What is the significance of a negative work done?

A negative work done signifies that energy is being taken away from the system.

In physics, work is defined as the amount of energy transferred by a force over a distance. It is calculated as the product of the force applied and the distance over which it is applied, and it is also dependent on the angle between the force and the direction of motion. When work is done on an object, energy is transferred to that object. However, if the work done is negative, it means that energy is being removed from the object or system.

This typically happens when the force applied is in the opposite direction to the motion of the object. For example, if you push a box across the floor, you are doing positive work on the box because the force you apply (the push) and the direction of the box's motion are in the same direction. However, if you try to push the box but it slides back towards you (perhaps because the floor is sloped), then you are doing negative work on the box. The force you apply is in one direction, but the box moves in the opposite direction. This means that energy is being taken away from the system - in this case, from your efforts to push the box.

Negative work is also associated with resistive forces like friction or air resistance. These forces always act in the opposite direction to the motion, and so they do negative work on the object. This is why when you slide a book across a table, it eventually stops. The friction between the book and the table does negative work on the book, removing energy from it and eventually bringing it to a stop.

In summary, negative work is a concept in physics that represents the removal of energy from a system. It occurs when the force applied to an object is in the opposite direction to its motion, and is often associated with resistive forces like friction or air resistance.