# plzzzz.... explain meaning of conservative force feilds with an example

deeksha sharma
40 Points
11 years ago

conservative force is the force, work done by which is independent of the path followed but depends just on the initial and the final points.

Example is gravitational force.

Explanation: suppose a body reaches a height H by first stairs, then by lift, and finally via an inclined plane. In all the cases net displacement is the same, <mind it not the distance>

So the magnitude of work done will also be the same which is weight of the body*displacement.

So the work done against gravitational force will be same.

DO APPROVE IF YOU LIKE

DEEKSHA

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419 Points
11 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:

 (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

 (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.