Why is the work done by a spring considered negative when stretched from its equilibrium position?

The work done by a spring is considered negative when it is stretched from its equilibrium position because the spring force acts in the opposite direction of the displacement caused by stretching. When you stretch a spring, you do work against the restorative force exerted by the spring, which attempts to return the spring to its equilibrium position.

As you apply a force to stretch the spring, you are indeed putting energy into the system. This energy is stored in the spring as potential energy, commonly referred to as elastic potential energy. However, since the direction of the spring's force opposes the direction of your applied force (the force you exert to stretch it), the work done by the spring is termed negative.

Thus, when considering the choices, the understanding revolves around the energy dynamics at play: the work done against the spring's restoring force reflects that the energy associated with stretching (stored as potential energy) contributes to the negative work done by the spring itself. Therefore, while it is accurate to say that the spring does work on the system negatively (indicating it is returning to its equilibrium), it also holds true that all of these statements together represent the complete view of why the work done is considered negative.