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Conservative force

  • In conservative field, work done by the force (line integral of the force, i.e., 39132.png) is independent of the path followed between any two points.
     
    From Fig. 6,
     
    40824.png 
39126.png
Fig. 6
  • In conservative field, work done by the force (line integral of the force, i.e., 39113.png) over a closed path/loop is zero.
     
    From Fig. 7,
     
    WA→B + WB→A = 0
     
    or 40835.png = 0
39107.png
Fig. 7
 
Example

Electrostatic forces, gravitational forces, elastic forces, magnetic forces, etc., and all the central forces are conservative in nature.

 

Non-conservative forces

A force is said to be non-conservative, if work done by or against the force in moving a body from one position to another, depends on the path followed between these two positions, and for complete cycle this work done can never be a zero.
 
Example

Frictional force, viscous force, airdrag, etc.

 

 

Note: Work depends on frame of reference. With change of frame of reference (inertial) force does not change while displacement may change. So, the work done by a force will be different in different frames.




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