(a) Explanation Given information: The mass ( m A ) of car A is 1 , 600 kg . The mass ( m B ) of car B is 900 kg The velocity ( v A ) of car A is 90 km / h . The velocity ( v B ) of car B is 60 km / h . 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) (b) To determine Find the energy of car A and B .

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259977251

Author: BEER

Publisher: MCG

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Chapter 14.2, Problem 14.35P

(a)

To determine

Prove that EAEB=mBmA such that amount of energy absorbed by each vehicle is inversely proportional to its mass.

(b)

To determine

Find the energy of car A and B.

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Chapter 14.2, Problem 14.34P

Chapter 14.2, Problem 14.36P

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Prove that E A E B = m B m A such that amount of energy absorbed by each vehicle is inversely proportional to its mass.

Solution Summary: The author demonstrates that the amount of energy absorbed by each vehicle is inversely proportional to its mass.