Forces are categorized based on how they interact with a system’s energy. Conservative forces allow energy to be stored and fully recovered, such as the force of gravity when lifting an object. Non-conservative forces fundamentally change the amount of usable mechanical energy within a system. This distinction determines whether a system’s energy can be simply converted or whether some energy will be permanently lost from the system in its original form. Understanding these forces helps explain why a swinging pendulum eventually stops or why a car needs continuous fuel to maintain speed.
Defining Path Dependence
The defining characteristic of a non-conservative force is that the work it does on an object depends on the path taken between the starting and ending points. This property is known as path dependence. For instance, imagine moving a heavy box from one corner of a room to the opposite corner.
If you push the box in a straight line, the force of friction acts over a shorter distance than if you push the box in a zigzag pattern. Because friction acts against the motion, the total work done is greater over the longer path. This means the energy expended is determined by the actual distance traveled, not just the initial and final locations.
A force is considered non-conservative if an object moved in a closed loop—returning to its starting point—results in a net amount of non-zero work done by that force. The work done is cumulative along every segment of the path, illustrating why the total length is important for these forces.
Non-Conservative Forces and Energy Transformation
Non-conservative forces remove energy from a system’s mechanical energy, which is the sum of kinetic energy (energy of motion) and potential energy (stored energy). When these forces act, they dissipate mechanical energy by transforming it into non-mechanical forms. This process most commonly results in the generation of thermal energy, or heat, but it can also produce sound or light.
For example, when an object slides across a rough surface, friction converts the object’s kinetic energy into heat, which raises the temperature of the surfaces. This heat then spreads into the surrounding environment and is not readily available to return to the object as mechanical energy.
While the total energy of the universe remains conserved, according to the First Law of Thermodynamics, the total mechanical energy within the specific system is not conserved when non-conservative forces are present. The work done by these forces equals the change in the system’s mechanical energy. If the force opposes the motion, the work done is negative, and the system loses mechanical energy.
Identifying Common Examples
Non-conservative forces are common in everyday life and include several easily recognizable examples.
Kinetic friction is the classic example, acting between surfaces that are moving relative to one another. This force always opposes the direction of motion, meaning the longer an object slides, the greater the distance over which friction acts, leading to a greater loss of mechanical energy as heat.
Air resistance, also known as drag, acts on objects moving through a fluid like air or water. The magnitude of the drag force depends on factors such as the object’s speed, cross-sectional area, and the density of the fluid. As an object falls, air resistance converts its energy into heat in the air and on the object’s surface.
An applied force, such as a person pushing or pulling an object, can also be non-conservative. If a person pushes a box along a long route, they perform more total work than if they pushed the box in a straight line to the same final spot. This external push or pull adds or removes energy from the system based on the distance over which the force is maintained.