 # Conservative Force

The concept of force is a crucial aspect for physicists to learn in detail. When studying it, one should not neglect its various types, including conservative and non-conservative forces. Consequently, a vital topic for students is to understand how to define conservative force.

What is Conservative Force?

Conservative force is any force necessary to move a particle from one point to another, independent of this particle’s path. Therefore, the work done by conservative force only relies on the start and end-point, and not on the path taken.

Fig Conservative force in the form of gravity

One of the most common conservative force examples is gravity. Other examples are magnetic, electrostatic and elastic force.

Conservative force relies on the principles of conservation of energy. Conservation of energy primarily deals with conservation of kinetic energy.

Example – 1

Suppose you drop a ball from the top of a ladder. As a conservative force, the gravity will be calculated while the ball is at the maximum height and again when it reaches the ground.

Gravitational force = m x g

Where m = ball’s mass

g = gravitational acceleration

Therefore, we can say that work done on the body is

Wg = -mgh

Here, h refers to the difference between the final position of a body and its initial position.

Understanding the Properties of Conservative Force

Now that you know the conservative force definition, let us proceed to some of the known properties of it.

• When you consider a loop, the work completed by a conservative force will always be zero. This is because there is no defined starting or ending point inside a loop.

• You can easily reverse the work completed when it comes to a force which is conservative. Therefore, work done by a gravitational force can be easily reversed.

• Lastly, the conservative force is only dependent on the final and initial position of the object. All other positions in between do not affect the final outcome.

Now that you know what is conservative force, you must also assess what non-conservative force means.

What is Non-conservative Force?

Non-conservative force refers to any force where the path taken by the object defines the work done using that force. You can consider friction as an example of non-conservative force.

Example – 2

Suppose a body moves from point A to point B. Another body moves from point A to Point B, after visiting point C. Therefore, the second body will require greater force to complete its journey to point B.

As you can see, here, the path of a body greatly determines the force acting on it and the resulting work done.

Refer to the table below to understand the distinction between a conservative force field and a non-conservative one.

## Differences Between Conservative Force and Non-conservative Force

 Non-conservative Force Conservative Force Work done by a non-conservative force inside an enclosed path is never zero. Work done by conservative force inside a closed loop is always nil. Non-conservative force is any force where the path taken by an object determines the work done by or against that body. Conservative force is any force where the initial and final position of a body determines the work done by or against it. Common examples include frictional force, cyclotron’s induction force, viscous force and more. Examples of conservative forces is electrostatic force, gravitational force, magnetic force, etc.

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