What is the mass m of the ball in the following case?
A ball of mass m moving at 15 m/s has an elastic collision with a ball of mass 2 kg after which it moves back at 12 m/s and the other ball moves forward at 6 m/s.
In an elastic collision the total momentum as well as total kinetic energy of the system is conserved.
Using the conservation of momentum and the values given in the problem:
15*m + 0*2 = -12*m + 2*6
=> 27m = 12
=> m = 12/27
But for this value of mass, the initial total kinetic energy of the system is (1/2)*(12/27)*15^2 + 0 = 50 J
And the final kinetic energy is (1/2)*(12/27)*12^2 + (1/2)*2*6^2 = 68 J
The given values of initial and final velocity of the colliding bodies do not satisfy the conditions for an elastic collision for any value of m.
It is not possible to find a value of m that satisfies the essential condition of an elastic collision that the total initial kinetic energy of the system is equal to the total final kinetic energy of the system. The collision is inelastic for all values of m.