# 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"? – CuriousOne Mar 20 '16 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. – Mahathi Vempati Mar 20 '16 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? – CuriousOne Mar 20 '16 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. – Mahathi Vempati Mar 20 '16 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. – CuriousOne Mar 20 '16 at 4:42

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 $F\cos\theta$.
• @user93868: oops, yes, $\sin$ not $\cos$. Well spotted :-) – John Rennie Mar 20 '16 at 15:21