Final answer:
a) The final velocity vectors of the two spheres are v1f = [0.05,-0.0866] m/s and v2f = [0.0866,-0.05] m/s, respectively.
b) This collision is inelastic.
c) In the inelastic collision, 1.595938 J of energy is converted to another form.
Step-by-step explanation:
a) To calculate the final velocity vectors of the two spheres, we will use the principles of conservation of momentum and conservation of kinetic energy. Since m2 is at rest initially, the momentum and kinetic energy will be conserved. Using Newton’s laws and trigonometry, we can find the final velocity vectors of m1 and m2.
Let's perform the calculations. The final velocity vector of m1 is given by v1f = [m1*cos(θ), m1*sin(θ)]. Substituting the given values, we have v1f = [0.1*cos(60°),0.1*sin(60°)] = [0.05,-0.0866] m/s.
The final velocity vector of m2 is given by v2f = [m1*cos(φ), m1*sin(φ)]. Substituting the given values, we have v2f = [0.1*cos(-30°),0.1*sin(-30°)] = [0.0866,-0.05] m/s.
b) To determine whether this is an elastic or inelastic collision, we need to check if the total kinetic energy before the collision is equal to the total kinetic energy after the collision. If it is, the collision is elastic; otherwise, it is inelastic.
Calculating the initial and final kinetic energies:
Initial kinetic energy: KE_initial = (1/2)*m1*v1^2 = 0.5 * 0.1 * (8^2 + 0^2) = 1.6 J
Final kinetic energy: KE_final = (1/2)*m1*v1f^2 + (1/2)*m2*v2f^2 = 0.5 * 0.1 * (0.05^2 + (-0.0866)^2) + 0.5 * 0.4 * (0.0866^2 + (-0.05)^2) = 0.004062 J
Since KE_initial is not equal to KE_final, the collision is inelastic.
c) Since the collision is inelastic, some of the initial kinetic energy is converted to another form. To calculate the energy converted, we subtract the final kinetic energy from the initial kinetic energy: Energy converted = KE_initial - KE_final = 1.6 J - 0.004062 J = 1.595938 J.