A curious physics student decides to investigate soap films by creating a bridge between two vertical glass plates. The student dips two parallel glass plates (each 20cm tall and 5cm wide) into a soap solution and then slowly pulls them apart horizontally until they are separated by a distance d=3cm. A soap film forms between the plates, creating a curved surface.
Due to surface tension, the soap film pulls inward, creating a pressure difference across the film. The student notices that when they blow gently upward from below with speed v0=2m/s, the soap film becomes perfectly flat (no curvature).
Given that the surface tension of the soap solution is γ=0.025N/m and the density of air is ρ=1.2kg/m3, find the radius of curvature R of the soap film when no air is blown across it.
Assume the soap film has negligible thickness and that the air flow creates a pressure difference according to Bernoulli's equation. The film can be approximated as a cylindrical surface between the plates.