The kinetic energies of particles A and B, where A is 5 times more massive than B, can be calculated using the conservation of energy and momentum. Particle A's kinetic energy will be 1/25 of the spring's energy, 83 J, while particle B's will be 5 times that of particle A.
To determine the kinetic energies of particles A and B after being pushed apart by a compressed spring, we need to apply the law of conservation of energy and the conservation of momentum. Given that the mass of particle A is 5 times that of particle B, we can denote the mass of particle B as m and the mass of particle A as 5m. All the energy stored in the spring, 83 J, converts into the kinetic energy of the two particles once the spring is released.
According to the conservation of momentum, if the two particles fly off in opposite directions, the magnitude of their momenta will be equal and opposite. If particle B has a velocity v, then particle A will have a velocity v/5 due to its larger mass. The kinetic energy of a particle is given by the formula KE = 0.5 × mass × velocity2. So, the kinetic energy of particle A will be KEA = 0.5 × 5m × (v/5)2 and that of particle B will be KEB = 0.5 × m × v2.
Due to the conservation of energy, the total kinetic energy (KEA + KEB) will be equal to the stored energy in the spring (83 J). By combining the equations and solving for v, we can find the separate kinetic energies of each particle. The kinetic energy of particle A will be 1/25 of the total energy (83 J), and the kinetic energy of particle B will be 5 times greater than that of particle A due to the mass relationship and conservation of energy.
The exact values for the kinetic energies of particles A and B can be found by solving the system of equations derived from the conservation laws.