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Center of Percussion. A baseball bat rests on a

University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman ISBN: 9780321675460 31

Solution for problem 99P Chapter 10

University Physics | 13th Edition

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University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman

University Physics | 13th Edition

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Problem 99P

Center of Percussion. ?A baseball bat rests on a frictionless, horizontal surface. The bat has a length of 0.900 m, a mass of 0.800 kg, and its center of mass is 0.600 m from the handle end of the bat (Fig. P10.99). The moment of inertia of 2? the bat about its center of mass is 0.0530 kg · m? . The bat is struck by a baseball traveling perpendicular to the bat. The impact applies an impulse at a point a distance x from the handle end of the bat. What must x be so that the handle end of the bat remains at rest as the bat begins to move? [?Hint:? Consider the motion of the center of mass and the rotation about the center of mass. Find ?x so that these two motions combine to give ?v ?= 0 for the end of the bat just after the collision. Also, note that integration of Eq. (10.29) gives (see 10.92).] The point on the bat you have located is called the ?center of percussion. ?Hitting a pitched ball at the center of percussion of the bat minimizes the “sting” the batter experiences on the hands Eq. 10.29 See page 2 for problem 10.92 10.92 The solid wood door of a gymnasium is 1.00 m wide and 2.00 m high, has total mass 35.0 kg, and is hinged along one side. The door is open and at rest when a stray basketball hits the center of the door head-on, applying and average force of 1500 N to the door for 8.00 ms. Find the angular speed of the door after the impact. [?Hint:? Integrating Eq. (10.29) yields The quantity is called angular impulse.]

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Textbook: University Physics
Edition: 13
Author: Hugh D. Young, Roger A. Freedman
ISBN: 9780321675460

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Center of Percussion. A baseball bat rests on a