- #1
Rubber Ducky
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Homework Statement
Two relativistic particles "L" and "R", each of rest mass ##m_0##, are moving at speed ##v## towards each other (in the frame of an observer). They collide squarely and are stationary afterwards.
(a) From the perspective of one particle, what is the oncoming speed of the other?
(b) What is the rest mass, relativistic mass, total energy, kinetic energy, and momentum of each particle before the collision in the frame of the observer?
(c) Repeat (b) in the rest frame of particle "L"
(d) What is the total momentum and energy before and just after the collision, in the observer's frame?
Homework Equations
##u'=\frac{u-v}{1+\frac{v^2}{c^2}}##
##m=\frac{m_0}{\sqrt{1-\frac{u^2}{c^2}}}##
##E=\frac{m_0c^2}{\sqrt{1-\frac{u^2}{c^2}}}=K+m_0c^2=\sqrt{(pc)^2+(m_0c)^2}##
##p=\frac{m_0u}{{\sqrt{1-\frac{u^2}{c^2}}}}##
The Attempt at a Solution
(a) If the observer is in frame ##S##, and the frame of L is ##S'##, then ##\left |u'_R\right |=\frac{v+v}{1+\frac{v^2}{c^2}}=\frac{2v}{1+\frac{v^2}{c^2}}##
(b) ##m_L=\frac{m_0}{\sqrt{1-\frac{u^2}{c^2}}}=m_R##
The rest of this part is relatively (heh) straight forward, I think. I'm not sure how to apply the same formulas to part (c), though. For example, for the mass of R with respect to L, would I copy the formula from part (b), but replace ##u## by what I found in (a)?
Also, in the frame of L, shouldn't its rest mass be equal to its relativistic mass, since particle L is at rest in this frame, and rest mass is defined as the mass measured by a frame in which the object is at rest?