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 5.00 times the mass of B, and the energy stored in the spring was 64 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?
J (particle A)
J (particle B)

Explanation / Answer

conserving momentum,

5m*v + m*v' = 0

So, v' = 5v

conserving energy,

0.5*5m*v^2 + 0.5*m*v'^2 = 64

So, 5m*v^2+m*25v = 128

So, 30*mv^2 = 128

So, mv^2 = 128/30

So, K.E of A = 0.5*(5m)*v^2 = 2.5*mv^2 = 2.5*128/30 = 10.67 J

K.E of B = 64-10.67 = 53.3 J

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