• # Conservative and non-conservative forces

Posted by on May 4, 2023 at 12:15 PM

A good way to think of conservative forces is to consider what happens on a round trip. A conservative force is a force with the property that the total work is done in moving a particle between two points is independent of the taken path.

If a particle travels in a closed loop, and the kinetic energy is the same after a round trip, the force is a conservative force, or at least is acting as a conservative force. Informally, a conservative force can be thought of as a force that conserves mechanical energy.

A conservative force is dependent only on the position of the object. If a force is conservative, it is possible to assign a numerical value for the potential at any point. When an object moves from one location to another, the force changes the potential energy of the object by an amount that does not depend on the path taken. If the force is not conservative, then defining a scalar potential is not possible, because taking different paths would lead to conflicting potential differences between the start and end points.

Consider gravity; you throw a ball straight up, and it leaves your hand with a certain amount of kinetic energy. At the top of its path, it has no kinetic energy, but it has a potential energy equal to the kinetic energy it had when it left your hand. When you catch it again it will have the same kinetic energy as it had when it left your hand. All along the path, the sum of the kinetic and potential energy is a constant, and the kinetic energy at the end, when the ball is back at its starting point, is the same as the kinetic energy at the start, so gravity is a conservative force.

Kinetic friction, on the other hand, is a non-conservative force, because it acts to reduce the mechanical energy in a system. Note that non-conservative forces do not always reduce the mechanical energy; a non-conservative force changes the mechanical energy, so a force that increases the total mechanical energy, like the force provided by a motor or engine, is also a non-conservative force.

For macroscopic systems, the non-conservative approximation is far easier to deal with than millions of degrees of freedom. Examples of non-conservative forces are friction and non-elastic material stress.

Other examples of conservative forces are: force in elastic spring, the electrostatic force between two electric charges, and magnetic force between two magnetic poles. The last two forces are called central forces as they act along the line joining the centers of two charged/magnetized bodies. Thus, all central forces are conservative forces.

Other examples of non-conservative forces are: frictional forces, viscous forces, induction forces, air resistance force, tension in a string, normal force, propulsion force of the rocket, propulsion force of the boat.

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