# Non-Conservative Forces: What is it & Why it Matters (w/ Examples)

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A car driving on a winding route, perhaps with multiple stops along the way, will wear down its tires faster than one which takes the straighter highway path from Point A to B.

This is because the tires feel the force of friction at every moment they are in contact with the road; the longer the journey, the more friction and thus the more thermal energy, or heat, that is generated and lost to the environment.

The heat from friction is no longer available to the car to continue doing work – the only way to keep it going is to add fuel. Thus the force of friction has not resulted in any stored energy. In fact, it resulted in something of the opposite – a transformation of energy from a more useful to a less useful form.

## Definition of a Non-Conservative Force

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• A non-conservative force does not result in any stored energy.

The work done by a non-conservative force depends on the path taken; the longer the path, the more thermal energy that is dissipated to the surrounding environment. This energy cannot be reused entirely (even if some of it were retained, 100 percent of it could not be reused for more work).

Because the law of conservation of energy dictates that the total energy in a closed system cannot change, the total work done by non-conservative forces must equal the change in mechanical energy of the system. In other words, all the energy that is "lost" in a closed system is a result of non-conservative forces.

In contrast, a conservative force results in work that stores potential energy that can be reused later. The net work done by a conservative force, and thus the amount of stored energy, depends on the object's total displacement in a straight line rather than distance traveled - it is path independent.

## Examples of Non-Conservative Forces

Friction and air resistance (which is really another form of friction) both result in thermal energy, sound energy and possibly surface deformations, all of which are "lost" from the system and therefore represent energy that it cannot reuse.

For example, as a boulder falls off a cliff, it experiences the force of air resistance on the way down. The air resistance generates heat and sound, both forms of thermal energy that dissipate into the environment. Thus, non-conservative forces are sometimes referred to as dissipative forces.

When the boulder hits the ground, the force of friction it feels with the surface results in more heat and sound, plus a large crater in the ground. The boulder can't get back the lost heat or sound, nor will the ground bounce back to its original shape.

## Why Non-Conservative Forces Matter

Non-conservative forces (and the law of energy conservation) explain why perpetual motion machines are not possible!

In a world full of friction, potential energy and kinetic energy do not always neatly convert back and forth. As long as an object is in motion, some of the total will always be transformed into heat from non-conservative friction forces. It follows that the amount of all energy in the universe in the form of heat is always increasing and, eventually, no more useful energy will remain. This is sometimes referred to as the "heat death" of the universe.

Thus, a perpetual motion machine – or any such "endless energy" invention – is physically impossible, because not all forces are conservative.

## Conservative vs Non-Conservative Forces

In contrast, conservative forces are forces for which the amount of work done in moving from point A to point B is path independent. Conservative forces include the gravitational force and elastic forces such as the spring force.