Explanation Write the expression for momentum: p → = m v → Here, m is the mass of object, v → is the velocity of object and p → is the momentum of object. The conservation of momentum of an object ceases when the velocity of object approaches the velocity of light. To conserve it at very high speed, an additional term named relativistic constant is multiplied to the momentum. Write the expression for relativistic momentum: p → = m γ v → (I) Here, γ is the relativistic constant. Substitute 1 1 − v 2 / c 2 for γ in equation (I) p → = m v → 1 − v 2 / c 2 Newton’s second law state that rate of change of momentum with respect to time is equal to the force acting on a body. Write the expression for Newton’s second law: F → = d p → d t (II) Here, F → is the force acting on body, d p → is the change in momentum and d t is the time interval. Substitute m v → 1 − v 2 / c 2 for p → in equation (II) F → = d d t ( m v →

Modern Physics for Scientists and Engineers

4th Edition

ISBN: 9781133103721

Author: Stephen T. Thornton, Andrew Rex

Publisher: Cengage Learning

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Chapter 2, Problem 57P

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To show F→=mγa→ if force is always parallel to the velocity.

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Modern Physics for Scientists and Engineers

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To show F → = m γ a → if force is always parallel to the velocity.

Solution Summary: The author explains how Newton's second law states that the rate of change of momentum with respect to time is equal to the force acting on a body.

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To show F→=mγa→ if force is always parallel to the velocity.

Chapter 2 Solutions