Force distribution T/R on a cylinder due to one full wire wrap?
Force distribution T/R on a cylinder due to one full wire wrap?
(OP)
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
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





RE: Force distribution T/R on a cylinder due to one full wire wrap?
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)=∫xπ/2Rrcos t dt
(R=radial distributed force, r=cylinder radius)
This is clearly satisfied only by
R=T/r
prex
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