Proving Work is Same for All Paths of a Conservative Force

[Dustinsfl]

So for a force to be conservative it can only depend on position and the work as to be the same for all paths.

The force mass time gravity is conservative but how do I show the all paths are the same?

 

[Dick]

So for a force to be conservative it can only depend on position and the work as to be the same for all paths.

The force mass time gravity is conservative but how do I show the all paths are the same?

Why don't you just show the force can be defined as the gradient of a potential? Guess the potential if you have to.

 

[Dustinsfl]

Since gravity is acting along the radius to the center of earth, then would $\mathbf{F}(\mathbf{r}) = -m\mathbf{r}$?

 

[Dick]

Since gravity is acting along the radius to the center of earth, then would $\mathbf{F}(\mathbf{r}) = -m\mathbf{r}$?

That is a conservative force, but I don't think Newton would agree it has much to do with gravity. What are you thinking?

 

[Dustinsfl]

That is a conservative force, but I don't think Newton would agree it has much to do with gravity. What are you thinking?

I wrote why I put that.

I said since gravity is acting along the raidus vector to the center of Earth then could I wrtie F in such a manner.

 

[Dick]

I wrote why I put that.

I said since gravity is acting along the raidus vector to the center of Earth then could I wrtie F in such a manner.

There are a LOT of possible forces that would act along a radius vector to the center of the earth. Gravity is a special one. Not that it even matters for showing it's conservative, but don't you know more about gravity than that? -mr increases in magnitude as you move away from the earth. That's not gravity.