To understand why the initial kinetic energy of the single billiard ball will be evenly distributed among the 15 balls after the collision, we need to consider the principles of conservation of momentum and conservation of kinetic energy.
Conservation of momentum states that the total momentum of a system before a collision is equal to the total momentum after the collision, provided there are no external forces acting on the system. In this case, since there are no external forces acting on the system of 15 balls, the total momentum of the system will remain constant.
Now let's break down the collision:
1. Initially, there is a single billiard ball moving with a certain velocity. Let's call this ball Ball A.
2. The other 14 balls, which are initially at rest, form a cluster. Let's call this cluster Cluster B.
When Ball A collides with Cluster B, it exerts a force on the balls in the cluster, causing them to start moving. The transfer of momentum from Ball A to Cluster B causes Ball A to slow down, while the balls in Cluster B gain momentum.
Since the total momentum of the system remains constant, the decrease in Ball A's momentum is equal to the increase in momentum of Cluster B. Therefore, the momentum transferred from Ball A to Cluster B is distributed evenly among the 14 balls in the cluster.
Now let's consider the conservation of kinetic energy. When Ball A collides with the cluster, some kinetic energy is transferred from Ball A to the balls in the cluster, causing them to gain kinetic energy and start moving. If we assume all the balls in the cluster are the same mass, the kinetic energy will be evenly distributed among the 15 balls due to the principle of conservation of kinetic energy.
So, in conclusion, the initial kinetic energy of the single billiard ball will be evenly distributed among the 15 balls in the cluster after the collision, provided there are no external forces acting on the system.