Relativistic Mass, Momentum and Energy

• Conservation of Momentum
• Newton's Third Law
• Mechanical Universe Video ( Program 44: Chapters 4 - 28)
• Elastic Collision (Kinetic Energy Conserved)
• A is in Frame S
• B is in frame S'
• round trip time for A in frame S
• T₀ = Y/V_A
• round trip time for B in frame S'
• T₀ = Y/V_B
• Conservation of Linear Momentum in Frame S
• m_AV_A = m_BV_B
• but what is V_B in frame S
• V_B = Y/T where T is the measured time for B in frame S
• T = gT₀
• V_B = Y/gT₀
• V_A = Y/T₀
• Conservation of Momentum only holds if
• m_A = m_B/g
• Relativistic Mass
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• Relativistic Momentum



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• Newton's Second Law is still valid but not as F = ma
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• if the speed of the object varies with time, then the mass will also vary



• Mass and Energy
• The change in the kinetic energy of an object is equal to the work done on the object.



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• need the time derivative of the momentum in terms of its position, not always convenient, useful, or available.
• Application of chain rule and other steps to be demonstrated in class.



• KE = gm₀c² - m₀c²



• In the classical limit with v<<c, this reduces to the familiar form.



• m₀c² is the rest mass energy, and the total energy is the kinetic energy plus this term.
• Momentum-Energy Relationship



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