Quick A conservative force is a force in which a two-way conversion between potential energy and kinetic energy can take place.
A nonconservative force is a force in which the two-way conversion can not occur.
Conservative Force
The work done by a conservative force always agrees with these conditions:
• It can always be expressed as the difference between the initial and final values of a potential energy function.
• It is reversible.
• It is independent of the path of the body and depends only on the starting and ending points.
• When the starting and ending points are the same, the total work is zero.
Two examples of a conservative force are the gravitational force and the spring force.
A force that offers this opportunity of two-way conversion between kinetic and potential energies is called a conservative force. An essential feature of conservative forces is that their work is always reversible. Anything what is deposited in the energy "bank" can later be withdrawn without loss. Another important aspect of conservative forces is that a body may move from point 1 to point 2 by various paths, but the work done by a conservative force is the same for all of these paths. Thus if a body stays close to the surface of the earth, the gravitational forcemg is independent of height, and the work done by this force depends only on the change in height. If the body moves around a closed path, ending at the same point where it started, the total work done by the gravitational force is always zero.
An example: Kinetic energy can be "stored" by converting it to potential energy. It can then be retrieved later as kinetic energy. When a ball is thrown in the air, it slows down as kinetic energy is converted into potential energy. But on the way down, the conversion is reversed, and the ball speeds up as potential energy is converted back to kinetic energy. If there is no air resistance, the ball is moving just as fast on the way down at the point at which it was released.
Another example: If a glider moving on a frictionless horizontal air track runs into a spring bumper at the end of the track, the spring compresses and the glider stops. But then it bounces back, and if there is no friction, the glider has the same speed and kinetic energy it had before the collision. Again, there is a two-way conversion from kinetic to potential energy and back. In both cases it is found that a potential-energy function can be defined so that the total mechanical energy is constant or conserved during the motion.
Nonconservative Force
A force that is not conservative is called a nonconservative force. A nonconservative force has the opposite properties of the conservative force:
• There is no potential-energy function for the friction force.
• It is not reversible.
• It is dependent of the path of the body, therefore it depends on the path as well as on the starting and ending points.
• When the starting and ending points are the same, the total work is not zero.
Some examples of nonconservative forces are the friction force and the force of fluid resistance.
Consider the friction force acting on the crate sliding on a ramp. When the body slides up and then back down to the starting point, the total work done on it by the friction force is not zero. When the direction of motion reverses, so does the friction force, and friction does negative work in both directions. When a car with its brakes locked skids across the pavement with decreasing speed (and decreasing kinetic energy), the lost kinetic energy cannot be recovered by reversing the motion or in any other way, and mechanical energy is not conserved. In the same way, the force of fluid resistance is not conservative. If a ball is thrown up in the air, air resistance does negative work on the ball while it's rising and while it's descending. The ball returns to your hand with less speed and less kinetic energy than when it left, and there is no way to get back the lost mechanical energy.
The work done by a nonconservative force cannot be represented by a potential-energy function. Some nonconservative forces, like kinetic friction or fluid resistance, cause mechanical energy to be lost or dissipated; a force of this kind is called a dissipative force. There are also nonconservative forces that increase mechanical energy. The fragements of an exploding firecracker fly off with very large kinetic energy, thanks to a chemical reaction fo gunpowder with oxygen. The forces unleashed by this reaction are nonconservative because the process is not reversible.