Exerting torque on an extension spring to overcome friction in a helical tube

[bill nye scienceguy!]

Does anyone know of an equation that models the build up of potential energy in an extension spring induced by twisting it when its motion is otherwise constrained in the transverse direction?

 

[timthereaper]

You could calculate the strain energy due to bending the spring into a larger (or smaller) radius from the torsion. If it doesn't plastically deform the spring, the strain energy would be that increase in potential energy.