What is the solution to this basic surface tension problem?

[pavichokche]

Hello,
I've been studying for a physics exam and this problem has driven me almost nuts. It's incredibly simple and yet I can never get the exact answer. I've seen it in several variations (different numbers, asking for a different variable) and in all cases it makes no sense. Here it is:

[PLAIN]http://img543.imageshack.us/img543/7009/capturemqc.png

The formula for surface tension that we've been shown (we barely studied this) is γ=F/d where γ is the surface tension, F is the force it applies (and the force needed to balance it) and d is the length over which this force is applied.

Doing the obvious (multiplying 2γ by d to solve for F) does not get me the right answer.Just using this formula does not get me the correct answer in any variation of this problem.

Someone please help me understand how this problem works.

 

[nasu]

You need to calculate the length of the wire attached to the membrane. I mean the length of wire between the points of intersection with the circle.
Have you done this?

 

[pavichokche]

No, I haven't. How would that help, though? Also, I don't think I know how to calculate that length...

 

[nasu]

No, I haven't. How would that help, though? Also, I don't think I know how to calculate that length...

This is the length d over which the force is applied. Without it, how would you calculate the force?

You can calculate by using the Pythagorean theorem.

 

[pavichokche]

You can calculate by using the Pythagorean theorem.

But I can't. I'm given the height, and am trying to solve for the base. The hypotenuse eludes me. There are no similar triangles or angles I can use...

I've tried everything I can think of, clearly there is something here I just don't know how to do.

 

[nasu]

The hypotenuse is the radius of the circle.

 

[pavichokche]

Oh, I was thinking of a triangle going from P to the wire...
Thank you very much

 

[nasu]

Oh, I was thinking of a triangle going from P to the wire...
Thank you very much

Take the triangle "going" from the center of the circle to the end wire and to the middle of the wire.