Final answer:
Potential energy can be negative depending on the chosen reference point, while kinetic energy must always be positive or zero. Total mechanical energy can be negative if the magnitude of negative potential energy exceeds that of kinetic energy. The total mechanical energy remains constant if only conservative forces are at work.
Step-by-step explanation:
Can potential energy be negative? The answer is yes; potential energy can be negative, as its value is relative to a chosen zero level or reference point. For gravity, this often means the ground, but it could technically be any point. On the other hand, kinetic energy must always be positive or zero because it is defined by the mass and the square of the velocity of an object (1/2 mv^2), both of which are inherently positive values or zero, and cannot be negative.
As for total mechanical energy, which is the sum of kinetic and potential energy, it can be negative if the negative potential energy is greater than the kinetic energy. This is because while kinetic energy cannot be negative, potential energy can offset the total value if it is negative and greater in magnitude. It's important to remember that the Law of Conservation of Mechanical Energy states that if no non-conservative forces (like friction or air resistance) are acting on a system, the total mechanical energy remains constant, but this does not imply that it cannot be negative.
Lastly, a system's kinetic energy and potential energy can change without work being done if these changes are due to conservative forces, like gravity, as these forces can convert energy between kinetic and potential forms. This conservation implies that while the individual forms of energy may vary, the total mechanical energy of the system remains constant in the absence of non-conservative forces.