Questioning My Conception of Surface Tension

[Ezio3.1415]

I was solving a problem from fluid mechanics... But that led me to question my conception abt surface tension...
The problem stated that the max force needed to uphold a needle(ignore its weight)from the water surface is F... The needle is L m long... What is the surface tension?
They found it by T=F/2L
I know how surface tension works... But I fail to grasp this problem... Why do we need force at all to take out the needle?

 

[Ezio3.1415]

I just did an experiment... The needle press down a little on the water... Water gets a little dowm near the edge...so surface tension has a perpendicular downward component... So I need to give an F to pull up the needle... Am I right?

 

[Pagan Harpoon]

The source of surface tension is the fact that water (or other liquid) molecules like to be near to each other. A water molecule at the water-air interface has a higher energy than a molecule that is surrounded by other water molecules. Thus, to increase the area of the water-air interface costs energy. When you pull the needle away from the water, you are doing exactly that - you distort the water surface such that the water-air interface becomes larger. This costs energy, so you need to apply a force.

 

[Pagan Harpoon]

I just did an experiment... The needle press down a little on the water... Water gets a little dowm near the edge...so surface tension has a perpendicular downward component... So I need to give an F to pull up the needle... Am I right?

In this experiment, it is gravity that pulls the needle down. Surface tension is acting vertically upwards, preventing it from sinking.

Edit - I think some diagrams to show the shape of the water surface around the needle might be informative. I'll draw some and add them shortly.

 

[Pagan Harpoon]

http://oi50.tinypic.com/s1p7iv.jpg

In this diagram, I have attempted to show the needle on the water surface, subject to gravity and surface tension. I have shown it from three directions, the two horizontal views are rotated 90 degrees from each other.

Moving the needle down by a small distance distorts the water surface which creates a larger water-air interface. This interface has energy associated with it, E = Aγ, where A is the area of new surface and γ is the surface tension of the water. If you differentiate that equation with respect to the vertical direction, you will obtain the expression for the upward force on the needle due to surface tension.

In your original problem, you were considering pulling the needle up out of the water. In that case, the water would simply bulge up instead of down and the force will hold the needle down instead of pulling it up.

 

[Ezio3.1415]

I am again back to my previous confusion... If surface tension acts upward,then why do I have to pull with a force when the needle is weightless...
"In your original problem, you
were considering pulling the
needle up out of the water. In
that case, the water would
simply bulge up instead of
down and the force will hold
the needle down instead of
pulling it up."
I didn't understand this part...

 

[Pagan Harpoon]

http://oi50.tinypic.com/dyohup.jpg

In this diagram, I have tried to illustrate the difference between what happens when gravity is pulling the needle down and what happens when you pull it up with some external force. F_st is surface tension and F_ext is whatever external force you use to pull at it.

It might be useful to think of the water surface as a sheet of elastic material. When gravity pulls the needle down, it pulls the sheet down a bit with it. The sheet wants to spring back up, so it exerts a force in that direction.

When you pull the needle up with some external force (with a string attached to it or whatever), you pull the surface up with it. The sheet wants to spring back down, so it exerts a force downwards. If the force you exert is strong enough, the restorative force of the sheet can't hold the needle, the sheet breaks and you lift the needle away.

 

[Ezio3.1415]

Thank you very much for the help... The figure explains it all...