 Solution

ID: past-exam-of-the-relativity-course-of-the-university-of-cambridge/2014/paper-1/1/a/solution

With

γ = (1 - v^{2} / c^{2})^{- 1/2}

E = (γ m_{1} + m_{2}) c^{2}

p = γ m_{1} v

. The compound system therefore has

M = m_{1}^{2} + m_{2}^{2} + 2 γ m_{1} m_{2}, V = \frac{γ m _{1}}{γ m _{1} + m _{2}} v .

Here

M^{2} c^{4} = E^{2} - c^{2} p^{2}

. The excess over

m_{1} + m_{2}

is retained internal energy, assuming absorption without escaping radiation.

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