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Solutions to Homework 05 - Chapter 5 Problem 6 The National...

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Unformatted text preview: Chapter 5, Problem 6 The National Aeronautics and Space Administration (NASA) studies the physiological effects of large accelerations on astronauts. Some of these studies use a machine known as a centrifuge. This machine consists of a long arm, to one end of which is attached a chamber in which the astronaut sits. The other end of the arm is connected to an axis about which the arm and chamber can be rotated. The astronaut moves on a circular path, much like a model airplane flying in a circle on a guideline. The chamber is located 14.0 m from the center of the circle. At what speed must the chamber move so that an astronaut is subjected to 3.21 times the acceleration due to gravity? (L l a“; '5 :3 ‘7 ”V: #ch =J[J.ZI($8%IEI9M {VI 20.2”? M6 ._..—————— u...— Chapter 5, Problem 10 A computer is reading data from a rotating CD—ROM. At a point that is 0.0195 m from the center of the disk, the centripetal acceleration is 101 m/sz. What is the centripetal acceleration at a point that is 0.0796 m from the center of the disc? Number 41'§_:2:g_717948_7i§0 Units m/sAz 7. ‘7— _'2 a, s 2 (20777) 9/! F C r a s = ‘— => c; f T2 , 2fi/ T 47116 ’1 , '7. g) at 72 ,. Q /72 ’— —’—' Z '- 6’“ 77 C /°/',7' f‘, .77. r o 97‘7é , 4/23 \ 5 ‘l. Chapter 5, Problem 12 In a skating stunt known as "crack—the-whip," a number of skaters hold hands and form a straight line. They try to skate so that the line rotates about the skater at one end, who acts as the pivot. The skater farthest out has a mass of 66.0 kg and is 7.30 m from the pivot. He is skating at a speed of 7.10 m/s. Determine the magnitude of the centripetal force that acts on him. Number 425,5.V7V61'621'3835671V6' Units N f" (\jQ {—C c m 2 4,537; N F r: Chapter 5, Problem 15 At an amusement park there is a ride in which cylindrically shaped chambers spin around a central axis. People sit in seats facing the axis, their backs against the outer wall. At one instant the outer wall moves at a speed of 3.27 m/s, and an 77.3-kg person feels a 282—N force pressing against his back. What is the radius of a chamber? Number “2931067978723 Units m ‘2 MN F: :— :: 2.2l3 M r-C’ ,— Chapter 5, Problem 22 On a banked race track, the smallest circular path on which cars can move has a radius of 102 m, while the largest has a radius of 169 m, as the drawing illustrates. The height of the outer wall is 16.6 m. Find (a) the smallest and (b) the largest speed at which cars can move on this track without relying on friction. (a) Number 2 15737283423521 Units m/s (b) Number 20256902269405 Units m/s 2 "V xv; (it {9119' {Mng ‘9 F3 No.6”) 57m Chapter 5, Problem 26 The drawing shows a baggage carousel at an airport. Your suitcase has not slid all the way down the slope and is going around at a constant speed on a circle (1‘: 9.30 m) as the carousel turns. The coefficient of static friction between the suitcase and the carousel is 0.590, and the angle 6 in the drawing is 12.9 °. How much time is required for your suitcase to go around once? l a) h . +‘D 2 r: O a ' W F Wt]? saw . 715 N > 3 38 :9 r— m”;- , ~ 1 )9“, flaw Cu: Cas‘S-i/QJSMS' c; '— ’T f“ Chapter 5, Problem 30 A satellite is in a circular orbit about the earth (M = 5.98 x 1024 kg). The period of the satellite is 2.10 x 104 s. What is the speed at which the satellite travels? Number f 4923.370629274632 Units m/s 27F ’V: ':‘ l h __\r 3/1 3/2 I \/6'M5 I 3 2,7? r——-1 \IGME Z 2. 3/ ”T 6M6 ”‘3 (F): 217 '2 a re ’7” CMC Chapter 5, Problem 35 Multiple—Concept Example 14 deals with the issues upon which this problem focuses. To create artificial gravity, the space station ShOWn in the drawing is rotating at a rate of 1.40 rpm. The radii of the cylindrically shaped chambers have the ratio rA/IB = 6.00. Each chamber A simulates an acceleration due to gravity of 7.60 m/sz. Find values for (a) Q, (h) IE, and (c) the acceleration due to gravity that is simulated in chamber B. Cham tel“ , .5. l i (91) a ‘5 Kid 7 Q 2 V‘ CR Chamber : l —M4€ Chag'It-elhm L3- S (\j‘ 2.3—]; | I‘ c i (a) Number 35359625371._'1_’9179____é Units m (b) Number 58.93170885'3'195"?Unitsm r.) (c)Nu1nber;r-126666666666? Units m/s"2 r14 :2 3g 3. C: M f“: ’— (—— F [9) F355“ P€§fim T ll Chapter 5, Problem 36 A roller coaster at an amusement park has a dip that bottoms out in a vertical circle of radius r. A passenger feels the seat of the car pushing upward on her with a force equal to 2.87 times her weight as she goes through the dip. If F: 24.5 Hi, how fast is the roller coaster traveling at the bottom of the dip? Number ‘21.i'8”93‘1—3'§44231_: Units m/s Chapter 5, Problem 40 A motorcycle is traveling up one side of a hill and down the other side. The crest is a circular arc with a radius of 45.0 in. Determine the maximum speed that the cycle can have while moving over the crest without losing contact with the road. Number 5 21“ :Units m/s thOZr— 17V and m g {'c, :+m3——f~ are Mi F G ,— .m'v'z some $760.90“ ’— ? :1: Closes-e F r“ F ' a! Gr) ...
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