Physics Times 07.2019

(Kiana) #1

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
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