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Physics / Classical Mechanics 0 / Chapter 7 / Problem 7.20

Classical Mechanics | 0th Edition | ISBN: 9781891389221 | Authors: John R Taylor

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A smooth wire is bent into the shape of a helix, with

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QUESTION:

A smooth wire is bent into the shape of a helix, with cylindrical polar coordinates p = R and z = X0, where R and X are constants and the z axis is vertically up (and gravity vertically down). Using z as your generalized coordinate, write down the Lagrangian for a bead of mass m threaded on the wire. Find the Lagrange equation and hence the bead's vertical acceleration E. In the limit that R 0, what is i? Does this make sense?

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QUESTION:

A smooth wire is bent into the shape of a helix, with cylindrical polar coordinates p = R and z = X0, where R and X are constants and the z axis is vertically up (and gravity vertically down). Using z as your generalized coordinate, write down the Lagrangian for a bead of mass m threaded on the wire. Find the Lagrange equation and hence the bead's vertical acceleration E. In the limit that R 0, what is i? Does this make sense?

ANSWER:

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The smooth wire is bent into the helix.

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