What is the solution to this basic surface tension problem?

In summary, the conversation revolves around solving a physics problem involving surface tension and the length of wire attached to a membrane. The formula for surface tension is given, but multiplying it by the length does not yield the correct answer. The person seeking help is unsure of how to calculate the length of the wire, but is given hints to use the Pythagorean theorem and to consider the hypotenuse as the radius of the circle. Finally, the correct approach is suggested involving a triangle from the center of the circle to the end of the wire and to the middle of the wire.
  • #1
pavichokche
4
0
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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  • #2
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?
 
  • #3
No, I haven't. How would that help, though? Also, I don't think I know how to calculate that length...
 
  • #4
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.
 
  • #5
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:
  • #6
The hypotenuse is the radius of the circle.
 
  • #7
Oh, I was thinking of a triangle going from P to the wire...
Thank you very much
 
  • #8
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.
 

Related to What is the solution to this basic surface tension problem?

1. What is surface tension?

Surface tension is a physical property of liquids that causes the surface of the liquid to behave like an elastic membrane. It is a result of the cohesive forces between the molecules of the liquid.

2. How is surface tension measured?

Surface tension is typically measured in units of force per unit length, such as newtons per meter (N/m) or dynes per centimeter (dyn/cm). The measurement is often done by using a tensiometer, which measures the force required to pull a wire or plate from the surface of the liquid.

3. What factors affect surface tension?

The surface tension of a liquid is affected by various factors such as temperature, type of liquid, and the presence of impurities. Higher temperatures generally decrease surface tension, while impurities can either increase or decrease it depending on their properties. The type of liquid also plays a role, with water having a higher surface tension than most other liquids.

4. How does surface tension affect the behavior of liquids?

Surface tension plays a crucial role in many natural phenomena, such as the formation of droplets, capillary action, and the movement of insects on water. It also affects the behavior of liquids in containers, causing them to form a curved meniscus at the edges. In addition, surface tension can prevent objects from fully submerging in liquids, leading to the formation of floating objects.

5. Can surface tension be manipulated?

Yes, surface tension can be manipulated by adding surfactants or changing the temperature of the liquid. Surfactants are substances that can lower the surface tension of a liquid, making it easier for other substances to mix or dissolve in it. Changing the temperature can also alter the surface tension, as mentioned earlier. Additionally, mechanical agitation can also affect the surface tension of a liquid.

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