v 1 v 2 Circular Motion F c =mv 2 /r a c =v 2 /r Fc=4π 2 mr/t 2 ac=4π 2 r/t 2 Centripetal Force Problem Types: 1. Rock on a String Fc = T (Tension)

Transcription

1 Circular Motion F c =mv 2 /r =v 2 /r =4π 2 mr/t 2 ac=4π 2 r/t 2 v tan Centripetal Force Problem Types: 1. Rock on a String = T (Tension) v 2. Moon & Planet = F G (Gravitational Force) 3. Car on a Curve = f (Friction) v 2 v 1 4. *Deflected Ion Beam = F E and/ or F B 1

2 A 28 gram rubber stopper is attached to a string and whirled clockwise in a horizontal circle with a radius of 0.80 meter. The diagram below represents the motion of the rubber stopper. The stopper maintains a constant speed of 2.5 meters per second. v tan 1. On the diagram, draw an arrow showing the direction of the centripetal force acting on the stopper when it is at the position shown. 2. Calculate the magnitude of the centripetal acceleration of the stopper. [Show all work, including the equation and substitution with units.] 2

3 3. A student on an amusement park ride moves in ircular path with a radius of 3.5 meters once every 8.9 seconds. The student moves at an average speed of m/s m/s m/s m/s 4. A stone on the end of a string is whirled clockwise at constant speed in a horizontal circle as shown in the diagram. Which pair of arrows best represents the directions of the stone s velocity, v, and acceleration, a, at the position shown? 3

4 5. The centripetal force acting on the space shuttle as it orbits Earth is equal to the shuttle s 1. inertia 2. momentum 3. velocity 4. weight 6. The magnitude of the centripetal force acting on an object traveling in a horizontal, circular path will decrease if the 1. radius of the path is increased 2. mass of the object is increased 3. direction of motion of the object is reversed 4. speed of the object is increased The larger the radius, the less required force 4

5 Base your answer to this question on the information below. In an experiment, a kilogram rubber stopper is attached to one end of a string. A student whirls the stopper overhead in a horizontal circle with a radius of 1.0 meter. The stopper completes 10 revolutions in 10 seconds. 7. Calculate the magnitude of the centripetal force on the whirling stopper. 8. Determine the speed of the whirling stopper. 1 rev = 1 go around Period, T = time per go around 5

6 9. The diagram below represents a mass, m, being swung clockwise at constant speed in a horizontal circle. At the instant shown, the centripetal force acting on mass m is directed toward point 1. A 2. B 3. C and ac always point towards center 4. D Direction of Tangential velocity 10. Base your answer to the question on the information below. A go cart travels around a flat, horizontal, circular track with a radius of 25 meters. The mass of the go cart with the rider is 200. kilograms. The magnitude of the maximum centripetal force exerted by the track on the go cart is 1200 newtons. Which change would increase the maximum speed at which the go cart could travel without sliding off this track? 1. Decrease the coefficient of friction between the go cart and the track. 2. Decrease the radius of the track. (requires more force or less speed) 3. Increase the radius of the track. (requires less force allows more speed) 4. Increase the mass of the go cart. (requires more force or less speed) 6

7 11. A car travels at constant speed around a section of horizontal, circular track. Which diagram below correctly represents the direction of the centripetal acceleration of the car when it is at point P? F c and always point to center 12. Centripetal force F c acts on ar going around a curve. If the speed of the car were twice as great, the magnitude of the centripetal force necessary to keep the car moving in the same path would be: (hold m & r) 3. / Force varies as v 2. If you double the speed, you quadruple the required force to hold the turn. 13. Which graph best represents the relationship between the magnitude of the centripetal acceleration and the speed of an object moving in ircle of constant radius? 7

8 14. A 1750 kilogram car travels at onstant speed of 15.0 meters per second around a horizontal, circular track with a radius of 45.0 meters. The magnitude of the centripetal force acting on the car is N N N N 15. A car rounds a horizontal curve of constant radius at onstant speed. Which diagram best represents the directions of both the car s velocity, v, and acceleration, a? 16. A car moves with onstant speed in lockwise direction around a circular path of radius r, as represented in the diagram. When the car is in the position shown, its acceleration is directed toward the 1. north 2. west 3. south 4. east 8

9 17. A ball attached to a string is moved at constant speed in a horizontal circular path. A target is located near the path of the ball as shown in the diagram. At which point along the ball s path should the string be released, if the ball is to hit the target? 1. A 2. B 3. C 4. D 18. In the diagram, art travels clockwise at constant speed in a horizontal circle.at the position shown in the diagram, which arrow indicates the direction of the centripetal acceleration of the cart? 1. A 2. B 3. C 4. D 9

10 19. The diagram below shows a 5.0 kilogram bucket of water being swung in a horizontal circle of 0.70 meter radius at onstant speed of 2.0 meters per second. The magnitude of the centripetal force on the bucket of water is approximately N N N N 20. A kilogram car travels at onstant speed of 20. meters per second around a horizontal circular track. Which diagram correctly represents the direction of the car s velocity (v) and the direction of the centripetal force (F c ) acting on the car at one particular moment? 10

11 Base your answer to the question on the information and diagram. In an experiment, a rubber stopper is attached to one end of a string that is passed through a plastic tube before weights are attached to the other end. The stopper is whirled in a horizontal circular path at constant speed. The weight of the hanging object provides the Tension which is the centripetal force. Fg =. 21. The rubber stopper is now whirled in a vertical circle at the same speed. Which of the following diagrams best represents vectors to indicate the direction of the weight (F g ) and the direction of the centripetal force (F c ) at the position shown? 22. Which one of the following measurements would not need to be taken to show that the magnitude of the centripetal force is equal to the balancing weights? [Neglect friction.] 1. the mass of the stopper 2. the radius of the path 3. the force of the weights (this is calculated based on formula) 4. the length of the string used 23. What would happen to the radius of the circle if the student whirls the stopper at a greater speed without changing the balancing weights? 1. The radius would increase. 2. The radius would decrease. 3. The radius would remain the same. 24. As viewed from the top, which of the following best represents the path of the rubber stopper if the string breaks at the position shown? 1. path 1 2. path 2 3. path 3 4. path 4 11

12 25. The diagram below represents a 0.40 kilogram stone attached to a string. The stone is moving at onstant speed of 4.0 meters per second in a horizontal circle having a radius of 0.80 meter. The magnitude of the centripetal acceleration of the stone is m/s 2 = v 2 / r = 4 2 /.8 = 20 m/s m/s m/s 2 = mv 2 / r =.4*4 2 /.8 = 8N m/s 2 Base your answer on the diagram and information below. The diagram shows a student seated on a rotating circular platform, holding a 2.0 kilogram block with a spring scale. The block is 1.2 meters from the center of the platform. The block has onstant speed of 8.0 meters per second. [Frictional forces on the block are negligible.] 26. The reading on the spring scale is approximately N N N N = mv 2 / r = 2*8 2 /1.2 = 106 N 27. Which statement best describes the block s movement as the platform rotates? 1. Its velocity is directed tangent to the circular path, with an inward acceleration. 2. Its velocity is directed tangent to the circular path, with an outward acceleration. 3. Its velocity is directed perpendicular to the circular path, with an inward acceleration. 4. Its velocity is directed perpendicular to the circular path, with an outward acceleration. 12

13 An athlete in a hammer throw event swings a 7.0 kilogram hammer in a horizontal circle at a constant speed of 12 meters per second. The radius of the hammer's path is 2.0 meters. 28. If the hammer is released at the position shown, it will travel toward point 1. A 2. B 3. C 4. D 29. What is the magnitude of the centripetal acceleration of the hammer? m/s m/s a 2 c = v 2 / r = 12 2 /2 = 72 m/s m/s 2 = mv 2 / r = 7*12 2 /2 = 504 N m/s At the position shown, the centripetal force acting on the hammer is directed toward point 1. A Centripetal Force always points to center 2. B 3. C 4. D 13