Circular Motion PreTest Date: 06/03/2008 Version #: 0 Name:
1. In a series of test runs, a car travels around the same circular track at different velocities. Which graph best shows the relationship between its centripetal acceleration, a c, and its velocity, v? 2. A figure-skater follows the path of the curve shown below. The arc is circular in shape with P, Q and R due south, east, and north of the circle's center. While the skater coasts along the path shown, her speed decreases uniformly because of friction. Her acceleration is due west at: A. point P B. some point between P and Q C. point Q D. some point between Q and R E. point R 3. What is the period of an object orbiting a planet at a constant distance of 7 x 10 7 m from the planets centre, in an orbit where the acceleration due to gravity is 4.0 m/s 2? 4.2 x 10 3 s 1.5 x 10 4 s 2.6 x 10 4 s 6.9 x 10 8 s 4. A ferris wheel at a carnival has a diameter of 10 m. It rotates at a rate of one revolution every minute. The magnitude of the centripetal acceleration on a student sitting in one of the ferris wheel chairs is: A. 0 m/s 2 B. 0.05 m/s 2 C. 0.1 m/s 2 D. 7.0 m/s 2 E. 385 m/s 2 5. A ball moves at a constant speed in a vertical circle when the string breaks at the position shown. The ball would then move along which of the indicated paths? A. P B. Q C. R D. S 6. A 0.090 m diameter computer floppy disk spins at a constant speed of 1.40 m/s measured at its rim. What is the centripetal acceleration at the rim of this floppy disk? A. 16 m/s 2 B. 22 m/s 2 C. 31 m/s 2 D. 44 m/s 2 7. A small spider is accidentally taking a ride on a CD rotating with a period T. Its centripetal acceleration is 10 m/s 2. The CD player is turned off and the disc slows down. What is the spider s centripetal acceleration when the disc has slowed so the period is 2T? 2.5 m/s 2 5.0 m/s 2 20 m/s 2 40 m/s 2
8. A proton situated in a magnetic field is observed to travel in a circular path. The positions of the proton at times T, 2T, and 3T are shown in the figure below. Which vector best represents the acceleration of the proton at t=2t? E. 9. What is the period of an object orbiting a planet at a constant distance of 7.0 x 10 7 m from the planets centre, in an orbit where the acceleration due to gravity is 4.0 m/s 2? A. 4.2 x 10 3 s B. 1.5 x 10 4 s C. 2.6 x 10 4 s D. 6.9 x 10 8 s 10. Which of the following best describes uniform circular motion? A. B. C. D. SPEED VELOCITY ACCELERATION constant constant constant constant constant changing constant changing changing changing changing changing 11. An airplane is flying north at 200 m/s. It makes a gradual turn maintaining a constant speed. 20.0 s later it completes the turn and is moving east at 200 m/s. The magnitude of its average acceleration while making its turn, in meters per second squared is: A. 400 B. 200 C. 15.7 D. 10.0 E. 0 12. An airplane is flying in a horizontal circle at a speed of 86 m/s. The 72 kg pilot does not want his centripetal acceleration to exceed 68.6 m/s 2. What is the minimum radius of the circular path? A. 90 m B. 110 m C. 750 m D. 7700 m 13. A 1200 kg car is travelling around a horizontal path of diameter 124 m. The coefficient of friction between the tires and the road is 0.67. What is the maximum speed of the car on this path? A. 7.9 m/s B. 20 m/s C. 24 m/s D. 29 m/s 14. A 500 N man travels in a circular path on a ferris wheel. Which free body diagram best shows the forces which could act on the man as he passes the lowest point?
15. A 1200 kg car travelling at 25 m/s goes around a circular path of radius 350 m. What is the net force on the car? A. 1.8 N B. 86 N C. 2 100 N D. 12 000 N 16. How much centripetal force is required to keep a 12 kg object revolving 5 times per second in an orbit of radius 6.0 m? A. 1.1 x 10 2 N B. 5.7 x 10 2 N C. 7.1 x 10 4 N D. 3.6 x 10 5 N 17. What is the maximum speed a car can travel along a level circular path (as shown below) if the coefficient of friction is 0.86? A. 4.1 m/s B. 8.0 m/s C. 25 m/s D. Depends on the mass of the car 18. As a simple pendulum swings from one side to the other, the tension in the supporting thread is best represented by which graph? 19. A 1200 kg car travels with a maximum speed of 24 m/s in a circular path on a dry level road surface where µ = 0.90 between the car tires and the road. What is the radius of this circular path? A. 27 m B. 59 m C. 65 m D. 640 m 20. An object attached to a rotating table is moving in a circular path with a constant speed. Which is the correct free body diagram for the object? 21. An object is kept in uniform circular motion with a period of 5 s by an applied centripetal force F c. What centripetal force will be required to keep the same object in uniform circular motion with the same radius but with a period of 10 s? A. (1/4) F c B. (1/2) F c C. 2 F c D. 4 F c
22. A roller coaster car is moving past the top of a loop of diameter 14 m as shown below. The normal force (directed downwards) provided by the track at the top of the loop is equal to one-half the weight of the car. What is the speed of the coaster car at this point? A. 5.9 m/s B. 8.3 m/s C. 10 m/s D. 14 m/s 23. In an amusement park, a 2.8 m radius "drum" rotates such that a person does not fall when the "floor" drops away. If the coefficient of friction between the person and the wall is 0.35, what is the maximum period of the rotation so that a person will not fall? A. 2.0 s B. 3.4 s C. 5.7 s D. 18 s 24. A 0.20 kg object moves at a constant speed in a horizontal circular path as shown. What is the speed of this object? A. 2.3 m/s B. 3.2 m/s C. 3.4 m/s D. 4.4 m/s 25. A toy airplane, suspended by a light thread, is moving in a circular path at a constant speed as shown. Which of the following is the correct free body diagram for the toy airplane?
26. A mass is moving at a constant speed in a horizontal circle (conical pendulum) as shown. Which one of the following is the unlabelled free body diagram for the mass? A. B. C. D. 27. The bob of a pendulum revolves in a horizontal circle as shown. The forces on it are the force of tension F t in the string and the force of gravity F g on the bob. Which one of the vectors below represents the centripetal force on the bob? A. F g B. F t C. F t - F g D. F t + F g Use the following information to answer the next 2 questions. The diagram shows a toy plane flying in a circle of radius 1.20 m, supported by a string which makes an angle of 28 with the vertical. The tension in the string is 1.80 N. 28. What is the mass of the plane? (3.00 marks) 29. How long does the plane take to complete one orbit? (4.00 marks) 30. What angle would a road have to be banked so that a 1.2 x 10 3 kg car could go around a 72 m corner at 22 m/s with-out any frictional forces acting on the tires? (3.00 marks)
31. Three balls are placed in line on a horizontal surface, as shown below. What is the magnitude of the net gravitational force exerted on Y due to X and Z? A. 6.7 x 10-11 N B. 1.9 x 10-11 N C. 1 x 10-10 N D. 0 32. What is the acceleration due to gravity at the surface of a planet whose mass is 1.88 x 10 21 kg and whose radius is 4.34 x 10 5 m? 3.08 x 10-3 m/s 2 0.666 m/s 2 9.80 m/s 2 2.89 x 10 5 m/s 2 33. What is the mass of a planet given that a satellite revolving around it has a period of orbit of 8.5 x 10 5 s, and a radius of orbit of 1.2 x 10 9 m? (4.00 marks) 34. What is the acceleration of a satellite orbiting Earth in a circle with a radius of 7.3 x 10 6 m? 7.48 m/s 2 8.56 m/s 2 9.80 m/s 2 11.2 m/s 2 35. A planet moves in an elliptical orbit around a sun as shown below. The direction of the planet's acceleration vector at R is: E. 36. The diagram below shows the elliptical orbit of a comet about the sun. Which arrow represents the direction of the net force on the comet in the position below? A. 1 B. 2 C. 3 D. 4 37. Which of the following explains why the moon remains in orbit around Earth? A. The acceleration of the Moon is zero relative to Earth. B. The force of gravity exerted by Earth on the Moon balances the force of gravity exerted by the Moon on Earth. C. The centrifugal and centripetal forces on the Moon balance. D. The gravitational force between Earth and the Moon is equal to the centripetal force necessary to keep the Moon in its orbit. 38. The force of attraction between any two particles in the universe is directly proportional to: A. the sum of their masses B. the product of their masses C. the square of the distance between their centers D. one divided by the distance between their centers
39. Which of the following represents the gravitational force F versus distance d for a rocket leaving Earth? 40. What is the force of gravity on a 52 kg astronaut orbiting the Earth at an altitude of 25,600 km above the surface of the Earth? A. 0N B. 2.1N C. 20N D. 32N 41. Geostationary satellites appear to remain stationary to an observer on Earth. Such satellites are placed in orbit far above the equator. Using principles of physics, explain why such satellites all have the same orbital radius. (4.00 marks) 42. A satellite orbits a planet of mass 4.0 x 10 25 kg at a velocity of 5.8 x 10 3 m/s. What is the radius of this orbit? A. 6.4 x 10 6 m B. 7.9 x 10 7 m C. 1.6 x 10 8 m D. 1.2 x 10 19 m 43. A satellite is placed in circular orbit at an altitude of 4.8 x 10 5 m above the Earth's surface. What is the satellite's orbital period? (5.00 marks) 44. The work required to move an object in a planet's gravitational field can be determined graphically by calculating the A. slope of a graph of gravitational force versus separation distance. B. area under a graph of gravitational force versus separation distance. C. slope of a graph of gravitational potential energy versus separation distance. D. area under a graph of gravitational potential energy versus separation distance. 45. What minimum kinetic energy would a spacecraft of mass 1.2 x 10 4 kg need at the surface of the Earth so that is could escape to infinity? A. 1.1 x 10 4 J B. 1.2 x 10 5 J C. 7.5 x 10 11 J D. an infinite amount 46. The diagram above( left) shows a single object which is moved from position 1 to position 2 in a gravitational field. Which one of the regions on the graph above (right) represents work done in moving the object from position 1 to position 2? A. P only B. Q only C. P + Q D. P - Q
47. A 120 kg astronaut stands on the surface of an asteroid of radius 600 m. The astronaut leaves the surface with 15 J of kinetic energy and reaches a maximum height of 300 m above the surface. What is the mass of the asteroid? A. B. C. D. 5.6 x 10 11 kg 2.2 x 10 12 kg 3.4 x 10 12 kg 5.1 x 10 12 kg 48. How much gravitational potential energy does a 225 kg satellite gain when it is lifted from the surface of the Earth to a height of 3.25 x 10 7 m from the Earth's center? (4.00 marks) 49. A 4.00 x 10 3 kg object is lifted from the earth s surface to an altitude of 3.2 x 10 5 m. How much work does this require? (7.00 marks) 50. An 884 kg satellite in orbit around a planet has a gravitational potential energy of -5.44 x 10 10 J. The orbital radius of the satellite is 8.52 x 10 6 m and its speed is 7.84 x 10 3 m/s. a) What is the mass of the planet? (3 marks) b) What is the kinetic energy of the satellite? (2 marks) c) What is the total energy of the satellite? (2 marks)