gorica
  • gorica
How to show that force is conservative?
Physics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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anonymous
  • anonymous
We can do that if it is possible for it to write in terms of a gradient along with a negative sign.
gorica
  • gorica
can you do that for \[\vec F=-mg \vec k\]
naveenbabbar
  • naveenbabbar
The work done by a conservative force over a closed loop/path is always zero.

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naveenbabbar
  • naveenbabbar
Work done by the force is independent of nature of path followed and depends on initial and final position. the force involved is then conservative.
naveenbabbar
  • naveenbabbar
Example :- Gravitational force, Electrostatic force
gorica
  • gorica
@naveenbabbar I would appreciate if you could show it on example. Only theory doesn't help me much.
anonymous
  • anonymous
This relation is a simple form of a complicated formula \[F=mM/r ^{2}\] so we can write,\[F=-gradV=-grad(mM/r ^{1})=mM/r ^{2}\] where \[V=-mM/r\] is potential function of the body.
naveenbabbar
  • naveenbabbar
ok wait a minute
anonymous
  • anonymous
Ok!
naveenbabbar
  • naveenbabbar
naveenbabbar
  • naveenbabbar
Look for the attachment and try to solve this question
gorica
  • gorica
@Saeeddiscover can you do that using (iii) from this proposition?
1 Attachment
gorica
  • gorica
Can I do that writing like this\[\vec F d \vec r=-dΦ\] where \[dΦ\neq0\]? If it is =0, will it be conservative force?
anonymous
  • anonymous
it should be, because curl of a gradient is always zero. or\[Curl F=Curl(grad V)=0\]
anonymous
  • anonymous
No it doesn't show the axiom.
gorica
  • gorica
no, I am not asking you to prove axiom, but if I can show that way that a force is conservative
anonymous
  • anonymous
I strongly recommend looking at some mathematical textbooks such as George B. Arfken's.
anonymous
  • anonymous
Nothing can be adopted if you wish to consider the case \[d \theta=0\]
anonymous
  • anonymous
Any questions!
gorica
  • gorica
I don't understand it much, but thanks anyway.

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