Chapter 15: Problem 65
The relativistic kinetic energy of a particle is \(T=(\gamma-1) m c^{2} .\) Use the binomial series to express \(T\) as a series in powers of \(\beta=v / c .\) (a) Verify that the first term is just the non relativistic kinetic energy, and show that to lowest order in \(\beta\) the difference between the relativistic and non relativistic kinetic energies is \(3 \beta^{4} m c^{2} / 8 .\) (b) Use this result to find the maximum speed at which the non relativistic value is within \(1 \%\) of the correct relativistic value.
Short Answer
Step by step solution
Key Concepts
These are the key concepts you need to understand to accurately answer the question.