# Understanding Conservative and Non-conservative Force

Understanding the difference between conservative and non-conservative forces is crucial for understanding how external factors impact how physical objects behave. These ideas are essential to understanding how interactions control particle motion and energy changes in systems. Conservative forces, like gravity and spring tension, have amazing characteristics in that they conserve mechanical energy in a system without caring exactly which path an object takes. On the other hand, non-conservative forces have a distinct function and are represented by phenomena like air resistance and friction.

They move mechanical energy, and the specific path an object follows determines the work it accomplishes. Well, in this article, I’ll be discussing the definition, characteristics, formula, examples, and the difference between conservative and non-conservative forces.

Contents

## What is Conservative Force?

A conservative force is a force that doesn’t depend on a path taken between two points; rather, it depends only on the initial and final positions of an object. Because they conserve mechanical energy within a system, these forces are conservative. Put simply, a conservative force produces work that is path-independent or identical along every path that connects two points. Conservative forces include the force of gravity, an electrostatic force, and a spring’s force.

## Characteristics of Conservative Forces

• Path-Independence: Regardless of the precise path followed, a conservative force must exert the same amount of effort to move an object between two points.
• Conservation of Mechanical Energy: A system’s total mechanical energy, which is the sum of its kinetic and potential energy, is constant in the absence of non-conservative forces like friction or air resistance.

## Formula

Work done by a conservative force (W):

W  = −ΔU

Where:

W is the work done by the conservative force.

ΔU is the change in potential energy.

Conservation of Mechanical Energy:

Emechanical ​= KE + PE

Where:

Emechanical​ is the total mechanical energy, which is the sum of kinetic energy (KE) and potential energy (PE).

In the absence of non-conservative forces, Emechanical​ remains constant.

## Examples of Conservative Force

The following are examples of conservative force:

### Gravitational Force

A popular illustration of a conservative force is gravity. The effort required to raise an object against gravity to a given height and then release it is stored as potential energy. This potential energy is transformed back into kinetic energy as the object descends. The object’s path has no bearing on the result in the end. Assuming no non-conservative forces (such as air resistance) are present, the total mechanical energy (potential + kinetic) remains constant.

### Spring Force

Another example of a conservative force is the force generated by a spring. A spring’s potential energy is directly proportional to its deformation when it is compressed or stretched. It is possible to transform this potential energy into kinetic energy and vice versa. The mechanical energy is conserved, and the final result is unaffected by the precise path chosen to compress or stretch the spring.

## What is a non-conservative force?

Conversely, forces that fail to conserve mechanical energy within a system are known as non-conservative forces. Non-conservative forces operate not only on an object’s initial and final positions but also on its particular path. Non-conservative forces include friction, air resistance, and applied forces (such as pushing or pulling an object).

In other words, a force is said to be a non-conservative force if it results in a change in mechanical energy, which is nothing but the sum of potential and kinetic energy. The work done by a non-conservative force adds or removes mechanical energy. For example, when work is done by friction, thermal energy is dissipated. The energy lost cannot be fully recovered.

## Characteristics of Non-Conservative Forces

Path-Dependence: The work done by non-conservative forces varies depending on the path taken by an object.
Mechanical Energy Dissipation: Non-conservative forces lead to a dissipation of mechanical energy, converting it into other forms, such as thermal energy (heat).

## Formula

Mathematically, for a non-conservative force, the work done is given by:

W = ΔEmechanical​

Where:

is the work done by the force.

ΔEmechanical​ is the change in mechanical energy, which is the sum of kinetic and potential energy.

## Examples

The following are examples of non-conservative forces:

### Friction

A common example of a non-conservative force is friction. The quantity of work that friction does when pushing an object along a rough surface—like a block on a table—depends on the precise route the object travels. Additionally, heat is released as a result of the dissipation of mechanical energy. This indicates that because friction is non-conservative, neither the system’s initial nor final mechanical energy is conserved; instead, the energy is lost as heat.

### Air Resistance

When an object moves through the atmosphere, it will encounter air resistance, a non-conservative force. The volume of work that air resistance does when an object, such as a parachute jumper, falls through the air depends on the object’s velocity and the exact path that it takes. The system’s mechanical energy is not conserved because air resistance causes some of it to be lost as heat.

## Difference between conservative and non-conservative forces

The key differences between conservative and non-conservative forces are as follows:

### Path Independence vs. Path Dependence

Conservative forces don’t care about a path. meaning that the work performed by a conservative force is the same regardless of the exact path an object takes to get from one point to another. The initial and final positions are the only ones that affect the work. Non-conservative forces, however, depend on the path taken. Depending on the precise route an object takes between two points, non-conservative forces perform different amounts of work. The entire path—rather than just the starting and finishing points—determines the work.

### Conservation of Mechanical Energy

• In the absence of non-conservative forces, conservative forces conserve mechanical energy within a system. The total mechanical energy (the sum of kinetic and potential energy) remains constant. On the other hand, non-conservative forces do not conserve mechanical energy. They often lead to the dissipation of mechanical energy into other forms, such as heat or sound. The mechanical energy of the system is not conserved.

### Work Calculation

The work done by a conservative force is calculated as the negative change in potential energy:
W = −ΔU.
The work done by a non-conservative force is calculated as the change in mechanical energy:
W = ΔEmechanical

### Examples

Examples of conservative forces include gravitational force, spring force, and electrostatic force. In contrast, examples of non-conservative forces include friction, air resistance, and applied forces (e.g., pushing or pulling an object).

## Conclusion

In summary, conservative forces are path-independent and conserve mechanical energy, and their work depends on the change in potential energy. Non-conservative forces are path-dependent and dissipate mechanical energy, and their work accounts for the change in mechanical energy. These distinctions are crucial for understanding the behavior of objects in the physical world and have practical applications across various fields of science and engineering.