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Relativistic Mechanics

Problem 1.380

Proceeding from the fundamental equation of relativistic dynamics, find: (a) under what circumstances the acceleration of a particle coincides in direction with the force \(\mathbf{F}\) acting on it; (b) the proportionality factors relating the force \(\mathbf{F}\) and the acceleration \(\mathbf{w}\) in the cases when \(\mathbf{F} \perp \mathbf{v}\) and \(\mathbf{F} \| \mathbf{v},\) where \(\mathbf{v}\) is the velocity of the particle.

Reveal Answer
 1.380. (a) In two cases: F∥v and F⊥v; (b) F⊥=m0w1−β2 , F∥=m0w/(1−β2)3/2, where β=v/c\begin{aligned} &\text { 1.380. (a) In two cases: } \mathbf{F} \| \mathbf{v} \text { and } \mathbf{F} \perp \mathbf{v} ; \text { (b) } \mathbf{F}_{\perp}=m_{0} \mathbf{w} \sqrt{1-\boldsymbol{\beta}^{2}} \text { , }\\ &\mathbf{F}_{\|}=m_{0} \mathbf{w} /\left(1-\beta^{2}\right)^{3 / 2}, \text { where } \beta=v / c \end{aligned}
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