The shape of the surface of a soap film

[Raihan amin]

I don't understand that.would you please do it for me?

 

[timetraveller123]

no i can't help you do it but
$\frac {10}{r_0} = cosh(L/2 r_0)\\ \frac{1}{ r_0} = x\\ 10 x = cosh (Lx /2)$
now you can think of it graphically what is necessary for x to have solution

 

[LordGfcd]

Hi. I was trying to solve the same problem you submitted. And I've read Chestermiller's solution to the problem. But I don't understand why in the post #13 there is a sqrt(1+(dr/dz)^2)) ? I would appreciate the help. Thank you.

 

[TSny]

Hi. I was trying to solve the same problem you submitted. And I've read Chestermiller's solution to the problem. But I don't understand why in the post #13 there is a sqrt(1+(dr/dz)^2)) ? I would appreciate the help. Thank you.

The square root factor is associated with getting the z-component of the surface tension force.

 

[Chestermiller]

Hi. I was trying to solve the same problem you submitted. And I've read Chestermiller's solution to the problem. But I don't understand why in the post #13 there is a sqrt(1+(dr/dz)^2)) ? I would appreciate the help. Thank you.

Let's see your derivation of the force balance on the film.

 

[LordGfcd]

Ok thanks very much. It was the project of the tension on the z-axis.
My solution had the same idea as Raihan's - pressure equillibrium.