Final Answer:
As Johanna's little brother swings, there is a continuous interchange between kinetic and potential energy. At the highest point of the swing, the potential energy is maximized, while at the lowest point, kinetic energy is at its peak.
Step-by-step explanation:
The transformation between kinetic and potential energy during the swinging motion adheres to the principles of mechanical energy conservation. When Johanna's little brother is at the highest point of the swing, all of his energy is in the form of potential energy.
The potential energy (PE) can be calculated using the formula PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height. As he descends, this potential energy is converted into kinetic energy (KE), given by the formula KE = 1/2 * mv², where m is the mass and v is the velocity. At the lowest point of the swing, when potential energy is at its minimum, kinetic energy is at its maximum.
Throughout the swinging motion, the sum of potential and kinetic energy remains constant, neglecting factors such as air resistance and friction. This conservation of mechanical energy is a manifestation of the law of conservation of energy. It implies that as the little brother swings back and forth, the energy transformation between kinetic and potential states is continual, resulting in a dynamic and entertaining experience at the playground.