Answer
In a completely inelastic collision, the two colliding objects stick together and move as a single unit after the collision. In this case, the two balls of equal mass collide head on and come to rest after the collision.
(a) The kinetic energy is not conserved in a completely inelastic collision. Before the collision, the balls have some initial kinetic energy due to their motion, but after the collision, the balls come to rest and all of their kinetic energy is lost. This lost kinetic energy is converted into other forms of energy, such as heat and deformation of the balls. Therefore, the kinetic energy is not conserved in this type of collision.
(b) The momentum is conserved in the collision. Momentum is conserved in all types of collisions, including inelastic collisions. Before the collision, the two balls have opposite momenta of equal magnitudes. Since the balls stick together after the collision and move as a single unit, their final momentum is zero. Therefore, the total momentum of the system is conserved, as the sum of the initial momenta is equal to the final momentum, which is zero.
In summary, in a completely inelastic collision between two balls of equal mass colliding head on, the kinetic energy is not conserved, but the momentum is conserved.
Work Step by Step
It must be true that
$\vec{v_i} = \vec{-v_f}$
