Question

Proceeding from the fundamental equation of relativistic dynamics, find:
(a) under what circumstances the acceleration of a particle coincides in direction with the force F acting on ti,
(b) the proportionality factors relating the force F and the acceleration w in the cases when `F_|_v` and `F||v`, where v is the velocity of the particle.

Answer 1

`vecF=(d)/(dt)((m_0vecv)/(sqrt(1-v^2/c^2)))=m_0(vecv)/(sqrt(1-v^2/c^2))+m_0vecv/c^2vecv*vecv(1)/((1-v^2/c^2)^(3//2))`
Thus `vecF_(_|_)=m_0(vecw)/(sqrt(1-beta^2)), vecw=vecv, vecw_|_vecv`
`vecF_(||)=m_0(vecw)/((1-beta^2)^(3//2)), vecw=vecv, vecw_(||)vecv`