To determine which equation correctly represents how the total mechanical energy (ME) of a system relates to its kinetic energy (KE) and gravitational potential energy (GPE), we need to understand the principle behind mechanical energy in classical mechanics.
Total mechanical energy in a system is the sum of its kinetic energy and gravitational potential energy. This is because mechanical energy is conserved in a closed system where only conservative forces are acting (such as gravity).
Let's review the options given:
A. \( ME = GPE - KE \)
- This equation implies that total mechanical energy is found by subtracting the kinetic energy from the gravitational potential energy, which contradicts our understanding that they are summed up.
B. \( ME = KE - GPE \)
- This equation suggests that mechanical energy is obtained by subtracting gravitational potential energy from the kinetic energy, which is also incorrect based on the established relationship.
C. \( ME = GPE \times KE \)
- This implies the total mechanical energy is the product of gravitational potential energy and kinetic energy, which is incorrect since mechanical energy is additive, not multiplicative.
D. \( ME = KE + GPE \)
- This correctly states that total mechanical energy is the sum of kinetic energy and gravitational potential energy. This is aligned with the principle of conservation of mechanical energy in classical mechanics.
Therefore, the correct equation that represents how the total mechanical energy (ME) of a system relates to its kinetic energy (KE) and gravitational potential energy (GPE) is:
[tex]\( \boxed{D. \ ME = KE + GPE} \)[/tex]
