Kinetic energy and potential energy are two fundamental forms of mechanical energy in physics, and their relationship is governed by the principles of conservation of energy.
To understand why kinetic energy can’t exceed potential energy, consider an object moving within a closed system, like a pendulum. At the highest point of its swing, the pendulum has maximum potential energy and zero kinetic energy. As it falls, potential energy is converted into kinetic energy. At the lowest point, potential energy is at its minimum, while kinetic energy reaches its maximum.
The key point is that the total mechanical energy in this system remains constant, barring any friction or external work. Thus, when kinetic energy increases, potential energy decreases in such a way that the total energy is preserved. Therefore, at any given moment, the maximum kinetic energy will always be limited to the amount of potential energy available in the system.
In summary, while kinetic energy can approach the value of potential energy, it cannot exceed it due to the conservation of energy. This principle ensures that the energy is merely transformed between these two states but remains confined within the total mechanical energy of the system.