An unstable particle at rest breaks up into two fragments of unequal mass. The rest mass of the lighter particle is 2.5 x 10(adsbygoogle = window.adsbygoogle || []).push({}); ^{-28}kg, and that of the heavier fragment is 1.67 x 10^{-27}kg. If the lighter fragment has a speed of 0.983c after the breakup, what is the speed of the heavier fragment?

What is the idea here? Where does the energy come from, from an external source, or from the mass in the particles? (note: lower case m corresponds to the mass of the light particle and upper case M corresponds to the mass of the heavy particle)

v_{1}: speed of the lighter particle

v_{2}: speed of the heavier particle

We know that the total relativistic energy is:

E = KE + m_{o}c^{2}

KE = 1/2mv_{1}^{2}, m is the relativistic mass

So if relativistic energy of thelightparticle is conserved we get this equation.

mc^{2}= 1/2mv^{2}+ m_{o}c^{2}

We can also conserve the relativistic mass of both particles:

(m + M)c^{2}= 1/2mv_{1}^{2}+ 1/2Mv_{2}^{2}+ (m_{o}+ M_{o})c^{2}

Is this the correct way to setup the problem?

I tried solving for v_{2}without any luck. So I hope there is an easier way--the correct way.

Thanks

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# Relativistic particle problem.

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