Particle A and particle B are held together witha compressed spring between them

Question

Particle A and particle B are held together witha compressed spring between them. When they are released, thespring pushes them apart and they then fly off in oppositedirections, free of the spring. The mass of A is 3.0 timesthe mass of B, and the energy stored in the spring was 82J. Assume that the spring has negligible mass and that all itsstored energy is transferred to the particles. Once that transferis complete, what are the kinetic energies of (a)particle A and (b) particle B?

Explanation / Answer

conservation of linear momentum : MaVa = MbVb   =>   (MaVa)^2 = (MbVb)^2 => Ma*Ka = Mb*Kb => Kb = 3Ka Conservation of energy : Ka + Kb = 82 J => 4Ka = 82 J => Ka = 20.5 J Kb = 61.5 J

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