What is the solution to this basic surface tension problem?

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Discussion Overview

The discussion revolves around a surface tension problem encountered in a physics exam, specifically focusing on the application of the formula for surface tension and the calculation of the length of wire attached to a membrane. Participants explore the geometry involved in the problem and the necessary steps to derive the correct force.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant expresses confusion over the surface tension formula γ=F/d and its application to the problem, noting that their attempts to solve it have not yielded the correct answer.
  • Another participant suggests calculating the length of the wire attached to the membrane, indicating that this length is crucial for determining the force.
  • A participant questions how to calculate the length of the wire and expresses uncertainty about the geometric relationships involved.
  • There is a suggestion to use the Pythagorean theorem to find the necessary lengths, although one participant indicates difficulty in applying this method due to the information provided.
  • Clarification is provided that the hypotenuse of the relevant triangle corresponds to the radius of the circle involved in the problem.
  • A participant acknowledges a misunderstanding regarding the geometry of the triangle and expresses gratitude for the clarification.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the correct approach to solving the problem, as there are differing levels of understanding regarding the geometry and calculations involved.

Contextual Notes

There are unresolved aspects regarding the specific geometric relationships and the application of the Pythagorean theorem, as well as the interpretation of the problem's parameters.

pavichokche
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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.
 
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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?
 
No, I haven't. How would that help, though? Also, I don't think I know how to calculate that length...
 
pavichokche said:
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.
 
nasu said:
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.
 
Last edited:
The hypotenuse is the radius of the circle.
 
Oh, I was thinking of a triangle going from P to the wire...
Thank you very much
 
pavichokche said:
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.
 

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