STEMS 2021 Phy Cat A Q2
Source:
January 23, 2021
Problem Statement
A regular tetrahedral massless frame whose side length is physically variable (with the constraint of the tetrahedron being regular) is dipped in a soap solution of surface tension , taken outside and allowed to settle after a little wiggle.\\
The soap film is formed such that there is no volume in space that is enclosed by any of the surfaces soap film and all the soap film surfaces are planar. You may assume the configuration of the soap film without proof.\\
Now 4 point charges of charge are fixed at the vertices of the tetrahedron.\\
The system now sets into motion with the shape and nature of soap film being unaltered at all times.
[*] Describe the shape of the soap film you observe and your speculations on why it is formed this way. Also shew that the area spanned by the soap film is less than the total surface area of the tetrahedron.[/*]
[*] Find the side length of the tetrahedron for which the system attains mechanical equilibrium. [/*]