Particle A and particle B are held together with a compressed spring between the

Question

Particle A and particle B are held together with a compressed spring between them. When they are released, the spring pushes them apart, and they then fly off in opposite directions, free of the spring. The mass of A is 3.00 times the mass of B, and the energy stored in the spring was 94 J. Assume that the spring has negligible mass and that all its stored energy is transferred to the particles. Once that transfer is complete, what are the kinetic energies of each particle?
Particle A = 23.5 J
Particle B=_____??????

Explanation / Answer

Let mass of B = m, speed of B = v. Then mass of A = 3m and speed of A = v/3 (by momentum conservation.)

So kinetic energy of B is (1/2)mv2 and kinetic energy of A is (1/2)(3m)(v/3)2 = (1/6)mv2.

Therefore kinetic energy of B is (1/2)/(1/2 + 1/6) = 0.75 of the total = 70.5 joules.

Note that this is the same answer you would get just from energy conservation given your statement that the kinetic energy of A is 23.5 joules: 94 - 23.5 = 70.5

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