CHAPTER 3 Review K/U Knowledge/Understanding T/I Thinking/Investigation C Communication A Application

Knowledge 6. Which of the following causes merry-go-round riders For each question, select the best answer from the four to feel as if they are being pushed away from the alternatives. centre of the ride? (3.4) K/U (a) being in an inertial reference frame 1. Which of the following describes an inertial frame (b) the Coriolis force of reference? (3.1) K/U (c) centripetal acceleration (a) one in which Newton’s first law of motion holds true (d) centrifugal force (b) one in which Newton’s first law of motion does Indicate whether each statement is true or false. If you think not apply the statement is false, rewrite it to make it true. (c) one in which Newton’s second law of motion no longer applies 7. An ride moving down with a constant velocity is an example of a non-inertial (d) one in which Newton’s third law of motion no frame of reference. (3.1) K/U longer applies 8. The law of inertia does not hold in a non-inertial 2. Which of the following is an example of a non- frame of reference. (3.1) K/U inertial frame of reference? (3.1) K/U (a) a spinning centrifuge 9. The direction of centripetal acceleration for a car on a banked curve is always down the incline parallel to (b) a digital clock on a moving bus the road surface. (3.2) K/U (c) an airplane moving with a constant velocity 10. The magnitude of an object’s centripetal acceleration (d) a stationary DVD increases with the mass, the radius of the circular 3. Which of the following describes an object that path, and the velocity of the object. (3.2) K/U follows a circular path at a constant speed? (3.2) K/U 11. An observer looking down on a passenger in a car (a) inertial motion driving around a sharp curve would see that the (b) uniform circular motion passenger is being pushed by the car in the direction (c) motion with constant acceleration of the curve. (3.3) K/U A (d) motion with constant velocity 12. The Moon is not an example of an object in uniform 4. Which of the following would result if a tetherball circular motion. (3.4) K/U A on a rope came off the rope midway through its path 13. Objects moving in a rotating frame of reference around the pole? (3.3) K/U A experience a force parallel to the velocity of the object (a) The ball would continue its circular path around in the rotating frame. (3.4) K/U the pole, eventually dropping with the force 14. A Foucault pendulum demonstrates that Earth is not of gravity. a rotating frame of reference. (3.4) K/U (b) The ball would fly away from the pole in the 15. A car in free fall has no apparent straight-line direction it was travelling at the weight. (3.4) K/U A moment it came off the rope. (c) The ball would drop to the ground at the moment Write a short answer to each question. it came off the rope. 16. You are swinging your keys at the end of a lanyard (d) The ball would continue to move in its circular in a horizontal circle around your head. What is the path around the pole but with a decreasing radius. effect on the magnitude of the centripetal acceleration 5. In which of the following directions is the centripetal of the keys in each case? (3.2) K/U force acting on an object undergoing circular motion? (a) You keep the radius of the circle constant but (3.3) K/U double the speed. (a) in a straight line away from the centre of the (b) The speed of the keys stays the same, but you object’s path double the radius of the circle. (b) in a straight line away from the object at 17. Two cars with the same mass are driving around a 8 a 90 angle curved road at different velocities. Which car will (c) toward the centre of the circular path experience a greater centripetal force, the one moving (d) along the object’s path with the faster velocity or the one moving with the slower velocity? (3.3) K/U A

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8160_CH03_p135-157.indd 140 4/26/12 9:55 AM 18. How are centrifuges used in blood analysis? 22. You are operating a remote-controlled car around a (3.4) K/U C circular path in an open field. The car is undergoing 2 19. Identify the force that is causing the centripetal force centripetal acceleration of 33.8 m/s . The radius of in each situation. (3.3, 3.4) K/U the car’s path is 125 m. Calculate the car’s speed. K/U T/I A (a) the Moon orbiting Earth (3.2) (b) a car turning a corner 23. WindSeeker, a 30-storey at Canada’s (c) a rock twirled on the end of a string Wonderland, ascends 91.7 m, spreads its metal arms, and swings riders at speeds up to 50.0 km/h. Understanding Calculate the ride’s centripetal acceleration when the ride operates at maximum speed and at full swing 20. While riding in a car heading east, you hold an with a diameter of 33.5 m. (3.2, 3.3) K/U T/I A accelerometer in your hand, like the one in Figure 1. 24. The track near the top of your favourite roller coaster The angle of the bead changes with the acceleration is looped with a diameter of 20 m. When you are at K/U T/I C of the car. (3.1) the top, you feel as if you weigh one-third of your vertical true weight. How fast is the roller coaster moving? K/U T/I A 80 (3.3) 80 70

60 70 50 60 25. A locomotive engine of mass 3m, pulling an empty 40 50 30 40 20 30 cargo car of mass m, is making a turn on a track. 10 0 10 20 Assuming that the engine and cargo car are moving at the same speed, compare the centripetal forces acting bead on each. Explain your answer. (3.3) K/U T/I A 26. You are riding on Air Gliders, a thrill ride at Calaway Figure 1 Park, Calgary, that swings riders around in a circle while (a) How must you hold the accelerometer so that metal arms move the cars up and down. (3.3) K/U T/I A it correctly measures acceleration? Explain (a) What is the centripetal force experienced by a your answer. 90 kg rider swinging around at 20 m/s in a circle (b) Describe what happens to the bead when the with a 16 m radius? vehicle is at rest. (b) Calculate the force when the ride’s arms close to (c) Describe what happens to the bead when the a radius of 10 m. vehicle is accelerating toward the east. (c) Calculate the force when the ride slows to 5 m/s, (d) Describe what happens to the bead when the keeping the radius at 10 m. vehicle is moving with a constant velocity. 27. A discus thrower at a track meet hurls a 2.0 kg (e) Describe what happens to the bead when the discus. She exerts a horizontal force of 2.8 3 102 N vehicle begins to slow down while moving toward on it as she spins. She rotates the disc, with her arm the east. outstretched, in uniform circular motion, with a (f) The bead is at an angle of 138 from the vertical. radius of 1.00 m. How fast will the discus travel Calculate the magnitude of the car’s acceleration. when released? (3.4) K/U T/I A 21. Determine the magnitude of the centripetal 28. A 2.0 kg jewellery box is sitting at the edge of acceleration in each scenario. (3.2) K/U T/I A a rotating shelf in a mechanical display case. (a) A penny is 13 cm from the centre of a vinyl The radius of the rotating shelf is 0.50 m. record. The record is playing on a turntable at Calculate the centripetal force when 33.5 rpm. (a) the shelf is rotating at 1.0 rpm (b) A rodeo performer is twirling his lasso with (b) the shelf frequency increases to 5.0 rpm uniform circular motion. One complete (c) the shelf frequency decreases to 0.50 rpm revolution of the rope takes 1.2 s. The distance (3.3, 3.4) K/U T/I A from the end of his rope to the centre of the circle 29. On the at Canada’s Wonderland, riders is 4.3 m. free-fall 23 storeys at speeds close to 100 km/h. (c) An electron is travelling around a nucleus at At some point during the ride, a person experiences 2.18 3 106 m/s. The diameter of the electron’s a force equivalent to 2g and the ride’s seat is pushing 2 orbit is 1.06 3 10 10 m. up with a force of 1.1 3 103 N. What is the person’s weight at this point? (3.4) K/U T/I A

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8160_CH03_p135-157.indd 141 4/26/12 9:55 AM Analysis and Application 35. A rock tied to a string spins in a circle of radius 1.5 m, as shown in Figure 5. The speed of the rock 30. The blades of a blender of radius 0.030 m are is 10.0 m/s. (3.3) K/U T/I C A spinning at a rate of 60 rpm. What is the centripetal acceleration of a single point on the edge of one of the blades? (3.2) K/U T/I A 31. The rock in Figure 2 is moving with uniform circular ␪ r motion in a horizontal circle on a frictionless surface. The string is old and can only exert a maximum force of 25 N on the rock. Determine the minimum speed the rock Figure 5 can have without breaking the string. (3.3) K/U T/I A (a) Draw two simple diagrams: one that shows a m ϭ 1.5 kg top view and one that shows a side view of the r ϭ 0.50 m motion of the rock. (b) Draw an FBD for the rock. (c) Determine the total force on the rock directed toward the centre of its circular path. Express Figure 2 your answer in terms of the (unknown) tension in the string, FT. 32. A roller coaster car is near the bottom of its track, as (d) Apply Newton’s second law along the vertical and shown in Figure 3. At this point, the normal force the horizontal directions to calculate the angle on the roller coaster is 3.5 times its weight. The speed the string makes with the horizontal. of the roller coaster is 26 m/s. Determine the radius of 36. A car with a mass of 1.7 3 103 kg is travelling the track’s curvature. (3.3) T/I A without slipping on a flat, curved road with a radius of curvature of 35 m. The speed of the car is 12 m/s. Calculate the frictional force between the road and r v the tires. (3.3) K/U T/I A 37. A stone with a mass of 0.30 kg is tied to a string with a length of 0.75 m and is swung in a horizontal circle Figure 3 with speed v. The string has a breaking-point force of 33. A 35 kg child sits on a Ferris wheel that has a 50.0 N. What is the largest value v can have without diameter of 22 m. The wheel rotates 3.5 times the string breaking? Ignore any effects due to gravity. K/U T/I A per minute. (3.3) T/I C A (3.3) (a) What force does the seat exert on the child at the 38. A hammer thrower is swinging a ball on a rope. top of the ride? The mass of the ball is 70.0 kg, and it is swinging (b) What force does the seat exert on the child at at 2.0 m/s in a circle of radius 1.0 m. Calculate the the bottom of the ride? centripetal force. (3.3) K/U T/I A 34. A rock with a mass of 1.5 kg attached to a light rod 39. A 30.0 kg child is riding a bicycle around a with a length of 2.0 m twirls in a vertical circle as circular driveway with a diameter of 20.0 m. He is shown in Figure 4. The speed v of the rock is constant; experiencing 32 N of centripetal force. How fast is that is, it is the same at the top and at the bottom of the the child cycling? (3.3) K/U T/I A circle. The tension in the rod is zero when the rock is at 40. Roller coaster cars are travelling around a clothoid its highest point. Calculate the tension when the rock is loop in the track at 55 m/s. The cars have a mass of at the bottom. (3.3) T/I A 125 kg, and the loop has a radius of 25 m. Calculate the centripetal force. (3.3, 3.5) K/U T/I A side y y y view 41. A child is operating a remote-controlled boat around the edge of a pond with a radius of 2 m. The boat is mg F T moving with a speed of 2 m/s. The centripetal force is x x x K/U T/I A FT 16 N. (3.3) (a) Determine the mass of the boat. (b) In order to decrease the centripetal force to 4 N, (b) mg (a) (c) how fast should the boat go? Figure 4

142 Chapter 3 • Uniform Circular Motion NEL

8160_CH03_p135-157.indd 142 4/26/12 9:55 AM 42. Figure 6 shows a car travelling around a curve in the 46. In an amusement park ride, a motor rotates two road. (3.3.) K/U T/I A platforms with a period of 4.0 s in a vertical circle (Figure 9). Th e mass of platform 1 is 1200 kg, and the mass of platform 2 is 1800 kg. Calculate the tension v in each support when the platforms are at the bottom as shown in the fi gure. (3.3, 3.4) K/U T/I A

Fc support A r 4.0 m platform 1 support B 3.0 m Figure 6 platform 2 (a) If the car doubles its speed, how much of an Figure 9 increase in centripetal force from friction is needed to keep the car in a circular path? 47. Th e amusement park ride shown in Figure 10 is a (b) What would happen to the car’s path if the road large, rapidly spinning cylindrical room with a radius was covered in ice and there was no friction? of 3.0 m. Th e riders stand up against the wall, and the 43. Determine the centripetal force needed to keep a 105 kg room starts to spin. Once the room is spinning fast motorboat moving in a circular path on a lake at 7.0 m/s. enough, the riders stick to the wall. Th en the fl oor slowly lowers, but the riders do not slide down the Th e radius of the path’s curve is 15 m. (3.3) K/U T/I A wall. Assume the coeffi cient of friction between 44. Two masses are tied together by strings as shown in the wall and the riders is 0.40. (3.3, 3.4) K/U T/I C A Figure 7 and swung around in a horizontal circle with a period of 2.00 s on a frictionless surface. Mass 1 is 3.00 kg, and mass 2 is 5.00 kg. Determine the tension in each string. (3.3) K/U T/I string A 4.00 m string B 2.00 m

Figure 10 mass 2 (a) Draw an FBD of a person on the ride. What force mass 1 or forces cause the net force on the rider? (b) Calculate the minimum speed of the rider Figure 7 required to keep the person stuck to the wall 45. Mass 1 (2.0 kg) sits on top of mass 2 (5.0 kg), which when lowering the fl oor. rests on a frictionless surface (Figure 8). Th e coeffi cient 48. A 6.0 kg object is attached to two 5.0 m–long strings of static friction between mass 1 and mass 2 is 0.30. (Figure 11) and swung around in a circle at 12 m/s. A string of length 5.0 m is tied to mass 2, and both Determine the tension in the two strings, and masses are swung around in a horizontal circle. explain why the tensions are not the same. Calculate (a) the maximum speed of the masses (3.3, 3.4) K/U T/I A and (b) the tension in the string. (3.3) K/U T/I

mass 1 5.0 m mass 2 A 8.0 m Figure 8 B 5.0 m

Figure 11

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8160_CH03_p135-157.indd 143 4/26/12 9:55 AM 49. A race car driver wants to complete two laps in 56. Two skaters are performing on ice. One skater is 1 min around a circular track with a 30.0 m radius. gripping the other’s hand and spinning her in an arc The combined mass of her body and her car equals around his body. The distance between the skaters’ 9.8 3 102 kg. What is the magnitude of centrifugal grip and the outer edge of the arc is 3.0 m. The skater force she will feel? (3.4) K/U T/I A is being swung around at 2.0 rpm and has a mass of 50. A top-loading washing machine with 2.0 kg of 54 kg. Calculate the centripetal force. (3.4) K/U T/I A clothes inside is on spin cycle. The tub, with a radius 57. A horse trainer is leading a 450 kg horse on a long of 0.35 m, is rotating at 50.0 rpm. Determine the lead rope around a training pen, making one rotation centripetal force acting on the clothes. (3.4) K/U T/I A around the ring per minute. The centripetal force on 51. A coin is resting on a vinyl record. The coin slips the horse is 48 N. Determine the length of the lead off the record when the rotation rate is 0.30 rps rope. (3.4) K/U T/I A (rotations per second). Determine the coefficient 58. Consider the performer in Figure 13. How fast of static friction between the coin and the record. must the horse go around a circus ring with a radius The radius of the record is 15 cm. (3.4) K/U T/I A of 25 m in order to maintain constant centripetal 52. A roller coaster car is at the lowest point on its track, acceleration of 1.0g? Give your answer in where the radius of curvature is 20.0 m. At this point, kilometres per hour. (3.5) K/U T/I A the apparent weight of a passenger on the roller coaster is 3.00 times her true weight. What is the speed of the roller coaster? (3.4, 3.5) K/U T/I A 53. A space station is rotating at 12 m/s. The artificial gravity is equal to 50.0 % of that found on Earth. What is the radius of the station? (3.4) K/U T/I A 54. A bucket of water is attached to a rope and is being swung around in a vertical circle. (3.4) K/U T/I A (a) What force is responsible for keeping the bucket moving in a circle? (b) Identify the source of the force in (a). (c) The water-filled bucket has a mass of 15 kg and is Figure 13 swinging at a velocity of 2 m/s in a circle with a radius of 2 m. Calculate the magnitude of the force. Evaluation 55. A popular circus act features a daredevil motorcycle 59. Using your knowledge of forces, explain the following rider encased in a spherical metal cage, as shown in a format of your choice. (3.1, 3.2, 3.3) T/I C in Figure 12. The diameter of the cage is 4 m. (a) centrifugal force (3.4) K/U T/I A (b) Coriolis force (c) fictitious forces, and why they are called that 60. Describe the effects on a person in each of the following frames of reference. (3.1) T/I C A (a) riding the elevator to the top of the CN Tower in Toronto (b) free falling in a skydive from an airplane Figure 12 61. Create a three-column table, either electronically or on paper. (3.2) K/U T/I C A (a) A 65 kg performer on a 95 kg motorcycle rides (a) In the first column, list the three equations for horizontally around the middle of the cage. He centripetal acceleration. In the second column, completes 22 loops in one minute. Calculate the identify the variables found in each equation. coefficient of friction he needs between his tires In the third column, identify the variables not and the cage to keep him in place. found in each equation. Give your table a title. (b) How many loops will the rider make per second? (b) In your own words, briefly describe how each (c) If the performer rides around the cage in vertical equation was derived. loops at 6 m/s, what force is needed at the top and bottom of the cage to support his mass?

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8160_CH03_p135-157.indd 144 4/26/12 9:55 AM 62. A rodeo performer spins a lasso above her head. 73. Gas centrifuge technology is an emerging technology. (3.2) T/I C A The technology enriches mined uranium to levels (a) Explain the purpose of twirling the rope before at which it can be used to generate nuclear power. throwing it. The use of centrifuges increases the concentration (b) Describe how she could maximize the distance of the isotope uranium-235 in the uranium. Research the rope can be thrown. the various applications of gas centrifuge technology. (c) Describe the path the rope will take once she How has it affected the efficiency of energy T/I C A releases it. production? 63. Explain how the principles of centripetal force 74. Astronauts undergo rigorous physical training to are used to make safer driving conditions. be able to function in the altered environments in space. Research astronaut training. How has astronaut (3.3) T/I C A training changed from the first piloted space 64. How would you explain the concepts of artificial mission to today’s missions? What are the health gravity to a fellow student who has not taken risks associated with space flight and travel? What T/I C A physics? (3.4) technologies are in development to help astronauts prepare for longer space travel than has ever Reflect on Your Learning been attempted? T/I C A 65. What did you learn in this chapter that was 75. The centrifuge is an integral piece of machinery in surprising? Explain your answer. T/I C many industries, from oil production to laundry 66. In this chapter, you learned how to solve some applications to the dairy industry. T/I C A types of centripetal force problems. What questions (a) Choose an industry, and trace the use of do you still have about solving centripetal force centrifuges in the industry over the past century. problems? T/I C A How have centrifuges contributed to advances 67. Prepare a Know–Want to Know–What You Learned in the industry? (K-W-L) chart on the topic of artificial gravity or (b) List two major implications of the use of another topic from this chapter. T/I C A centrifuges on society. 68. How has your understanding of uniform circular 76. Research the track layout and dimensions of the motion changed? Did you learn anything particularly Behemoth, a ride at Canada’s Wonderland. Prepare relevant to you on this topic? T/I C A a concept map on all the possible forces riders will 69. Consider the different topics you have studied in this experience at each new twist in the track. T/I C A chapter. Choose one that you feel has an important 77. Research windmills and wind turbines, how impact on your life. Write a one-page report about they work, and their effect on the environment. the topic, explaining why it is important to you. T/I C A What else would you like to know about this topic? (a) How do windmills and wind turbines use the How could you go about learning this? T/I C A principles of dynamics and circular motion to generate power? Include a simple diagram in Research WEB LINK your answer. 70. Research the history of roller coasters, showing how (b) What is the environmental impact of wind power the designs have changed over the centuries. Present and wind farms? your findings in a timeline, on paper, as a Wiki page, 78. Using an online resource, design your own roller as an electronic slide presentation, or in another coaster. List each design feature you have included format of your choosing. T/I C A and explain your reasoning. Explain how you have 71. Research the effects of the Coriolis force in kept the ride exciting while keeping it safe for meteorology. In your own words, describe the customers. Decide on a theme for your roller effect using the movement of a hurricane as an coaster, and try to include the theme in your K/U T/I C A example. C A design. 72. Research the effects of uniform circular motion on growing plants. What effects would a continuously spinning pot of soil have on the grass seed planted in it? How would the grass grow differently? T/I C A

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