# Floating of needle on water [duplicate]

An iron needle when placed horizontally on water, floats (sits) on the surface of the water. The phenomenon is usually justified as "surface tension".

From what I understand, for the needle to float without sinking, some force has to balance its weight. Since no part of the needle is under the water, buoyant force can be ruled out. I learnt that force due to surface tension always acts tangentially to a surface. So, this force should not have any vertical component. However, according to the first answer to this question How does surface tension enable insects to walk on water? "attractive forces of the water molecules result in a net upward force on the legs of the insect". The water surface near the needle is deformed due to the adhesive force between the needle and the water surface. Isn't the adhesive force an upward force on the water (or a force with some vertically upward component) due to the needle? It would imply that there is a downward force on the needle itself which will add to the weight.

I think the part where I describe the forces between the needle and the water is wrong. Can you tell me what is wrong?

• @JohnRennie Thanks a lot, this link exactly answers my doubt. Dec 26, 2018 at 14:42

"Since no part of the needle is under the water, buoyant force can be ruled out."

The needle is below the water level, so actually there is displaced water and a buoyant force. If the membrane where the surface tension is located is in equilibrium, it needs to receive an upward force. In figure A that upward force is the buoyant force due to the displaced water. (In B, a membrane suspended between two edges, the upward force is provided by the edges.)

• So, buoyant force does act here. But, surely that isn't the only reason the needle will float? I mean, can the buoyant force balance the weight of the needle completely provided the needle is made of iron which has higher density than water? Dec 26, 2018 at 14:45
• The buoyant force is required for keeping the needle afloat, but it is not a limiting factor. Surface tension is the only critical property of water. For example, the maximum diameter of a floating needle is determined by: $m = \rho \pi r^2 L$ and $m g= 2 \gamma L \rightarrow r = \sqrt{2 \gamma / (\pi \rho g)} \rightarrow d = 2 r = 1.5 mm$, where $\gamma$ is the surface tension of water. Dec 26, 2018 at 16:40

As described in this question, the water surface isn't flat at the point of contact. The surface tension is tangential to the water surface, and can thus have a vertical component if the surface is curved.

The free-body diagram below should explain the balance of forces between the needle and the water surface.

• Ah. @AnubhabDas, since the water is at rest, the net force on the water surface at the line of contact needs to be zero. Since the surface tension force has an upward component as you mentioned, there needs to be another force on the water surface with a downward component to balance this. This is the force exerted by the needle on the water surface. This means that the force on the needle due to the water surface has an upward component, which can balance the weight. Dec 26, 2018 at 12:31
• @AnubhabDas I've added free-body diagrams to show the balance of forces. Sorry for misreading your question earlier. Dec 26, 2018 at 12:40