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Chapter 9: Translational, Rotational, and Vibrational Energy

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Matter & Interactions
Pages: 349 - 382
Matter & Interactions

Matter & Interactions

Book edition 4th edition
Author(s) Ruth W. Chabay, Bruce A. Sherwood
Pages 1135 pages
ISBN 9781118875865

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Illustration

59 Questions for Chapter 9: Translational, Rotational, and Vibrational Energy

  1. Discuss qualitatively the motion of the atoms in a block of steel that falls onto another steel block. Why and how do large-scale vibrations damp out?

    Found on Page 376

  2. A solid uniform-density sphere is tied to a rope and moves in a circle with speed v. The distance from the center of the circle to the center of the sphere is d, the mass of the sphere is M, and the radius of the sphere isR. (a) What is the angular speed role="math" localid="1653899021129" ω? (b) What is the rotational kinetic energy of the sphere? (c) What is the total kinetic energy of the sphere?

    Found on Page 359

  3. A runner whose mass is 50kg accelerates from a stop to a speed of 10m/s in 3s. (A good sprinter can run 100m in about 10s, with an average speed of 10m/s.) (a) What is the average horizontal component of the force that the ground exerts on the runner’s shoes? (b) How much displacement is there of the force that acts on the sole of the runner’s shoes, assuming that there is no slipping? Therefore, how much work is done on the extended system (the runner) by the force you calculated in the previous exercise? How much work is done on the point particle system by this force? (c) The kinetic energy of the runner increases—what kind of energy decreases? By how much?

    Found on Page 363

  4. Consider the acceleration of a car on dry pavement, if there is no slipping. The axle moves at speed v, and the outside of the tire moves at a speedv relative to the axle. The instantaneous velocity of the bottom of the tire is zero. How much work is done by the force exerted on the tire by the road? What is the source of the energy that increases the car’s translational kinetic energy?

    Found on Page 377

  5. Two people with different masses but equal speeds slide toward each other with little friction on ice with their arms extended straight out to the slide (so each has the shape of a “I”). Her right hand meets his right hand, they hold hands and spin 90°, then release their holds and slide away. Make a rough sketch of the path of the center of mass of the system consisting of the two people, and explain briefly. (It helps to mark equal time intervals along the paths of the two people and of their center of mass.)

    Found on Page 377

  6. Three uniform-density spheres are positioned as follows:

    Found on Page 377

  7. A meter stick whose mass is 300glies on ice (Figure 9.49). You pull at one end of the meter stick, at right to the stick, with a force of 6N. The ensuing motion of the meter stick is quite complicated, but what are the initial magnitude and direction of the rate of change of the momentum of the stick, /dtdpsys, when you first apply the force? What is the magnitude of the initial acceleration of the center of the stick?

    Found on Page 377

  8. Determine the location of the center of mass of an L-shaped object whose thin vertical and horizontal members have the same length Land the same mass M. Use the formal definition to find the x and ycoordinates, and check your result by doing the calculation with respect to two different origins, one in the lower left corner at the intersection of the horizontal and vertical members and at the right end of the horizontal member.

    Found on Page 377

  9. A man whose mass is 80kg and a woman whose mass is 50kgsit at opposite ends of a canoe 5m long, whose mass is 30kg. (a) Relative to the man, where is the mass of the system consisting of man-woman, and canoe? (Hint: Choose a specific coordinate system with a specific origin.) (b) Suppose that the man moves quickly to the center of the canoe and sits down there. How far does the canoe move in the water? Explain your work and your assumptions.

    Found on Page 377

  10. If an object has a moment of inertia 19kg·m2 and rotates with an angular speed of 70rad/s, what is its rotational kinetic energy?

    Found on Page 377

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