momentum and conservation of energy

[soccerball3211]

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 5.2 times the mass of B, and the energy stored in the spring was 54 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 (a) particle A and (b) particle B?

 

[skeeter]

relationship between the masses ...

\(\displaystyle \L m_A = 5.2 m_B\)

since momentum is conserved ...

\(\displaystyle \L m_A|v_{Af}| = m_B|v_{Bf}|\)

kinetic energy is also conserved ...

\(\displaystyle \L \frac{1}{2}m_A(v_{Af})^2 + \frac{1}{2}(m_{Bf})^2 = 54\)

solve the system for the final speeds of A and B, then calculate the kinetic energy of both masses.