**Conservative Forces Class 11 Physics – Learn Example, Properties & Principle**

*In physics, there are different forces acting our surroundings, as we know that force is any interaction, that when unopposed, will change the motion of an object. Basically forces can be categorized as Conservative forces and Non-conservative forces. *

*Conservative forces are an important aspect of physics. Many forces of nature are conservative like*

*gravitational force, electrostatic force, magnetic force, and elastic force (spring’s force).*

**CONSERVATIVE FORCES**

A force is said to be **Conservative **if the work done by or against it in moving an object is independent of its object’s path.

*Conservative force can be defined as:*

*“A conservative force is a force whose work done is independent of the path taken and depends only on the initial and final positions”*

If a particle travels in a *closed-loop*, the net work done (*the sum of the force acting along the path multiplied by the displacement*) by a conservative force is ** zero** i.e. the total work done by a conservative force is independent of the path resulting in a given displacement and is equal to

*zero*when the path is a

*closed loop.*Stored energy, or

**, can be defined only for conservative forces.**

*potential energy*

It is possible to assign a **numerical value** for the *potential* at any point. When an object moves from one location to another, the force changes the potential energy of the object by an amount that does not depend on the ** path **taken, contributing to the

*mechanical energy*

*and the overall*

*conservation of energy*.

**EXAMPLES OF CONSERVATIVE FORCES**

The most common example of **conservative force** is a *gravitational force*, other examples are a *magnetic force, spring force, electrostatic force* and many others

The force exerted by a spring is another example of a conservative force. The total work done on a mass by a spring *does not depend on the path taken by the mass*. It only depends on the **initial** and **final positions** of the mass. The term conservative comes from the fact that conservative forces conserve mechanical energy, whereas non-conservative forces do not conserve mechanical energy. The most common example of **conservative force** is a *gravitational force*, other examples are a *magnetic force**, **spring force**, **electrostatic force* and many others.

**PRINCIPLE OF CONSERVATIVE FORCES**

A **conservative ****force** is dependent only on the position of the object and exists when the work done by that **force** on an object is independent of the object’s path. Instead, the work done by a **conservative force** depends only on the endpoints of the motion. An example of a** conservative force** is gravity

**WORK DONE BY CONSERVATIVE FORCE**

*The network done (the sum of the force acting along the path multiplied by the displacement) by a conservative force is zero.*

The work done by this force in moving this particle from one point to another is *independent* of the path taken. To put it another way, the work done depends only on the initial and final position of the particle (relative to some coordinate system)

Suppose a particle starts at point A, and there is a force *F* acting on it. Then the particle is moved around by other forces and eventually ends up at A again. Though the particle may still be moving, at that instant when it passes point A again, it has traveled a closed path. If the network done by *F* at this point is 0, then *F* passes the closed path test. Any force that passes the closed path test for all possible closed paths is classified as a ** conservative force**.

The work done by a conservative force is the same for

any path connecting two points:

*Work is done by gravitational force*

*Work is done by gravitational force*

The work done by gravity on the body is dependent only on the change in vertical height Δ*h* of the *center of mass *

of the body, as it moves from *A* to *B*.

If Δ*h* is equal to the final vertical position (at point *B*) of the center of mass minus the initial vertical position (at point *A*) of the center of mass, then the work (*W _{g}*) done by gravity on the body is given by the following scalar equation:

Note that it doesn’t matter at all how the body moves. We only need to know the change in vertical position of its center of mass (as it moves from *A* to *B*) to determine the work done on the body by gravity. Therefore, *gravity is a conservative force.*

**PROPERTIES OF CONSERVATIVE FORCES**

Conservative forces have following properties:-

- The force only dependent on the initial and final position irrespective of the path taken.
- In any closed path, the work done by a conservative force is zero.
- The work done by a conservative is reversible.
- A conservative force results in stored or potential energy.
- Work and energy associated with the force can be recovered.

When only conservative forces act on and within a system, the total mechanical energy is ** constant**. In equation form:

where i and f denote initial and final values. This is known as the *conservation of mechanical energy***.**

** **

**CONCLUSION**

The work done from two arbitrary positions would be conservative force is a force that generates zero networks when going applying a force from point A to point B and then from point B to point A. I don’t love this definition, but it’s what I can most closely describe it as given my new understanding of the math behind it. Say you have a central force

The work done from two arbitrary positions would be

For the force to be conservative, the work done from this path integral from r2 to r1 instead must be the exact same

The work of a conservative force does on an object is moving it from A to B is path independent –* it depends only on the endpoints of the motion.* Examples: the force of gravity and the spring force are conservative forces. For the force to be conservative, the work done from this path integral from r2 to r1 instead must be the exact same.

*The sum of the kinetic energies and potential energies remains constant if only conservative forces act on and within a system.*

Read another topic on **Scalar and vector**

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