CHAPTER 3 Review K/U Knowledge/Understanding T/I Thinking/Investigation C Communication A Application Knowledge For each question, select the best answer from the four alternatives. 1. Which of the following describes an inertial frame of reference? (3.1) K/U (a) one in which Newton s first law of motion holds true (b) one in which Newton s first law of motion does not apply (c) one in which Newton s second law of motion no longer applies (d) one in which Newton s third law of motion no longer applies 2. Which of the following is an example of a noninertial frame of reference? (3.1) K/U (a) a spinning centrifuge (b) a digital clock on a moving bus (c) an airplane moving with a constant velocity (d) a stationary DVD 3. Which of the following describes an object that follows a circular path at a constant speed? (3.2) K/U (a) inertial motion (b) uniform circular motion (c) motion with constant acceleration (d) motion with constant velocity 4. Which of the following would result if a tetherball on a rope came off the rope midway through its path around the pole? (3.3) K/U A (a) The ball would continue its circular path around the pole, eventually dropping with the force of gravity. (b) The ball would fly away from the pole in the straight-line direction it was travelling at the moment it came off the rope. (c) The ball would drop to the ground at the moment it came off the rope. (d) The ball would continue to move in its circular path around the pole but with a decreasing radius. 5. In which of the following directions is the centripetal force acting on an object undergoing circular motion? (3.3) K/U (a) in a straight line away from the centre of the object s path (b) in a straight line away from the object at a 908 angle (c) toward the centre of the circular path (d) along the object s path 6. Which of the following causes merry-go-round riders to feel as if they are being pushed away from the centre of the ride? (3.4) K/U (a) being in an inertial reference frame (b) the Coriolis force (c) centripetal acceleration (d) centrifugal force Indicate whether each statement is true or false. If you think the statement is false, rewrite it to make it true. 7. An amusement park ride moving down with a constant velocity is an example of a non-inertial frame of reference. (3.1) K/U 8. The law of inertia does not hold in a non-inertial frame of reference. (3.1) K/U 9. The direction of centripetal acceleration for a car on a banked curve is always down the incline parallel to the road surface. (3.2) K/U 10. The magnitude of an object s centripetal acceleration increases with the mass, the radius of the circular path, and the velocity of the object. (3.2) K/U 11. An observer looking down on a passenger in a car driving around a sharp curve would see that the passenger is being pushed by the car in the direction of the curve. (3.3) K/U A 12. The Moon is not an example of an object in uniform circular motion. (3.4) K/U A 13. Objects moving in a rotating frame of reference experience a force parallel to the velocity of the object in the rotating frame. (3.4) K/U 14. A Foucault pendulum demonstrates that Earth is not a rotating frame of reference. (3.4) K/U 15. A roller coaster car in free fall has no apparent weight. (3.4) K/U A Write a short answer to each question. 16. You are swinging your keys at the end of a lanyard in a horizontal circle around your head. What is the effect on the magnitude of the centripetal acceleration of the keys in each case? (3.2) K/U (a) You keep the radius of the circle constant but double the speed. (b) The speed of the keys stays the same, but you double the radius of the circle. 17. Two cars with the same mass are driving around a curved road at different velocities. Which car will experience a greater centripetal force, the one moving with the faster velocity or the one moving with the slower velocity? (3.3) K/U A 140 Chapter 3 Uniform Circular Motion NEL
18. How are centrifuges used in blood analysis? (3.4) K/U C 19. Identify the force that is causing the centripetal force in each situation. (3.3, 3.4) K/U (a) the Moon orbiting Earth (b) a car turning a corner (c) a rock twirled on the end of a string Understanding 20. While riding in a car heading east, you hold an accelerometer in your hand, like the one in Figure 1. The angle of the bead changes with the acceleration of the car. (3.1) K/U T/I C 70 60 50 Figure 1 80 40 30 20 vertical 10 0 10 bead 20 40 30 50 70 60 80 (a) How must you hold the accelerometer so that it correctly measures acceleration? Explain your answer. (b) Describe what happens to the bead when the vehicle is at rest. (c) Describe what happens to the bead when the vehicle is accelerating toward the east. (d) Describe what happens to the bead when the vehicle is moving with a constant velocity. (e) Describe what happens to the bead when the vehicle begins to slow down while moving toward the east. (f) The bead is at an angle of 138 from the vertical. Calculate the magnitude of the car s acceleration. 21. Determine the magnitude of the centripetal acceleration in each scenario. (3.2) K/U T/I A (a) A penny is 13 cm from the centre of a vinyl record. The record is playing on a turntable at 33.5 rpm. (b) A rodeo performer is twirling his lasso with uniform circular motion. One complete revolution of the rope takes 1.2 s. The distance from the end of his rope to the centre of the circle is 4.3 m. (c) An electron is travelling around a nucleus at 2.18 3 10 6 m/s. The diameter of the electron s orbit is 1.06 3 10 210 m. 22. You are operating a remote-controlled car around a circular path in an open field. The car is undergoing centripetal acceleration of 33.8 m/s 2. The radius of the car s path is 125 m. Calculate the car s speed. (3.2) K/U T/I A 23. WindSeeker, a 30-storey swing ride at Canada s Wonderland, ascends 91.7 m, spreads its metal arms, and swings riders at speeds up to 50.0 km/h. Calculate the ride s centripetal acceleration when the ride operates at maximum speed and at full swing with a diameter of 33.5 m. (3.2, 3.3) K/U T/I A 24. The track near the top of your favourite roller coaster is looped with a diameter of 20 m. When you are at the top, you feel as if you weigh one-third of your true weight. How fast is the roller coaster moving? (3.3) K/U T/I A 25. A locomotive engine of mass 3m, pulling an empty cargo car of mass m, is making a turn on a track. Assuming that the engine and cargo car are moving at the same speed, compare the centripetal forces acting on each. Explain your answer. (3.3) K/U T/I A 26. You are riding on Air Gliders, a thrill ride at Calaway Park, Calgary, that swings riders around in a circle while metal arms move the cars up and down. (3.3) K/U T/I A (a) What is the centripetal force experienced by a 90 kg rider swinging around at 20 m/s in a circle with a 16 m radius? (b) Calculate the force when the ride s arms close to a radius of 10 m. (c) Calculate the force when the ride slows to 5 m/s, keeping the radius at 10 m. 27. A discus thrower at a track meet hurls a 2.0 kg discus. She exerts a horizontal force of 2.8 3 10 2 N on it as she spins. She rotates the disc, with her arm outstretched, in uniform circular motion, with a radius of 1.00 m. How fast will the discus travel when released? (3.4) K/U T/I A 28. A 2.0 kg jewellery box is sitting at the edge of a rotating shelf in a mechanical display case. The radius of the rotating shelf is 0.50 m. Calculate the centripetal force when (a) the shelf is rotating at 1.0 rpm (b) the shelf frequency increases to 5.0 rpm (c) the shelf frequency decreases to 0.50 rpm (3.3, 3.4) K/U T/I A 29. On the Drop Tower at Canada s Wonderland, riders free-fall 23 storeys at speeds close to 100 km/h. At some point during the ride, a person experiences a force equivalent to 2g and the ride s seat is pushing up with a force of 1.1 3 10 3 N. What is the person s weight at this point? (3.4) K/U T/I A NEL Chapter 3 Review 141
Analysis and Application 30. The blades of a blender of radius 0.030 m are 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 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 can have without breaking the string. (3.3) K/U T/I A m 1.5 kg r 0.50 m Figure 2 32. A roller coaster car is near the bottom of its track, as shown in Figure 3. At this point, the normal force on the roller coaster is 3.5 times its weight. The speed of the roller coaster is 26 m/s. Determine the radius of the track s curvature. (3.3) T/I A Figure 3 v r 33. A 35 kg child sits on a Ferris wheel that has a diameter of 22 m. The wheel rotates 3.5 times per minute. (3.3) T/I C A (a) What force does the seat exert on the child at the top of the ride? (b) What force does the seat exert on the child at the bottom of the ride? 34. A rock with a mass of 1.5 kg attached to a light rod with a length of 2.0 m twirls in a vertical circle as shown in Figure 4. The speed v of the rock is constant; that is, it is the same at the top and at the bottom of the circle. The tension in the rod is zero when the rock is at its highest point. Calculate the tension when the rock is at the bottom. (3.3) T/I A side view (a) Figure 4 y x (b) y F T mg x (c) mg y F T x 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 is 10.0 m/s. (3.3) K/U T/I C A Figure 5 r (a) Draw two simple diagrams: one that shows a top view and one that shows a side view of the 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 your answer in terms of the (unknown) tension in the string, F T. (d) Apply Newton s second law along the vertical and the horizontal directions to calculate the angle the string makes with the horizontal. 36. A car with a mass of 1.7 3 10 3 kg is travelling 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 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 with speed v. The string has a breaking-point force of 50.0 N. What is the largest value v can have without the string breaking? Ignore any effects due to gravity. (3.3) K/U T/I A 38. A hammer thrower is swinging a ball on a rope. The mass of the ball is 70.0 kg, and it is swinging at 2.0 m/s in a circle of radius 1.0 m. Calculate the centripetal force. (3.3) K/U T/I A 39. A 30.0 kg child is riding a bicycle around a circular driveway with a diameter of 20.0 m. He is experiencing 32 N of centripetal force. How fast is the child cycling? (3.3) K/U T/I A 40. Roller coaster cars are travelling around a clothoid loop in the track at 55 m/s. The cars have a mass of 125 kg, and the loop has a radius of 25 m. Calculate the centripetal force. (3.3, 3.5) K/U T/I A 41. A child is operating a remote-controlled boat around the edge of a pond with a radius of 2 m. The boat is moving with a speed of 2 m/s. The centripetal force is 16 N. (3.3) K/U T/I A (a) Determine the mass of the boat. (b) In order to decrease the centripetal force to 4 N, how fast should the boat go? 142 Chapter 3 Uniform Circular Motion NEL
42. Figure 6 shows a car travelling around a curve in the road. (3.3.) K/U T/I A r F c v Figure 6 (a) If the car doubles its speed, how much of an increase in centripetal force from friction is needed to keep the car in a circular path? (b) What would happen to the car s path if the road was covered in ice and there was no friction? 43. Determine the centripetal force needed to keep a 105 kg motorboat moving in a circular path on a lake at 7.0 m/s. The radius of the path s curve is 15 m. (3.3) K/U T/I A 44. Two masses are tied together by strings as shown in 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 46. In an amusement park ride, a motor rotates two platforms with a period of 4.0 s in a vertical circle (Figure 9). The mass of platform 1 is 1200 kg, and the mass of platform 2 is 1800 kg. Calculate the tension in each support when the platforms are at the bottom as shown in the figure. (3.3, 3.4) K/U T/I A platform 1 platform 2 Figure 9 support A 4.0 m support B 3.0 m 47. The amusement park ride shown in Figure 10 is a large, rapidly spinning cylindrical room with a radius of 3.0 m. The riders stand up against the wall, and the room starts to spin. Once the room is spinning fast enough, the riders stick to the wall. Then the floor slowly lowers, but the riders do not slide down the wall. Assume the coefficient of friction between the wall and the riders is 0.40. (3.3, 3.4) K/U T/I C A string A 4.00 m string B 2.00 m Figure 7 mass 2 mass 1 45. Mass 1 (2.0 kg) sits on top of mass 2 (5.0 kg), which rests on a frictionless surface (Figure 8). The coefficient of static friction between mass 1 and mass 2 is 0.30. A string of length 5.0 m is tied to mass 2, and both masses are swung around in a horizontal circle. Calculate (a) the maximum speed of the masses and (b) the tension in the string. (3.3) K/U T/I Figure 10 (a) Draw an FBD of a person on the ride. What force or forces cause the net force on the rider? (b) Calculate the minimum speed of the rider required to keep the person stuck to the wall when lowering the floor. 48. A 6.0 kg object is attached to two 5.0 m long strings (Figure 11) and swung around in a circle at 12 m/s. Determine the tension in the two strings, and explain why the tensions are not the same. (3.3, 3.4) K/U T/I A Figure 8 mass 1 mass 2 8.0 m 5.0 m A B 5.0 m Figure 11 NEL Chapter 3 Review 143
49. A race car driver wants to complete two laps in 1 min around a circular track with a 30.0 m radius. The combined mass of her body and her car equals 9.8 3 10 2 kg. What is the magnitude of centrifugal force she will feel? (3.4) K/U T/I A 50. A top-loading washing machine with 2.0 kg of clothes inside is on spin cycle. The tub, with a radius of 0.35 m, is rotating at 50.0 rpm. Determine the centripetal force acting on the clothes. (3.4) K/U T/I A 51. A coin is resting on a vinyl record. The coin slips off the record when the rotation rate is 0.30 rps (rotations per second). Determine the coefficient of static friction between the coin and the record. The radius of the record is 15 cm. (3.4) K/U T/I A 52. A roller coaster car is at the lowest point on its track, where the radius of curvature is 20.0 m. At this point, 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 swinging at a velocity of 2 m/s in a circle with a radius of 2 m. Calculate the magnitude of the force. 55. A popular circus act features a daredevil motorcycle rider encased in a spherical metal cage, as shown in Figure 12. The diameter of the cage is 4 m. (3.4) K/U T/I A Figure 12 (a) A 65 kg performer on a 95 kg motorcycle rides horizontally around the middle of the cage. He completes 22 loops in one minute. Calculate the coefficient of friction he needs between his tires and the cage to keep him in place. (b) How many loops will the rider make per second? (c) If the performer rides around the cage in vertical loops at 6 m/s, what force is needed at the top and bottom of the cage to support his mass? 56. Two skaters are performing on ice. One skater is gripping the other s hand and spinning her in an arc around his body. The distance between the skaters grip and the outer edge of the arc is 3.0 m. The skater is being swung around at 2.0 rpm and has a mass of 54 kg. Calculate the centripetal force. (3.4) K/U T/I A 57. A horse trainer is leading a 450 kg horse on a long lead rope around a training pen, making one rotation around the ring per minute. The centripetal force on the horse is 48 N. Determine the length of the lead rope. (3.4) K/U T/I A 58. Consider the performer in Figure 13. How fast must the horse go around a circus ring with a radius of 25 m in order to maintain constant centripetal acceleration of 1.0g? Give your answer in kilometres per hour. (3.5) K/U T/I A Figure 13 Evaluation 59. Using your knowledge of forces, explain the following in a format of your choice. (3.1, 3.2, 3.3) T/I C (a) centrifugal force (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 61. Create a three-column table, either electronically or on paper. (3.2) K/U T/I C A (a) In the first column, list the three equations for centripetal acceleration. In the second column, identify the variables found in each equation. In the third column, identify the variables not found in each equation. Give your table a title. (b) In your own words, briefly describe how each equation was derived. 144 Chapter 3 Uniform Circular Motion NEL
62. A rodeo performer spins a lasso above her head. (3.2) T/I C A (a) Explain the purpose of twirling the rope before throwing it. (b) Describe how she could maximize the distance the rope can be thrown. (c) Describe the path the rope will take once she releases it. 63. Explain how the principles of centripetal force are used to make safer driving conditions. (3.3) T/I C A 64. How would you explain the concepts of artificial gravity to a fellow student who has not taken physics? (3.4) T/I C A Reflect on Your Learning 65. What did you learn in this chapter that was surprising? Explain your answer. T/I C 66. In this chapter, you learned how to solve some types of centripetal force problems. What questions do you still have about solving centripetal force problems? T/I C A 67. Prepare a Know Want to Know What You Learned (K-W-L) chart on the topic of artificial gravity or another topic from this chapter. T/I C A 68. How has your understanding of uniform circular motion changed? Did you learn anything particularly relevant to you on this topic? T/I C A 69. Consider the different topics you have studied in this chapter. Choose one that you feel has an important impact on your life. Write a one-page report about the topic, explaining why it is important to you. What else would you like to know about this topic? How could you go about learning this? T/I C A Research WEB LINK 70. Research the history of roller coasters, showing how the designs have changed over the centuries. Present your findings in a timeline, on paper, as a Wiki page, as an electronic slide presentation, or in another format of your choosing. T/I C A 71. Research the effects of the Coriolis force in meteorology. In your own words, describe the effect using the movement of a hurricane as an example. C A 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 73. Gas centrifuge technology is an emerging technology. The technology enriches mined uranium to levels at which it can be used to generate nuclear power. The use of centrifuges increases the concentration of the isotope uranium-235 in the uranium. Research the various applications of gas centrifuge technology. How has it affected the efficiency of energy production? T/I C A 74. Astronauts undergo rigorous physical training to be able to function in the altered environments in space. Research astronaut training. How has astronaut training changed from the first piloted space mission to today s missions? What are the health risks associated with space flight and travel? What technologies are in development to help astronauts prepare for longer space travel than has ever been attempted? T/I C A 75. The centrifuge is an integral piece of machinery in many industries, from oil production to laundry applications to the dairy industry. T/I C A (a) Choose an industry, and trace the use of centrifuges in the industry over the past century. How have centrifuges contributed to advances in the industry? (b) List two major implications of the use of centrifuges on society. 76. Research the track layout and dimensions of the Behemoth, a ride at Canada s Wonderland. Prepare a concept map on all the possible forces riders will experience at each new twist in the track. T/I C A 77. Research windmills and wind turbines, how they work, and their effect on the environment. T/I C A (a) How do windmills and wind turbines use the principles of dynamics and circular motion to generate power? Include a simple diagram in your answer. (b) What is the environmental impact of wind power and wind farms? 78. Using an online resource, design your own roller coaster. List each design feature you have included and explain your reasoning. Explain how you have kept the ride exciting while keeping it safe for customers. Decide on a theme for your roller coaster, and try to include the theme in your design. K/U T/I C A NEL Chapter 3 Review 145