All Problems

Laws of Conservation

Problem 1.149

Two small discs of masses \(m_{1}\) and \(m_{2}\) interconnected by a weightless spring rest on a smooth horizontal plane. The discs are set in motion with initial velocities \(v_{1}\) and \(v_{2}\) whose directions are mutually perpendicular and lie in a horizontal plane. Find the total energy \(\widetilde{E}\) 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)
Prev
Next