Final answer:
The law of conservation of energy dictates that the sum of potential and kinetic energy within a closed system remains constant, as energy can neither be created nor destroyed, only transformed from one form to another.
Step-by-step explanation:
Based on the law of conservation of energy, the sum of potential and kinetic energy is constant. This principle states that within a closed system, energy cannot be created or destroyed but can change from one form to another. Therefore, when potential energy is converted to kinetic energy or vice versa, the total energy remains unchanged. As an example, if you lift a ball to a certain height, it gains potential energy, which then converts to kinetic energy when the ball is released and falls, yet the sum of both types of energy throughout this process remains constant.