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Relativistic Mass, Energy, Momentum

Relativistic Mass, Energy, Momentum. Classical physics: p = mv. When consider relativity:. p = m 0 v/ √(1 – v 2 /c 2 ). m 0 = rest mass. Consider m = m 0 / √(1 – v 2 /c 2 ). mass as measured in a reference frame in which it moves at speed v. √(1 – v 2 /c 2 ).

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Relativistic Mass, Energy, Momentum

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  1. Relativistic Mass, Energy, Momentum

  2. Classical physics: p = mv When consider relativity: p = m0v/ √(1 – v2/c2 ) m0 = rest mass Consider m = m0 / √(1 – v2/c2 ) mass as measured in a reference frame in which it moves at speed v

  3. √(1 – v2/c2 ) As v  c, √(1 – v2/c2 )  0 m  ∞ To accelerate an object up to speed c would require an infinite amount of energy c is the speed limit of the universe if v > c, imaginary mass (tachyon)

  4. Relativistic Kinetic Energy KE = mc2 – m0c2 m is the relativistic mass m0 is the rest mass m0c2 is the rest energy for an object at rest, the equivalent amount of energy which can be produced from its mass E0 = m0c2

  5. Total energy: E = mc2 = m0c2 + KE Observe an increase in mass (m) due to an increase in KE If the energy of a system changes by ΔE, the mass of the system changes by Δm: ΔE = (Δm)c2

  6. π0 meson (m0 = 2.4 x 10-28 kg) travels at 0.80c relativistic mass: 4.0 x 10-28 kg total energy: 3.6 x 10-11 J rest energy: 2.16 x 10-11 J kinetic energy: 1.44 x 10-11 J

  7. Consequences of Special Relativity For an observer outside a moving frame of reference: length mass time speed of light decreases increases slows down is constant

  8. Albert Einstein (1905) relationship between: space and time mass and energy (E = mc2)

  9. Space and time exist within the universe Space-time: 3 dimensions of space 1 dimension of time Motion through space affects our motion in time As speed increases, time slows down

  10. Δy’ y’ L y Δy Δx’ Δx x’ x L = √(Δx)2 + (Δy)2 L = √(Δx’)2 + (Δy’)2

  11. 4-dimensional space-time interval s = √(Δx)2 + (Δy)2 +(Δz)2 –(c Δt)2

  12. In a different frame of reference, trade a little space for a little time.

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