# HATZIC SECONDARY SCHOOL

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1 HATZIC SECONDARY SCHOOL PROVINCIAL EXAMINATION ASSIGNMENT CIRCULAR MOTION MULTIPLE CHOICE / 30 OPEN ENDED / 65 TOTAL / 95 NAME:

2 1. An object travels along a path at constant speed. There is a constant net force acting on the object that remains perpendicular to the direction of the motion. Describe the path of the object. A. linear B. circular C. elliptical D. parabolic 2. An object of mass m is on a horizontal rotating platform. The mass is located 0.22 m from the axle and makes one revolution every 0.74 s. axle 0.22 m m The friction force needed to keep the mass from sliding is 13 N. What is the object's mass? A kg B. 1.3 kg C. 2.7 kg D. 5.2 kg 3. An object moves at a constant speed along a circular path as shown Which vector best represents the centripetal acceleration of the object at this point? A. 1 B. 2 C. 3 D

3 4. A child is riding on a merry-go-round which is rotating at a constant rate. Which of the following describes the child's speed, velocity, and magnitude of acceleration? SPEED VELOCITY MAGNITUDE OF ACCELERATION A. constant constant constant B. constant changing constant C. changing constant changing D. changing changing changing 5. A kg puck is attached to a kg mass M by a cord that passes through a hole in a frictionless table, as shown. The puck travels in a circular path of radius 0.25 m. What is the speed of the puck? A m/s B m/s C. 1.6 m/s D. 2.6 m/s puck 0.25 m M 6. A 500 N child travels in a circular path on a ferris wheel. Which free body diagram best shows the forces which could act on the child as she passes the lowest point? A. B. F N = 400 N C. F N = 500 N D. F N = 600 N F g = 500 N F g = 500 N F g = 500 N F g = 500 N - 2 -

4 7. A car travels at a uniform speed through a level circular curve in the road. Which of the following correctly describes the magnitude of the acceleration, velocity and force acting on the car? MAGNITUDE OF ACCELERATION MAGNITUDE OF VELOCITY MAGNITUDE OF FORCE A. constant constant constant B. constant changing changing C. constant changing constant D. changing changing changing 8. A student plots a graph of centripetal force F c versus the square of velocity v 2 for an object in uniform circular motion. F c What is the slope of this graph? v 2 A. m r B. r m C. 4π 2 r T 2 D. T 2 4π 2 r 9. Which of the following diagrams shows the instantaneous velocity v and centripetal force F for an object in uniform circular motion. A. v F B. F v C. F D. v v F - 3 -

5 10. An object travels with a constant speed in a circular path. The net force on the object is A. zero. B. towards the centre. C. away from the centre. D. tangent to the object's path. 11. A physics student swings a 5.0 kg pail of water in a vertical circle of radius 1.3 m. v r = m What is the minimum speed, v, at the top of the circle if the water is not to spill from the pail? A. 3.6 m s B. 6.1 m s C. 8.0 m s D. 9.8 m s 12. In a popular amusement park ride, a large cylinder is set in rotation. The floor then drops away leaving the riders suspended against the wall in a vertical position as shown. Rotating cylinder Which of the following is the correct free-body diagram for the person at the position shown? A. B. C. D

6 13. A 1. 2 m long pendulum reaches a speed of 4.0 m s at the bottom of its swing. 1.2 m 3.0 kg What is the tension in the string at this position? A. 11 N B. 29 N C. 40 N D. 69 N 14. A kg car rounds a flat circular section of road at 20 m s as shown in the diagram. v = 20 m s r = 85 m The coefficient of friction between the car tires and the road surface is What minimum friction force is required for the car to follow this curve? A N B N C N D N - 5 -

7 15. A person is on a horizontal rotating platform at a distance of 4.3 m from its centre. This person experiences a centripetal acceleration of 5.6 m/s 2. What centripetal acceleration is experienced by another person who is at a distance of 2.5 m from the centre of the platform? A. 2.3 m/s 2 B. 3.3 m/s 2 C. 5.6 m/s 2 D. 9.6 m/s A 1.2 kg mass on the end of a string is rotated in a vertical circle of radius 0.85 m. 1.2 kg r = 0.85 m If the speed of the mass at the top of the circle is 3.6 m/s, what is the tension in the string at this location? A. 6.5 N B. 12 N C. 18 N D. 30 N 17. Hans, whose mass is 50 kg, rides on a ferris wheel in a circular path at constant speed. When he is at the top of the wheel, the seat exerts an upward force of 420 N on Hans. What is the centripetal force on Hans at the top of the wheel? A. 70 N B. 420 N C. 490 N D. 910 N - 6 -

8 18. An object is attached to a string that can withstand a maximum tension force of 6.3 N. The object travels in a circular path of radius m with a period of 2.1 s. r = 0.40 m m What is the maximum mass of the object? A kg B kg C. 1.8 kg D. 3.6 kg 19. A 65 kg pilot in a stunt plane performs a vertical loop with a 700 m radius. The plane reaches a speed of 210 m s at the bottom of the loop. What is the upward force on the pilot at the bottom of the loop? A. 640 N B N C N D N 20. The diagram shows a 52 kg child riding on a Ferris wheel of radius 12 m and period 18 s. What force (normal force) does the seat exert on the child at the top and bottom of the ride? TOP BOTTOM A. 76 N 76 N r = 12 m B. 430 N 590 N C. 510 N 510 N D. 590 N 430 N - 7 -

9 21. A kg car is travelling at 25 m s on a horizontal surface in a circular path of radius 85 m. What is the net force acting on this car? A. 0 N B N C N D N 22. A 61 kg skateboarder is moving down a ramp with a 7.0 m radius of curvature. At the bottom of this ramp he reaches a speed of 7.8 m s. r = 7.0 m v = 7. 8 m s What upward force acts on the skateboarder at the bottom of the ramp? A N B N C N D N 23. A space station has an outer radius of 140 m. The station rotates so that the occupants at X at the outer wall experience an acceleration of 9.8 m s 2. What acceleration will the occupants at Y experience at the 100 m radius? A. 7.0 m s 2 B. 8.3 m s 2 C. 9.8 m s 2 D. 14 m s m 100 m v Y X - 8 -

10 24. A ball attached to a string is swung in a horizontal circle. View from Above II III IV I Which path will the ball follow at the instant the string breaks? A. I B. II C. III D. IV 25. A test tube rotates in a centrifuge with a period of s. The bottom of the test tube travels in a circular path of radius m. Side V iew Top View m m What is the centripetal force exerted on a kg amoeba at the bottom of the tube? A N B N C N D N - 9 -

11 26. 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? A. B. C. D. 27. A 65 kg student is in a car travelling at 25 m s on a hill of radius 110 m. When the car is at the top of the hill, what upward force does the seat exert on the student? A. 270 N B. 370 N C. 640 N D. 910 N 28. A 1200 kg car can travel without slipping at a maximum speed of 28 m s in a circular path of radius 70 m on a dry horizontal surface. When it rains, the coefficient of friction is reduced to one half its original value. What is the maximum speed under this wet condition? A. 7.0 m s B. 14 m s C. 20 m s D. 28 m s

12 29. A bus of weight F g is moving at a constant speed over a hill and dip that have the same radius of curvature. v v When the bus is passing over the crest of the hill, the road exerts a normal force on the bus equal to 3 three quarters of the bus's weight ( 4 F g ). What is the normal force the road exerts on the bus when the bus is passing through the bottom of the dip? A. B. C. D. 1 4 F g 3 4 F g 5 4 F g 7 4 F g 30. The diagram shows an object of mass 3.0 kg travelling in a circular path of radius 1.2 m while suspended by a piece of string of length 1.9 m. What is the centripetal force on the mass? 1.9 m 39 A. 19 N B. 23 N C. 24 N D. 29 N 1.2 m

13 1. 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 m a) What is the mass of the plane? (3 marks) b) How long does the plane take to complete one orbit? (4 marks)

14 2. A 35 kg child rides a ferris wheel of radius 12 m. The child moves in a vertical circle at a constant speed and completes one rotation every 9.0 s. 12 m a) As the child travels over the top, what is the magnitude of the force that the seat exerts on the child? (5 marks)

15 b) How does the magnitude of the child s acceleration at the top of the ride compare to her acceleration at the bottom? The child s acceleration at the top is: (circle one) (1 mark) i) less than at the bottom. ii) greater than at the bottom. iii) the same as at the bottom. Explain your choice using principles of physics. (3 marks)

16 3. A 3.5 kg object is suspended by a string and moves in a horizontal circle of radius 0.60 m. The tension in the string is 36 N. string kg r = 0.60 m a) What is the magnitude of the net force on the object? (3 marks) b) What is the period of revolution of the object? (4 marks)

17 4. A 6.1kg object on the end of a massless connecting rod moves in uniform circular motion in a vertical circle with radius 1. 2 m. The period of revolution is 0.80 s. 1.2 m connecting rod 6.1 kg constant v a) Draw and label a free body diagram for the object at the bottom of the circular path. (2 marks) b) Calculate the tension in the connecting rod at this position. (5 marks)

18 5. A space station of radius 90 m is rotating to simulate a gravitational field. 90 m v a) What is the period of the space station s rotation so that a 70 kg astronaut will experience a normal force by the outer wall equal to 60% of his weight on the surface of the earth? (5 marks)

19 b) What would be the effect experienced by the astronaut if the space station rotated faster so that the period of rotation was decreased? Explain your predicted effect. (4 marks)

20 6. A 85 kg acrobat supported by a 6.0 m rope swings along a circular path from rest at position X as shown below. The rope hangs from the end of a uniform boom of mass 54 kg. Find the tension force in the cable as the acrobat passes the lowest point, position Y. (9 marks) Cable X Hinge m 2.0 m 6.0 m Y

21 7. A racetrack surface has the shape of an inverted cone on which cars race in horizontal circles. For a steady speed of 29 m/s, to what distance d should a driver take her car, if she wishes to stay on a circular path without friction? (9 marks) d

22 8. A mass is suspended by a string attached to a spring scale that initially reads 14 N as shown in Diagram 1. F = 14 N Spring scale Rope The mass is pulled to the side and then released as shown in Diagram 2. Q F =? Spring scale Rope Q As the mass passes point Q, how will the reading on the spring scale compare to the previous value of 14 N? Using principles of physics, explain your answer. (4 marks)

23 9. During a roller coaster ride, the riders move through two loops, the second being one-half the radius of the first. The riders, however, travel at the same speed at the top of each of these two loops. v F N R v F N 1 R 2 Using principles of physics, explain why the riders would experience a greater normal force at the top of the second smaller loop than at the top of the first, larger loop. (4 marks)

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