What condition is necessary for potential energy to be negative, as seen in the example with the block?

Potential energy is often defined relative to a designated reference point, typically where potential energy is considered to be zero. This reference point can vary depending on the system being analyzed, such as the height of an object above ground level or the position of a block in a gravitational field.

When we say that potential energy is negative, we are typically referring to the situation where the object is located below that chosen reference level. For example, if the reference point is set at ground level and an object, like a block, is positioned below this level, then its gravitational potential energy will indeed be negative. This reflects the fact that the block is lower than the reference level, and hence, it would require energy input to raise it back up to that zero potential reference.

In contrast, other conditions mentioned, such as when an object is moving, having zero mass, or lacking energy input, do not inherently dictate the sign of potential energy. Movement does not affect the potential energy's reference point, mass only affects the calculation of potential energy in terms of gravitational influence, and energy input is not directly related to defining the sign of potential energy itself.

Thus, the correct condition for potential energy to be negative is indeed when it is below the designated zero potential energy