Friction as a Non-conservative force

Question

Intuitively, one can find friction to be a non-conservative force. How can one prove that it is non-conservative?

Answer 1

A conservative force must satisfy the property that the total work done must be independent of the path traveled. In physics, work is defined as the force along a given path times the distance of this path so that, simply:

$$ \text{work} = \sum_\text{paths} F\cdot l_\text{path} = \sum_\text{paths} \text{force along path}\times \text{path distance} $$

Since force of friction is along the direction one is traveling, taking a different path will accumulate work which is given by

$$ \text{work}_\text{friction} = \sum_\text{paths} F_\text{friction}\cdot l_\text{path} = F_\text{friction}\times\text{length of total path} $$

Finally, since the work done by the friction depends on the path one takes, it is not considered a conservative force.

On a less rigorous note, any force which converts some form of kinetic energy or potential energy into heat will not satisfy the property of a conservative force.

Answer 2

1.It does not follow law of conservation of mass

2.work done by this force in a loop is equal to zero

3.it depends on path followed by the object (body)