AP Physics 1 Lesson 9 Homework Outcomes Name Date 1. Define uniform circular motion. 2. Determine the tangential velocity of an object moving with uniform circular motion. 3. Determine the centripetal acceleration of an object moving with uniform circular motion. 4. Determine the centripetal force exerted on an object moving with uniform circular motion. 5. Determine the work done on an object moving with uniform circular motion by a centripetal force. 6. Solve problems connecting uniform circular motion and other concepts previously addressed (tension, friction, forces on inclines, etc.) Period Practice Problems 1. A 1500. kg car rounds a circular section of track of radius 75. m. The speed of the car is 50 km/hr. Pay attention to the units. a. Determine the tangential velocity of the car (Vc) in m/s. b. Determine the centripetal acceleration of the car. c. Determine the magnitude and direction of the net force exerted on the car. d. Determine the magnitude and direction of the friction force exerted on the car. e. Determine the coefficient of friction on the road. 2. An average rider is 75 kg. µs = 0.3 on the wall. The radius is 2.5m. During this ride the floor that the people stand on drops, so the riders only have their backs against the cage and are not supported by the floor any longer. a. What is the weight of an average rider? b. What minimum friction force must be exerted on the rider? c. What normal force must be exerted on the rider? d. What is the centripetal force experienced by the rider? 1
3.. A ball of mass M is attached to a string of length R and negligible mass. The ball moves clockwise in a vertical circle, as shown above. When the ball is at point P, the string is horizontal. Point Q is at the bottom of the circle and point Z is at the top of the circle. Air resistance is negligible. Express all algebraic answers in terms of the given quantities and fundamental constants. a. Prepare free-body diagrams for the object at locations P and Q shown above. b. Derive an expression for v min the minimum speed the ball can have at point Z without leaving the circular path. c. The maximum tension the string can have without breaking is T max Derive an expression for v max, the maximum speed the ball can have at point Q without breaking the string. d. Suppose that the string breaks at the instant the ball is at point P. Describe the motion of the ball immediately after the string breaks. 4. 2
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5. A roller coaster ride at an amusement park lifts a car of mass 700 kg to point A at a height of 90 m above the lowest point on the track, as shown above. The car starts from rest at point A, rolls with negligible friction down the incline and follows the track around a loop of radius 20 m. Point B, the highest point on the loop, is at a height of 50 m above the lowest point on the track a. Indicate on the figure the point P at which the maximum speed of the car is attained. b. Calculate the value v max of this maximum speed. c. Calculate the speed v B. of the car at point B. d. On the figure of the car below, draw and label vectors to represent the forces acting on the car when it is upside down at point B. e. Calculate the magnitude of all the forces identified in B. f. Now suppose that friction is not negligible. How could the loop be modified to maintain the same speed at the top of the loop as found in 3. Justify your answer. 5
1. 1. A racing car is moving around the circular track of radius 300 meters shown above. At the instant when the car's velocity is directed due east, its acceleration is directed due south and has a magnitude of 3 meters per second squared. When viewed from above, the car is moving (A) clockwise at 30 m/s (B) clockwise at 10 m/s (C) counterclockwise at 30 m/s (D) counterclockwise at 10 m/s (E) with constant velocity AP 2. The horizontal turntable shown above rotates at a constant rate. As viewed from above, a coin on the turntable moves counterclockwise in a circle as shown. Which of the following vectors best represents the direction of the frictional force exerted on the coin by the turntable when the coin is in the position shown? In which of the following situations would an object be accelerated? 3. I. It moves in a straight line at constant speed. II. It moves with uniform circular motion. III. It travels as a projectile in a gravitational field with negligible air resistance. (A) I only (B) III only (C) I and II only (D) II and III only (E) I, II, and III 4. An automobile moves at constant speed down one hill and up another hill along the smoothly curved surface shown above. Which of the following diagrams best represents the directions of the velocity and the acceleration of the automobile at the instant that it is at the lowest position, as shown. AP 6
5. A compressed spring mounted on a disk can project a small ball. When the disk is not rotating as shown in the view above, the ball moves radically outward. The disk then rotates in a counterclockwise direction as seen from above. and the ball is projected outward at the instant the disk is in the position shown left. Which of the following best shows the subsequent path of the ball relative to the ground? AP A steel ball supported by a stick rotates in a circle of radius r, shown above. The direction of the net force acting on the ball when it is in the position shown is indicated by which of the following 6. AP 7. 8. A satellite of mass M moves in a circular orbit of radius R at a constant speed v. Which of the following must be true? I. The net force on the satellite is equal to mv 2 and is directed toward the center of the orbit. R II. The net work done on the satellite by gravity in one revolution is zero. III. The angular momentum of the satellite is a constant. (A) I only (B) III only (C) I and II only (D) II and III only (E) I, II, and III Use this information for 8-11. The diagram below shows a 5.0-kilogram cart traveling clockwise in a horizontal circle of radius 2.0 meters at a constant speed of 4.0 meters per second. AP At the position shown, the centripetal acceleration of the cart is directed toward point A) Q B) P C) S D) R 9. 10. 11. What is the magnitude of the centripetal force acting on the cart? A) 40. N B ) 20. N C ) 50. N D ) 8.0 N At the position shown, the velocity of the cart is directed toward point A) S B) R C) Q D) P If the mass of the cart was doubled, the magnitude of the centripetal acceleration of the cart would be A) halved B) doubled C) unchanged D) quadrupled 7
12. Use this information for 12-16. At an amusement park, a passenger whose mass is 50. kilograms rides in a cage. The cage has a constant speed of 10. meters per second in a vertical circular path of radius R, equal to 10. meters. What is the magnitude of the centripetal acceleration of the passenger? A) 1.0 m/s 2 B) 5.0 x 102 m/s 2 C) 10. m/s 2 D) 2.0 x 103 m/s 2 13. 14. 15. 16. 17. 18. 19. What does the 50.-kilogram passenger weigh at rest? A) 1600 N B) 0 N C) 490 N D) 50. N What is the magnitude of the centripetal force acting on the passenger? A) 5.0 x 10 2 N B) 0 N C) 50. N D ) 4.9 x 10 2 N What is the direction of the centripetal acceleration of the passenger at the instant the cage reaches the highest point in the circle? A) up B) to the right C) down D) to the left As the time taken for a car to make one lap around a circular track decreases, the centripetal acceleration of the car A) decreases B) increases C) remains the same Use this information for 17-19. The diagram below shows a student spinning a 0.10- kilogram ball at the end of 0.50-meter string in a horizontal circle at a constant speed of 10. meters per second. [Neglect air resistance.] The magnitude of the centripetal force required to keep the ball in this circular path is A) 20. N B ) 10. N C ) 5.0 N D ) 200 N Which is the best description of the force keeping the ball in the circular path? A) perpendicular to the circle and directed toward the center of the circle B) tangent to the circle and directed opposite to the direction that the ball is moving C) perpendicular to the circle and directed away from the center of the circle D) tangent to the circle and directed in the same direction that the ball is moving If the magnitude of the force applied to the string by the student's hand is increased, the magnitude of the acceleration of the ball in its circular path will A) decrease B) remain the same C ) increase 20. A 60.-kilogram adult and a 30.-kilogram child are passengers on a rotor ride at an amusement park. When the rotating hollow cylinder reaches a certain constant speed, v, the floor moves downward. Both passengers stay "pinned" against the wall of the rotor, as shown in the diagram below. The magnitude of the frictional force between the adult and the wall of the spinning rotor is F. What is the magnitude of the frictional force between the child and the wall of the spinning rotor? A) F B) 2F C) ½ F D) ¼ F 21. A satellite of mass 3400 kg is in a circular orbit around a planet at a radius of 9.4 x 10 11 m from the planet s center. If the speed of the satellite is 20.5 m/s, what is the gravitational force acting on the satellite? A) 7.4 x10-8 N B) 1.5 x 10-6 N C) 50 N D) 150N 8
22. A coin of mass m is placed on a vinyl stereo record of radius R and moves at a constant tangential speed v. If the frictional force between the coin and the vinyl record is at its maximum value, then which of the following expressions can be used to find the value of the coefficient of friction between the coin and the vinyl record? An object revolves in uniform circular motion. Which of the graphs below best represents the centripetal force on the vertical axis vs. the speed of the object on the horizontal axis? A) µ = gr/ v B) µ = gv/ R C) µ = vgr D) µ = v2 /gr 23. 24. A 30 kg child sits on the edge of a merry go round at a radius of 6 m. The tangential speed of the child is 12 m/s. The work done by the centripetal force during one complete revolution is Use the diagram below for the following questions. A) 0J B) 1440 J C) 5760 J D) 18086 J Which of the following vectors represents the centripetal force acting on the ball at position I? 25. 9
26. 27. 28. If the string were suddenly cut when the ball is at position II shown in the figure above, the subsequent motion of the ball would be The tension in the string is The ball has a mass m and a speed v as it moves around the vertical circle of radius r. Which of the following expressions can be used to find the minimum speed of the ball at position I such that the circular path is maintained? 10