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Physics / Sears and Zemansky's University Physics with Modern Physics 13 / Chapter 10 / Problem 10.93

Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford

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Chapter 10, Problem 10.93

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QUESTION:

A target in a shooting gallery consists of a vertical square wooden board, 0.250 m on a side and with mass 0.750 kg, that pivots on a horizontal axis along its top edge. The board is struck faceon at its center by a bullet with mass 1.90 g that is traveling at and that remains embedded in the board. (a) What is the angular speed of the board just after the bullets impact? (b) What maximum height above the equilibrium position does the center of the board reach before starting to swing down again? (c) What minimum bullet speed would be required for the board to swing all the way over after impact?

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QUESTION:

A target in a shooting gallery consists of a vertical square wooden board, 0.250 m on a side and with mass 0.750 kg, that pivots on a horizontal axis along its top edge. The board is struck faceon at its center by a bullet with mass 1.90 g that is traveling at and that remains embedded in the board. (a) What is the angular speed of the board just after the bullets impact? (b) What maximum height above the equilibrium position does the center of the board reach before starting to swing down again? (c) What minimum bullet speed would be required for the board to swing all the way over after impact?

ANSWER:

Step 1 of 5

a. The angular momentum of the bullet will be

Where

is the distance from the axis we're interested in

denotes the length of the square target.

The angular moment after the impact will be

since both the target and the bullet move with the same angular speed.

The moment of inertia of the target will be

where we denote its mass by , and the moment of the bullet will be

We know that the total moment of inertia will be used even later in the exercise, therefore let's write an expression for it as

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