All Problems Laws of Conservation
Problem 1.147
In the reference frame \(K\) two particles travel along the \(x\) axis, one of mass \(m_{1}\) with velocity \(\mathbf{v}_ {1}\), and the other of mass \(m_{2}\) with velocity \(\mathbf{v}_{2} .\) Find: (a) the velocity \(\mathbf{V}\) of the reference frame \(K^{\prime}\) in which the cumulative kinetic energy of these particles is minimum; (b) the cumulative kinetic energy of these particles in the \(K^{\prime}\) frame.
1.147. (a) \(\mathbf{V}=\left(m_{1} \mathbf{v}_{1}+m_{2} \mathbf{v}_{2}\right) /\left(m_{1}+m_{2}\right)\) (b) \(T=\mu\left(\mathbf{v}_{1}-\right.\) \(\left.-\mathrm{v}_{2}\right)^{2} / 2,\) where \(\mu=m_{1} m_{2}\left(m_{1}+m_{2}\right)\)