Final answer:
A conservative force is a type of force in physics where the work done only depends on the starting and ending points and not on the path taken. These forces are associated with the conservation of energy, with examples including gravitational and electrostatic forces. The work done by a conservative force around a closed path is always zero. Therefore, the correct option is c).
Step-by-step explanation:
A conservative force is a concept in physics that describes a force whose work is independent of the path taken. Essentially, the work done by a conservative force moving an object from one point to another only depends on these two points and not on the trajectory the object takes between them. This characteristic of conservative forces implies that when dealing with them, energy within a system is conserved, leading to the law of conservation of energy. An example of a conservative force is gravity; when an object is moved in a gravitational field, the work done only depends on the initial and final heights, not on the path taken through the field. Furthermore, the work done by a conservative force around any closed path is zero, meaning if an object returns to its starting position, the total work done by the conservative force is nil.
The mathematical expression of a conservative force is interesting as well. The force can be described as the negative gradient of a potential energy function. This leads to the notion that a conservative force can be derived from a potential energy and thus, allows physicists to define potential energies (like gravitational potential energy) for forces with this property. As such, a conservative force is associated with the conservation of mechanical energy within a system, where the sum of kinetic and potential energies remains the same as long as only conservative forces are doing work. In summary, a conservative force plays a fundamental role in mechanics by ensuring that energy is not lost or gained when objects are moved within a force field, but rather transformed between different forms.