Negative work indicates that energy is being extracted from a system.

In physics, work is defined as the energy transferred by a force acting over a distance. It is calculated using the formula:

where $W$ represents work, $F$ is the applied force, $d$ is the distance over which the force acts, and $\theta$ is the angle between the direction of the force and the direction of motion. When work is done on an object, energy is transferred to that object. Conversely, if the work done is negative, it signifies that energy is being withdrawn from the object or system.

Negative work typically occurs when the force applied acts in the opposite direction to the object’s motion. For instance, when you push a box across the floor, you perform positive work on the box since both the force exerted (the push) and the box’s motion are aligned in the same direction. However, if you attempt to push the box but it slides back toward you—perhaps due to an incline—you are performing negative work on it. In this scenario, your applied force moves in one direction while the box moves in the opposite direction, resulting in energy being removed from the system—specifically, from your efforts to push the box.

Additionally, negative work is commonly associated with resistive forces such as friction or air resistance. These forces always act against the direction of motion, thereby performing negative work on the object. For example, when you slide a book across a table, it eventually comes to a stop because friction between the book and the table does negative work on the book, dissipating its energy and halting its motion.

In summary, negative work is a fundamental concept in physics that signifies the extraction of energy from a system. It arises when the force applied to an object opposes its motion and is frequently linked to resistive forces like friction and air resistance.