Chapter 3: Problem 7
\({ }^{\dagger}\) Two particles \(P_{1}\) and \(P_{2}\) have respective masses \(m_{1}\) and \(m_{2}\) and are attracted to each other by a force with time- independent potential \(U(\boldsymbol{r})\), where \(\boldsymbol{r}\) is the vector from \(P_{1}\) to \(P_{2}\). (1) Show that the motion of the centre of mass is the same as in the case \(U=0\). (2) Show that the motion of \(P_{2}\) relative to \(P_{1}\) is the same as in the case that \(P_{1}\) is fixed and \(P_{2}\) is attracted to \(P_{1}\) by a force with potential $$ V=\frac{m_{1}+m_{2}}{m_{1}} U . $$
Short Answer
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Key Concepts
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