AKASH GOYAL AskiitiansExpert-IITD
Last Activity: 14 Years ago
Dear Kedar
A conservative force is a force with the property that the work done in moving a particle between two points is independent of the path taken. Equivalently, if a particle travels in a closed loop, the net work done by a conservative force is zero
Suppose that a non-uniform force-field acts upon an object which moves along a curved trajectory, labeled path 1, from point to point . See Fig.. the work performed by the force-field on the object can be written as a line-integral along this trajectory:
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(1) |
Suppose that the same object moves along a different trajectory, labeled path 2, between the same two points. In this case, the work performed by the force-field is
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(2) |
Basically, there are two possibilities. Firstly, the line-integrals (1) and (2) might depend on the end points, and , but not on the path taken between them, in which case . Secondly, the line-integrals (1) and (2) might depend both on the end points, and , and the path taken between them, in which case (in general). The first possibility corresponds to what physicists term a conservative force-field, whereas the second possibility corresponds to a non-conservative force-field.
Figure : Two alternative paths between points and
Informally, a conservative force can be thought of as a force that conserves mechanical energy
The gravitational force, spring force, magnetic force (according to some definitions, see below) and electric force (at least in a time-independent magnetic field, see Faraday's law of induction for details) are examples of conservative forces, while friction and air drag are classical examples of non-conservative forces (in both cases, the energy is converted to heat and cannot be retrieved)
All the best.
AKASH GOYAL
AskiitiansExpert-IITD
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