Final answer:
When two boxes collide on a frictionless surface, the total momentum is conserved. The initial and final kinetic energies of the system are not equal, as the system slows down and eventually comes to a stop.
Step-by-step explanation:
In this scenario, a box is sliding on a frictionless surface and collides with and sticks to a second identical box which is initially at rest. Since the surface is frictionless, no external forces are acting on the system of the two boxes. Therefore, the law of conservation of momentum states that the total momentum of the system before the collision is equal to the total momentum of the system after the collision.
Before the collision, the first box has a momentum of mass A * initial velocity of A. The second box is initially at rest, so it has no momentum. After the collision, the two boxes stick together and move as one. Therefore, their combined momentum is the sum of their individual momenta after the collision.
Since the objects stick together and move as one, their final velocity will be the same. Therefore, their momentum after the collision is combined mass of A and B * final velocity.
As we can see, the initial and final kinetic energies of the system of two boxes are not equal. Initially, the system has kinetic energy due to the motion of the first box. After the collision, the system slows down and eventually comes to a stop. Therefore, the final kinetic energy of the system is zero.