How does surface tension explain the floating needle experiment?

Question

Part 1: After reading some explanation in internet I understood the fact that the molecules of water on the surface have no water molecules in the outward area so it feels a net force towards the water. Great! Part 2: another thing is, on the surface, water acts like elastic. So if you put the needle gently without breaking the surface tension, the water surface will slightly curve downward and due to elasticity it would cancel out the downward force of needle & therefore the needle will float. Did i get it right?

Now I do not get the relation between these two parts. If the surface molecules are pulled downwards then why elasticity forms on the surface? The molecules are pulled dowards, i put the needle and add more force to the molecules towards the water. It should stay like that. Where does the elasticity come from and cause an upward force?

Answer 1

Two phenomenons are competing here. On the one hand, the needle of mass $m$ is attracted downwards so as to minimize its potential energy. When its altitude decreases by $\delta h$, its potential energy decreases by $\delta E_p = m g \delta h$.

On the other hand, when the water surface curves downwards, it increases its total area by an amount $\delta A$. Doing so requires an energy $\delta E_S = \sigma \delta A$, $\sigma$ being the surface tension.

There exists an equilibrium position that minimizes the sum of these two contributions, hence the equilibrium position of the needle on the water surface.