# Surface tension: the paper clip experiment

In the paper clip experiment, the surface tension of water prevents the clip from falling, thus we can assume it exerts a force of $mg$ (weight of clip) upwards.

However, if you try to pull the clip out of water, surface tension opposes this motion also. If for simplicity we assume that the clip is a rectangle of length $l$ and breadth $b$, and the surface tension is $T$, then the liquid exerts a downward force of: $$T×2(l+b)$$

What is going on here? Why is there an inconsistency in the direction along which the force acts?

• Where is the "inconsistency"? Mar 20, 2016 at 2:51
• @CuriousOne in the first case surface tension acts away from the body of water, and in the second case towards. I'm confused about the direction in which it acts. Mar 20, 2016 at 3:04
• It acts in the direction of the surface. Maybe one could use this as help to remember the direction of the forces: it's a "surface tension", so the tension acts in the direction of the surface. If it acted in the direction of the liquid, it might be called a "liquid tension", instead. Would that work for you? Mar 20, 2016 at 3:09
• @CuriousOne maybe I don't understand the concept properly, but to me in both cases it looks like the resultant force is perpendicular to the surface direction. Mar 20, 2016 at 3:13
• Yes, I think that sounds about right for a qualitative explanation, but calculation is not always straight forward. Did you look at the Wikipedia page en.wikipedia.org/wiki/Surface_tension#Physics? It contains the diagram for the surface tension of a non-wetting needle lying on a liquid surface. The problem is that for objects that also get pulled into the surface, we also have to consider wetting, i.e. there is an attractive contact force between the liquid the solid. I am going to abstain from giving a precise answer... I am not sure I would get the quantitative explanation right. Mar 20, 2016 at 4:42

## 1 Answer

Surface tension always acts in the plane of the surface. The reason it can support a floating paperclip is because the weight of the paperclip deforms the surface downwards:

The surface tension always acts in the plane of the water surface, but because the water surface has been bent downwards to an angle $$\theta$$ by the weight of the clip there will be an upward component of the force equal $$F\sin\theta$$. The paperclip floats when this upward force $$F\sin\theta$$ balances the downward force $$mg$$ due to the weight of the paperclip.

The second diagram shows what happens as we pull the paperclip upwards. Because the water sticks to the paperclip the result is to deform the surface upwards and this produces a downwards force of $$F\sin\theta$$.

That's why the force due to the surface tension acts upwards in one case and downwards in the other.

• This is one of the standard methods of measuring surface tension Method 3 Wilhelmy plate or ring method in this link zzm.umcs.lublin.pl/Wyklad/FGF-Ang/… Mar 20, 2016 at 13:44
• I cannot thank you enough. This is very clear. I think from the diagram f sin theta is the resultant force, not the cos component- am I missing something? Mar 20, 2016 at 14:16
• Aren't you missing another force in this model? The body is certainly supported by the tension caused by the surface effects of the fluid, but doesn't the body also displace fluid? Doesn't Arcimedes principle also apply? Isn't there also a component of buoyant force, or does the body have to break the surface for that to apply? Mar 20, 2016 at 15:18
• @user93868: oops, yes, $\sin$ not $\cos$. Well spotted :-) Mar 20, 2016 at 15:21