Explanation Write the expression for relativistic constant: γ = 1 1 − v 2 / c 2 Here, γ is the relativistic constant, v is the velocity of object and c is the speed of light . Write the expression for relativistic momentum: p = γ m v Here, m is the mass of object and p is the momentum of object. Write the expression for force acting on the object: F = d p d t Here, F is the force, d p is the change in momentum and d t is the time interval. Write the expression for kinetic energy: K = ∫ 0 v F ⋅ d s K = ∫ 0 v d p d t ⋅ d s K = ∫ 0 v v ⋅ d p K = ∫ 0 v v ⋅ d ( γ m v ) Solve integration by parts: K = ∫ 0 v v ⋅ d ( m v 1 − v 2 c 2 ) K = v ⋅ m v 1 − v 2 c 2 − ∫ 0 v m v 1 − v 2 c 2 ⋅ d v K = m v 2 1 − v 2 c 2 − m ∫ 0 v v ( 1 − v 2 c 2

4th Edition

ISBN: 9780357644782

Author: Thornton

Publisher: CENGAGE L

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Relativistic Energy and Momentum

According to classical physics, time flow is the same for every observer. But according to einstein's theory, time flow is different for different observers. The idea that time flow is not the same for all may sound strange because we may not experience …

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Chapter 2, Problem 77P

To determine

The expression for the relativistic kinetic energy.

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Chapter 2, Problem 76P

Chapter 2, Problem 78P

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Exercise 1: (a) Using the explicit formulae derived in the lectures for the (2j+1) × (2j + 1) repre- sentation matrices Dm'm, (J/h), derive the 3 × 3 matrices corresponding to the case j = 1. (b) Verify that they satisfy the so(3) Lie algebra commutation relation: [D(Î₁/ħ), D(Î₂/h)]m'm₁ = iƊm'm² (Ĵ3/h). (c) Prove the identity 3 Dm'm,(Î²) = Σ (D(Î¡)D(Î¡))m'¡m; · i=1

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