(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two neutrons A and B are approaching each other along a common straight line. Each has a constant velocity v as measured in the laboratory. Show that the total energy of neutron B as observed in the rest frame of neutron A is given by,

[tex](1+\frac{v^2}{c^2})(1-\frac{v^2}{c^2})^{-1}m_pc^2[/tex]

2. Relevant equations

Either:

[tex]E=\gamma mc^2[/tex]

or

[tex]E^2 = m^2c^4 + p^2c^2[/tex]

3. The attempt at a solution

I'm completely stuck on this. I think that the best way to get to the required answer is via the first of the two equations that I wrote down. However I can't manipulate the fraction into what is required. I get close I think, but its never quite what is required. I think the closest I get is by doing the following:

[tex]E = \gamma mc^2 = \frac{mc^2}{(1-\frac{v^2}{c^2})^{\frac{1}{2}}} * \frac{(1-\frac{v^2}{c^2})^2}{(1-\frac{v^2}{c^2})^2} = \frac{mc^2(1-\frac{v^2}{c^2})^2}{(1-\frac{v^2}{c^2})} = mc^2(1-\frac{v^2}{c^2})[/tex]

From here I'm almost tempted to say that the bracket on the top is the difference of two squares, which would give me 2 brackets with the correct signs, but the v/c part wouldn't have the correct power, and the second bracket wouldn't be raised to the correct power either.

Another thought I had is that the velocity of B from A's reference frame is 2v (although I'm not 100% convinced about this - it involved some odd hand waving on my part to get to this result!), but i assume that once I have the answer in the correct form I should be able to insert the correct value and the answer will fall out properly.

If you should decide to help me I would appreciate an early step to help me on the way - I'd quite like the challenge of getting to the result by myself as much as possible. Its just I feel I may have gone wrong somewhere, or that I'm using the incorrect equations.

Thanks for reading this - I hope you can follow my above working/train of thought!

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# Homework Help: Relativistic energies

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