Explanation 1) Concept: Using the formula of conservation of the momentum, we can find the final velocity of the coupled freight car and caboose car. Using this velocity in the given relation between initial kinetic energy and lost kinetic energy, we can find the mass of the caboose car. 2) Formula: i) m F v F + m C v C = ( m C + m F ) V ii) K = 1 2 m v 2 3) Given: i) Mass of freight car m F = 3 . 18 × 10 4 k g ii) Initial velocity of the caboose car v C = 0.00 m / s iii) K f = 0.73 K i 4) Calculation: Let mass of the caboose car be m c and final velocity be V . Since the collision is inelastic collision, using the conservation of momentum, we have, m F v F + m C v C = ( m C + m F ) V m F v F = ( m C + m F ) V V = m F v F ( m C + m F ) Now, we have for initial kinetic energy, K i = 1 2 m F v F 2 And, for final kinetic energy, K f = 1 2 ( m C + m F ) V 2 As V = m F v F ( m C + m F ) K f = 1 2 ( m C + m F ) m F v F m C + m F 2 K f = 1 2 m F 2 v F 2 m C + m F We are given that 27 % of the original kinetic energy is lost, therefore, K f = 0

Fundamentals of Physics, Volume 1, Chapter 1-20

10th Edition

ISBN: 9781118233764

Author: David Halliday

Publisher: WILEY

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Question

Chapter 9, Problem 93P

To determine

To Find:

The mass of the caboose car

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Chapter 9, Problem 92P

Chapter 9, Problem 94P

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