Conservative forces - University physics help!

Can someone explain to me how to determine if a force is conservative ?
All of these forces act along the x axis only
fx=-kx+bx^2
fx=-Ae^(-bx)
fx=cx^3
I just want an explanation - you don't have to do them all - i am totally clueless :frown:

Thank you

Reply 1

uwins

you can check that the line interval is zero along any closed path
see if you can find a potential function whose -gradient is the same as the force function, intergration

Reply 2

x0x

Original post by uwins

you can check that the line interval is zero along any closed path
see if you can find a potential function whose -gradient is the same as the force function, intergration

can you please elaborate a bit? If it is ok with you to just get me started with one of them i will be very thankful :smile:

Reply 3

WishingChaff

Recall the definition for a force to be conservative:

A force

\textbf{F}

on a particle is conservative iff it satisfies two conditions:
(i)

\textbf{F}

depends only on the particle's position

\textbf{r}

; that is,

\textbf{F} = \textbf{F}(\textbf{r})

(ii) For any two points 1 and 2, the work done by

\textbf{F}

is the same for all paths between 1 and 2.

Now the first condition is easy to check, whilst the second is much harder. Fortunately there exist a nice theorem that says:

A force