Work Done by the Conservative Force in a Closed Path is Zero

Conservative force is the force applied to move a particle from one point to another. It is not dependent on the path taken by the particle. It only depends on two factors: the initial and final positions of the particle. The conservative force is responsible for the orderly motion of particles and atoms in a material. It is also responsible for energy conservation and the stability of matter.

A few examples of conservative forces are elastic spring forces, electrostatic forces, and gravitational forces. Work done by the conservative force in a closed path is zero, as the work done by a conservative force depends only on the initial and final positions of the objects involved, not on the journey between those two points.

Non-conservative Force

The force where the total work is done depends on the path taken. The resultant force changes mechanical energy and the sum of potential and kinetic energy, for instance, the work done by frictional force. The energy is spread in the form of thermal energy. This cannot be recovered entirely. 

A few examples of non-conservative forces are viscous force and frictional force.

Total Work Done By Gravity In a Particle

The conservative force formula calculates the forces between particles in contact with each other. It is also used to calculate the forces between masses and particles in contact. The conservative force formula is derived from the conservation of energy law, and it states that the total energy of a system remains constant over time – work done by conservative force is always positive.

The total work done by gravity on the body is given by the equation below:

Wg = -mg (Δh)

where,

•   Let A = the initial position
•   B= the final position
•   Δh = the final position between the two points (initial and final)
•   g = the acceleration due to gravity
•   m = the mass of the body

Properties: Conservative Forces

A force can be a conservative force if it has the following properties:

•   When the force is dependent on two factors, the initial and final positions, it doesn’t depend on the path taken
•   Work done by the conservative force in a closed path is zero
•   The work done can be reversed

To calculate the work done by a conservative force, you’ll need to know the magnitude of the force and the object’s displacement. So first, multiply the magnitude of the force by the distance it moves. It will give you the total work done by the force. Next, divide this number by the time it takes for the object to move that distance. It will give you the average power output of the force.

•     To calculate work done by a conservative force, use the following equation: W = Fd
•   where W is work done, F is the force acting on the object, and d is the distance between the force and the object and is a constant

Properties: Non-Conservative Forces

A force can be a non-conservative force if it has the following properties:

•   When the force is dependent on the path, it depends on the initial and final positions also
• Work done by non-conservative force in a closed path is not zero
•   The work done cannot be reversed (it is non-reversible)

Conclusion

Conservative force is not dependent on the path taken by the particle. It only depends on two factors: the initial and final positions of the particle. Conservative force is a physical force that preserves total energy. That means that the work done by a conservative force is always reversible. A conserveative force is always conservative because it respects the path’s independence. Additionally, the work done by a conservative force depends only on the initial and final positions of the objects involved, not on the journey between those two points.