Physics Times – July 2019

Introduction
Forces in nature can be divided into two types:
(i) Conservative force
(ii) Nonconservative force
In this article we have discussed two different
methods to verify a given force as
conservative or non-conservative. In one
method we assume a closed path of our choice
and find the work done in that path. The
second method is a short-cut method.

(i) Conservative force
If work done by the force around a closed
path is zero and it is independent of path
then it is a conservative force.
Consider two points A and B. A body can
be displaced by any of the three paths
shown in the figure.

Introduction

(i) Conservative force

(ii) Nonconservative force

(i) Conservative force
















If

Path I Path II Path III

W W WA B A B A B   

Path I Path II Path III

  Fdl Fdl Fdl.  ..

     

As work is independent of the path then
the force is conservative.

Eg : Gravitational force, Elastic force,

Electrostatic force etc.

All central forces are conservative forces.

A conservative force is only a function of

position not of velocity or time.

Under conservative force,

dU

F

dx

 where

U is Potential Energy.

Change in potential energy, dU F dx 

 

A conservative force is always related to

potential energy as

F U ,

 

i j k 

x y z

  

  

  

 

Where  is called as dell

The property of a conservative force is

     F U  U U 0 0

     

Where F

 

is also called as Curl F

 

0 0

x y z

i j k

F

x y z

F F F

      

  



 

 ^0

i Fz Fy j Fz Fx k Fy Fx

y z x z x y

        

          

         



z y 0 z y  i

F F F F

y z y z

   

    

   

By: ESWAR REDDY ALLA(Bangalore)

B. MADHU (Bangalore)

ESWAR REDDY ALLA ALLA

B. MADHU