All Problems

Laws of Conservation

Problem 1.149

Two small discs of masses m1m_{1} and m2m_{2} interconnected by a weightless spring rest on a smooth horizontal plane. The discs are set in motion with initial velocities v1v_{1} and v2v_{2} whose directions are mutually perpendicular and lie in a horizontal plane. Find the total energy E~\widetilde{E} of this system in the frame of the centre of inertia.

Reveal Answer
E~=μ(v12+v22)/2, where μ=m1m2/(m1+m2)\widetilde{E}=\mu\left(v_{1}^{2}+v_{2}^{2}\right) / 2, \text { where } \mu=m_{1} m_{2} /\left(m_{1}+m_{2}\right)
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