a. Explanation Given data: A bullet is fired into a block, and then the embedded bullet slides across a frictionless table and collides with a horizontal spring. The spring compresses by a length of d . Mass of the bullet ( m B ) is m . Mass of the block ( m BL ) is M . The length compressed by the spring ( x ) is d . The spring constant of the spring is k . Formula used: Consider the given system as two parts to analyze the required parameters. Consider the inelastic collision of the bullet with the block as part 1 and embedded block compresses to the spring as part 2. In part 1, the momentum of the system is conserved. Write the expression for momentum of conservation for part 1 of the system as follows. m B ( v B ) i + m BL ( v BL ) i = ( m B + m BL ) v f (1) Here, m B is the mass of the bullet, m BL is the mass of the block, ( v B ) i is the initial velocity of the bullet, ( v BL ) i is the initial velocity of the block, which is 0 m s , since the block initially at rest, and v f is the final velocity of the embedded bullet (bullet stick together with the block after the collision). Refer to the (10.8) in the textbook, and modify the expression for kinetic energy of the embedded block as follows. K = 1 2 ( m B + m BL ) ( v f ) 2 (2) Here, ( m B + m BL ) is the mass of the embedded block (mass of bullet and block). Refer to the (10.16) in the textbook, and modify the expression for stored elastic potential energy in the spring due to the compression of the spring by the embedded bullet as follows. U s = 1 2 k x 2 (3) Here, k is the spring constant, and x is the compression length of the spring. Explanation: Rearrange the expression in equation (1) for the initial speed of the bullet as follows. ( v B ) i = ( m B + m BL ) v f − m BL ( v BL ) i m B Substitute m for m B , M for m BL , and 0 m s for ( v BL ) i , ( v B ) i = ( m + M ) v f − M ( 0 m s ) m Simplify the expression as follows. ( v B ) i = ( m + M ) v f m (4) From the given data, the kinetic energy of the embedded bullet is equal to the elastic potential energy stored in the spring after it was compressed by the embedded bullet b. To determine To find: The bullet’s initial speed for the given values. c. To determine To find: The fraction of initial kinetic energy that lost in the given system and to explain the reason for lost energy.

4th Edition

ISBN: 9780134779218

Author: Knight

Publisher: PEARSON

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Question

Chapter 10, Problem 83GP

To determine

To find: The expression for the bullet’s initial speed.

To determine

To find: The bullet’s initial speed for the given values.

To determine

To find: The fraction of initial kinetic energy that lost in the given system and to explain the reason for lost energy.

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Chapter 10, Problem 82GP

Chapter 10, Problem 84GP

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