Particle A and particle B are held together with a compressed spring between the
ID: 1289571 • Letter: P
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 90 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
Final momentum = = the initial momentum
m1v1+m2v2= 0
3m2 v1 +m2v2= 0 since m1 = 3m2
3v1 +v2= 0
v2 = -3v1------------------1
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Kinetic energy of A = E1 = 0.5m1v1^2
Kinetic energy of B = E2 = 0.5m2v2 ^2
= (9/3) 0.5m1v1^2 = 3E1.since m2 = m1/3 and v2 =-3v1
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0.5kx^2 = E1 + E2 = 4E1
90 =4E1
E1 = 22.5J
E2 = 3E1 = 67.5 J
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Kinetic energy of particle Ais 22.5J
Kinetic energy of particle Bis 3*22.5 = 67.5 J
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