5, at points 2 and 3 or, if appropriate, write a: = 0. b. Determine whether a, is positive (+), negative (—), or zero (0). 2 21. A pendulum swings from its end point on the left (point 1) to its end point on the right (point 5). At each of the labeled points: a. Use a black pen or pencil to draw and label the vectors 5i, and a, at each point. Make sure the length indicates the relative size of the vector. b. Use a red pen or pencil to draw and label off-'0 the total acceleration vector 3 . | O o o) 7-8 CHAPTER 7 . Dynamics III: Motion inaCircle ...
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