Particles A and B are held together with a compressed (massless) spring between them. When they are released, the spring pushes them apart and they fly off in opposite directions, free of the spring. The mass of A is two times larger than the mass of B, and the energy stored in the spring was 120 J. Assuming that all the stored energy is transferred to the particles, the kinetic energies of particles A and B after the transfer of energy has taken place are
A) 0 J and 120 J respectively.
B) 40 J and 80 J respectively.
C) 60 J and 60 J respectively.
D) 80 J and 40 J respectively.
E) 120 J and 0 J respectively.

Question

Quizplus · Accepted Answer

The kinetic energy of a particle is given by KE = 1/2 mv^2, where m is the mass of the particle and v is its velocity. Since the total energy stored in the spring is 120 J, and all of this energy is transferred to the particles, the total kinetic energy of the particles is also 120 J. Since the mass of A is two times larger than the mass of B, the velocity of A will be half the velocity of B. Therefore, the kinetic energy of A will be 1/4 of the total kinetic energy, or 30 J, and the kinetic energy of B will be 3/4 of the total kinetic energy, or 90 J.

Particles a and B Are Held Together with a Compressed