Circular Motion Review

Part A: Multiple Choice 1. Which of the following statements are true of an object moving in a circle at a constant speed? Include all that apply. a. The object experiences a force which has a component directed parallel to the direction of motion. b. Inertia causes objects to move in a circle. c. There can be a force pushing outwards on the object as long as the net force in inwards. d. Because the speed is constant, the acceleration is zero. e. The acceleration and the net force vector are directed perpendicular to each other. f. If the net force acting upon the object is suddenly reduced to zero, then the object would suddenly depart from its circular path and travel tangent to the circle. g. The acceleration of the object is directed tangent to the circle. For Questions #2-#5, identify the type of force which causes the following bold-faced objects to travel along a circular path. a. gravity b. normal c. tension d. applied e. friction f. spring g. electrical h. magnetic 2. An eraser is tied to a string swung in a horizontal circle. 3. The moon orbits the earth. 4. A car makes a sharp right-hand turn along a level roadway. 5. A roller coaster car passes through a loop. Consider the car at the bottom of the loop. 6. A physics teacher ties an eraser to the end of a string and then whirls it in a counter-clockwise circle. If the teacher lets go of the string, then the eraser hits a student (or several students) in the classroom. If the string is let go when the eraser is at point X on the diagram at the right, then which student(s) in the class will the eraser hit? Write the initials in this space: ________________ 7. Which of the following statements are true about gravitational force? Identify all that apply. a. The gravitational force only acts between very, very massive objects. b. The gravitational force between an object and the earth is inversely related to the distance between the object's and the earth's center. c. The gravitational force can ALWAYS be accurately calculated by multiplying the object mass by the acceleration of gravity (m•g). d. The gravitational force acting upon an object is the same as the weight of the object. e. The gravitational force between two objects is independent of the mass of the smaller of the two objects. f. If object A gravitationally attracts object B with a force of X Newtons, then object B will also gravitationally attract object A with the same force of X Newtons. g. The doubling of the separation distance (measured from the center) between two objects will halve the gravitational force between the objects. h. It an object is placed two earth-radii above the surface of the earth, then the force of gravitational attraction between the object and the earth will be one-fourth the magnitude as on earth's surface. i. Orbiting astronauts do not experience a force of gravity; this explains why they feel weightless. 8. Which of the following statements are true about the acceleration of gravity? Identify all that apply. a. The acceleration of gravity experienced by objects located near to (and far from) from the earth depends upon the mass of the object. b. The acceleration of gravity experienced by objects located near to (and far from) from the earth depends upon the mass of the Earth. c. The acceleration of gravity experienced by objects located near to (and far from) the earth is inversely related to the distance between the center of the object and the center of the earth. d. Increasing the mass of an object will increase the acceleration of gravity experienced by the object. e. Doubling the distance between an object and the earth's center will decrease the acceleration of gravity by a factor of four. f. The acceleration of an orbiting satellite is equal to the acceleration of gravity at that particular location. g. If the mass of the Earth were doubled (without an alteration in its radius), then the acceleration of gravity on its surface would be approximately 20 m/s2. h. If the mass of the Earth were doubled and the radius of the earth were doubled, then the two changes would offset each other and the acceleration of gravity on its surface would still be approximately 10 m/s2. 9. Which of the following statements are true about satellites? Identify all that apply. a. Satellites are falling projectiles. b. All satellites follow circular paths. c. The orbital velocity required of a satellite is dependent upon the mass of the satellite; a more massive satellite would require a greater orbital speed. d. The orbital velocity of a satellite does not depend upon the mass of the planet around which it orbits. e. A high-altitude satellite will require a greater orbital speed than a low-altitude satellite. f. By definition, a geosynchronous satellite orbits the earth in a perfect circle, maintaining the same distance above the surface of the earth. g. Satellites travel faster along their orbital path when they are closest to the earth. h. The acceleration of a satellite varies inversely with its distance from the center of the earth. More distant satellites have smaller accelerations. 10. Which of the following statements are true about the motion of planets about the sun? Identify all that apply. a. The force of gravity is the only force which acts upon the planets. b. Their trajectories are highly elliptical. c. The planets which are furthest from the sun have the greatest period. d. For any given planet, the speed is greatest when the planet is closest to the sun. e. The velocity vector is directed tangent to the elliptical path. f. The net force vector is at all times directed perpendicular to the velocity vector. g. To keep the planet from escaping the sun's gravitational field, the net force vector is greatest when the planet is furthest from the sun. Part B: Short Answer 11. Explain how something can be moving at a constant speed yet be accelerating at the same time. 14. Describe the apparent weight of a person in an elevator while upward, accelerating downward, and not accelerating. Part C: Diagramming and Analysis 15. In the diagram at the right, draw vector arrows (straight lines with arrowheads) which indicate the following for an object which is moving in a clockwise circle. • the net force at point A. • the acceleration at point B. • the velocity at point C. 16. The diagram at the right shows a satellite orbiting the Earth in an elliptical path in a clockwise direction. a. Draw a vector representing the velocity of the object at position A. b. Draw a vector representing the force on the object at position D. c. Draw a vector representing the acceleration of the object at position C. d. At which of the four positions is the satellite moving fastest? 17. A 1.20-kg bucket is held by a string and whirled in a vertical circle. The radius of the circle is 1.30 m. The speed of the bucket is 3.70 m/s at the top of the loop and 7.10 m/s at the bottom of the loop. On the diagrams below, construct a free-body diagram (label all forces according to type) for the bucket at both the top and the bottom of the loop. Fill in the blanks and clearly indicate the magnitude of the individual force values on your free-body diagram. 18. Construct a free-body diagram showing the direction and types of forces acting upon the car at the top and the bottom of a loop. Be sure to label the forces according to type. Anna experiences a downward acceleration of 24.0 m/s2 at the top of the loop and an upwards acceleration of 12.0 m/s2 at the bottom of the loop. Use Newton's second law to fill in all the blanks and to ultimately determine the normal force acting upon Anna's 800. kg roller coaster car. PSYW Top Bottom Fnet = _______________ Fnet = _______________ Fnet = _______________ Fnet = _______________ Fgrav = _______________ Fgrav = _______________ 20. Pete Zaria is riding the Cliff Hanger at Great America. Pete enters a cylindrical barrel which makes 18.5 revolutions every minute. The diameter of the barrel is 6.92 m. Pete's mass is 64.7 kg. Construct a free-body diagram showing the forces acting upon Pete. Calculate the acceleration and net force acting upon Pete Zaria. PSYW Part D: Short Computations 21. Two objects attract each other with a force of gravity (Fgrav) of 36 N. If the distance separating the objects is doubled, then what is the new force of gravitational attraction? PSYW 22. Two objects attract each other with a force of gravity (Fgrav) of 36 N. If the distance separating the objects is doubled and the masses one of the objects is tripled, then what is the new force of gravitational attraction? PSYW 23. Two objects attract each other with a force of gravity (Fgrav) of 36 N. If the distance separating the objects is increased by a factor of 4 and the masses of both objects are tripled, then what is the new force of gravitational attraction? PSYW Part E: Problem-Solving 29. A roller coaster car loaded with passengers, has a mass of 500. kg; the radius of curvature of the track at the bottom point of a dip is 12.0 m. The vehicle has a speed of 18.0 m/s at this point. a. In the space below, draw a free-body diagram for the car (label forces according to type). b. Calculate the acceleration and the net force acting upon the car. PSYW c. Calculate the force exerted on the vehicle by the track? PSYW 31. What is the tension in a 0.500 meter rope which carries a 2.50 kg bucket of water in a vertical circle with a velocity of 3.00 m/s when the bucket is at the bottom of its swing? 32. A 53.5-kg rider on a roller coaster car is moving 10.3 m/s at the top of a loop which has a radius of curvature of 7.29 m. Determine the normal force experienced by the rider. 35. What is the reading of a bathroom scale when a man of mass 72 kg stands on it while riding in an elevator accelerating upwards 2 at 5.4 m/s ? 36. An airplane pilot makes a vertical loop with a 56.2-m radius. Determine the normal force acting upon the pilot's 62.6-kg body at the top of the loop if his air speed is 64.1 m/s.