The relationship between potential energy (PE) and kinetic energy (KE) for a person standing on a diving platform can be understood through the principles of energy conservation.
-
Potential Energy (PE): When the person is standing on the diving platform, they possess gravitational potential energy due to their height above the ground (or water surface). The potential energy can be calculated using the formula: \[ \text{PE} = mgh \] where \(m\) is the mass of the person, \(g\) is the acceleration due to gravity, and \(h\) is the height of the platform above the pool.
-
Kinetic Energy (KE): As the person dives off the platform, that potential energy begins to convert into kinetic energy as they fall. The kinetic energy of the person while falling can be expressed as: \[ \text{KE} = \frac{1}{2}mv^2 \] where \(v\) is the velocity of the person.
-
Energy Transformation:
- When the person is at rest at the top of the platform, all their energy is potential energy (PE is at its maximum, and KE is zero).
- As they begin to dive and fall, the potential energy decreases while the kinetic energy increases, assuming no other forces (like air resistance) are significantly acting on them.
- Just before entering the water, the person’s height (and thus their potential energy) is minimal, and their velocity is at its maximum, meaning kinetic energy is at its highest.
-
Conservation of Energy: According to the conservation of energy, the total mechanical energy (the sum of potential and kinetic energy) of the person in a closed system remains constant. Thus, neglecting air resistance and other dissipative forces: \[ \text{PE}{\text{initial}} + \text{KE}{\text{initial}} = \text{PE}{\text{final}} + \text{KE}{\text{final}} \] At the top: \(\text{PE}{\text{initial}} = mgh\), and \(\text{KE}{\text{initial}} = 0\). Just before entering the water: \(\text{PE}{\text{final}} = 0\), and \(\text{KE}{\text{final}} = \frac{1}{2}mv^2\).
Thus, as the person dives, the decrease in potential energy results in an equal increase in kinetic energy, illustrating the constant total energy in the absence of external work or losses.
1 answer