Concept explainers
The derivation of energy momentum relation.
Answer to Problem 60P
The derivation is given below.
Explanation of Solution
Write the expression for total energy
Here,
Write the expression for relativistic kinetic energy
Here,
Write the expression for Lorentz factor.
Here,
Write the expression for rest mass.
Here,
Square (I)
Square (II)
Multiply (II) by
Rearrange
Add (VII) and (VI)
Rearrange
Substitute for
Rearrange
Substitute
Rearrange
Substitute (IX) in (V)
Write the expression for relativistic momentum
Here,
Square the above equation
Substitute (XI) in (X)
The above equation is the energy momentum relation.
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