6 - Circular Motion and Other Applications of Newton's Laws

Attach a heavy object to one end of a spring and then

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Unformatted text preview: the path of a moving object if its acceleration is constant in magnitude at all times and (a) perpendicular to the velocity; (b) parallel to the velocity. 10. Analyze the motion of a rock falling through water in terms of its speed and acceleration as it falls. Assume that the resistive force acting on the rock increases as the speed increases. 11. Consider a small raindrop and a large raindrop falling through the atmosphere. Compare their terminal speeds. What are their accelerations when they reach terminal speed? PROBLEMS 1, 2, 3 = straightforward, intermediate, challenging = full solution available in the Student Solutions Manual and Study Guide WEB = solution posted at http://www.saunderscollege.com/physics/ = Computer useful in solving problem = Interactive Physics = paired numerical/symbolic problems Section 6.1 Newton’s Second Law Applied to Uniform Circular Motion 1. A toy car moving at constant speed completes one lap around a circular track (a distance of 200 m) in 25.0 s. (a) What is its average speed? (b) If the mass of the car is 1.50 kg, what is the magnitude of the force that keeps it in a circle? 2. A 55.0-kg ice skater is moving at 4.00 m/s when she grabs the loose end of a rope, the opposite end of which is tied to a pole. She then moves in a circle of radius 0.800 m around the pole. (a) Determine the force exerted by the rope on her arms. (b) Compare this force with her weight. 3. A light string can support a stationary hanging load of 25.0 kg before breaking. A 3.00-kg mass attached to the string rotates on a horizontal, frictionless table in a circle of radius 0.800 m. What range of speeds can the mass have before the string breaks? 4. In the Bohr model of the hydrogen atom, the speed of the electron is approximately 2.20 106 m/s. Find (a) the force acting on the electron as it revolves in a circular orbit of radius 0.530 10 10 m and (b) the centripetal acceleration of the electron. 5. In a cyclotron (one type of particle accelerator), a deuteron (of atomic mass 2.00 u) reaches a final speed of 10.0% of the speed of light while moving in a circular path of radius 0.480 m. The deuteron is maintained in the circular path by a magnetic force. What magnitude of force is required? 6. A satellite of mass 300 kg is in a circular orbit around the Earth at an altitude equal to the Earth’s mean radius (see Example 6.6). Find (a) the satellite’s orbital 7. 8. 9. 10. 11. speed, (b) the period of its revolution, and (c) the gravitational force acting on it. Whenever two Apollo astronauts were on the surface of the Moon, a third astronaut orbited the Moon. Assume the orbit to be circular and 100 km above the surface of the Moon. If the mass of the Moon is 7.40 1022 kg and its radius is 1.70 106 m, determine (a) the orbiting astronaut’s acceleration, (b) his orbital speed, and (c) the period of the orbit. The speed of the tip of the minute hand on a town clock is 1.75 10 3 m/s. (a) What is the speed of the tip of the second hand of...
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