The principle of mechanical energy conservation states that the total mechanical energy in a closed system remains constant, provided no non-conservative forces (like friction or air resistance) act on the system.
This total mechanical energy (\( E \) ) is the sum of kinetic energy (\( KE \) ) and potential energy (\( PE \) ):
\( E = KE + PE \)
In a frictionless environment, if an object's kinetic energy decreases, its potential energy increases by an equal amount, and vice versa. This concept is what allows us to predict the highest potential and kinetic energies. In the original exercise, both types of energy can reach 40 J because the total is conserved:
- **Greatest Kinetic Energy**: Achieved when all energy is kinetic, potential energy is zero.
- **Greatest Potential Energy**: Achieved when all energy is potential, kinetic energy is zero.
Understanding this conservation principle helps in analyzing how energy transfers and transforms in various physics problems, ensuring no energy is lost, only transformed.