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Laws of Conservation

Problem 1.147

In the reference frame KK two particles travel along the xx axis, one of mass m1m_{1} with velocity v1\mathbf{v}_ {1}, and the other of mass m2m_{2} with velocity v2.\mathbf{v}_{2} . Find: (a) the velocity V\mathbf{V} of the reference frame K′K^{\prime} in which the cumulative kinetic energy of these particles is minimum; (b) the cumulative kinetic energy of these particles in the K′K^{\prime} frame.

Reveal Answer
1.147. (a) V=(m1v1+m2v2)/(m1+m2)\mathbf{V}=\left(m_{1} \mathbf{v}_{1}+m_{2} \mathbf{v}_{2}\right) /\left(m_{1}+m_{2}\right) (b) T=μ(v1−T=\mu\left(\mathbf{v}_{1}-\right. −v2)2/2,\left.-\mathrm{v}_{2}\right)^{2} / 2, where μ=m1m2(m1+m2)\mu=m_{1} m_{2}\left(m_{1}+m_{2}\right)
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