In a frictionless system, energy is conserved. If the mechanical energy remains the same over time, which statement is true?

In a frictionless system, energy is conserved. If the mechanical energy remains the same over time, which statement is true?

• A. ME decreases
• B. ME increases
• C. ME depends on time
• D. ME remains constant

Answer: (D)

In a frictionless system, the total mechanical energy stays the same because there are no non-conservative forces taking energy away or adding energy to the system. Mechanical energy is the sum of kinetic energy (energy of motion) and potential energy (energy due to position). As the system evolves, energy simply shifts between these two forms—when speed is high, kinetic energy is high and potential energy is low, and when the object climbs or slows, kinetic energy decreases while potential energy increases. Yet their total remains constant. So the statement that the mechanical energy remains constant is the correct one. If mechanical energy were to decrease or increase, that would imply energy is being dissipated (like friction) or added from an external source, which isn’t present in a frictionless setup. If it depended on time, that would also contradict energy conservation in this ideal case.

In a frictionless system, the total mechanical energy stays the same because there are no non-conservative forces taking energy away or adding energy to the system. Mechanical energy is the sum of kinetic energy (energy of motion) and potential energy (energy due to position). As the system evolves, energy simply shifts between these two forms—when speed is high, kinetic energy is high and potential energy is low, and when the object climbs or slows, kinetic energy decreases while potential energy increases. Yet their total remains constant. So the statement that the mechanical energy remains constant is the correct one. If mechanical energy were to decrease or increase, that would imply energy is being dissipated (like friction) or added from an external source, which isn’t present in a frictionless setup. If it depended on time, that would also contradict energy conservation in this ideal case.