Explanation Calculation: Express the velocity of mass centre using conservation of momentum as follows: ( m A + m B ) v ¯ = m A v A + m B v B v ¯ = m A v A + m B v B m A + m B Express the velocities to the mass centre as follows: v ′ A = v A − v ¯ (1) Here, v ¯ is velocity of mass centre. Substitute m A v A + m B v B m A + m B for v ¯ in Equation (1). v ′ A = v A − m A v A + m B v B m A + m B = m B ( v A + v B ) m A + m B Express the velocities to the mass centre as follows: v ′ B = v B − v ¯ (2) Substitute m A v A + m B v B m A + m B for v ¯ in Equation (2). v ′ B = v B − m A v A + m B v B m A + m B = m A ( v A + v B ) m A + m B Express the energy ( E A ) using the relation as follows: E A = 1 2 m A v ′ A ⋅ v ′ A (3) Substitute m B ( v A + v B ) m A + m B for v ′ A in Equation (3). E A = 1 2 m A ( m B ( v A + v B ) m A + m B ) ⋅ ( m B ( v A + v B ) m A + m B ) = m A m B 2 ( v A + v B ) ( v A + v B ) 2 ( m A + m B ) 2 Express the energy ( E B ) using the relation as follows: E B = 1 2 m B v ′ B ⋅ v ′ B (4) Substitute m A ( v A + v B ) m A + m B for v ′ B in Equation (4). E B = 1 2 m B m A ( v A + v B ) m A + m B B ⋅ m A ( v A + v B ) m A + m B = m A 2 m B ( v A + v B ) ( v A + v B ) 2 ( m A + m B ) 2 Express the energy ( E A ) 0 , ( E B ) 0 test as follows: ( E A ) 0 = 1 2 m A v 0 2 ( E B ) 0 = 1 2 m B v 0 2 Write the expression for sever for automobile A as follows: S A = E A ( E A ) 0 (5) Here, E A is energy and ( E A ) 0 is energies from tests

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259638091

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 14.2, Problem 14.36P

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Verify the given described collision between two automobile is (mAmB)2 times more severe for the automobile B than for automobile A.

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Chapter 14.2, Problem 14.35P

Chapter 14.2, Problem 14.37P

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Vector Mechanics for Engineers: Statics and Dynamics

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Verify the given described collision between two automobile is ( m A m B ) 2 times more severe for the automobile B than for automobile A .

Solution Summary: The author explains that the collision between two automobiles is (m_A)2 times more severe for the automobile B than for automobile A.

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Verify the given described collision between two automobile is (mAmB)2 times more severe for the automobile B than for automobile A.

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Chapter 14 Solutions