Force distribution T/R on a cylinder due to one full wire wrap? 1

[crapman5]

Hi,

Does anyone know how to derive the resulting uniform force (T/R) distribution on a cylinder due to one full wire wrap (assume ideal, frictionless, massless wire)

Thank you for your help

 

[prex]

If I understand you correctly (a sketch would help) the radial force on the cylinder is uniform, but the tangential force is zero (frictionless).
By symmetry your problem is exactly the same as the one of a wire making a half turn, like in a pulley.
Taking this half turn as going from -[π]/2 to [π]/2, if we impose the equilibrium in the wire ends direction on a portion of the turn going from (positive) angle x to [π]/2 we get (tension T uniform in the wire):
T(1-sin x)=[∫]_x^[π]/2Rrcos t dt
(R=radial distributed force, r=cylinder radius)
This is clearly satisfied only by
R=T/r


prex

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