Particle A and particle B are held together with a compressed spring between the
ID: 1281161 • 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 2.00 times the mass of B, and the energy stored in the spring was 101 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
mass of B = m
mass of A = 2 m
momentum conservation 0 = (2m)vA + mvB
vB = -2vA
energy conservation: E = 121 J = (2m)vA2/2 + mvB2/2
= (2m)vA2/2 + m(2vA)2/2 = 6(mvA2/2)
kinetic energy of A = (2m)vA2/2
= 101/3 = 33.67 J
kinetic energy of B = 101 - 33.67
= 67.3 J