Particle on a Helical Wire A smooth wire is bent into the shape of a helix 5. with cylindrical polar coordinates p= R and : = dó, where R and A 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 . In the limit that R 0, what is 2? Does this make sense?

Question
Particle on a Helical Wire A smooth wire is bent into the shape of a helix
5.
with cylindrical polar coordinates p= R and : = dó, where R and A 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 . In the limit that
R 0, what is 2? Does this make sense?

Image Transcription

Particle on a Helical Wire A smooth wire is bent into the shape of a helix 5. with cylindrical polar coordinates p= R and : = dó, where R and A 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 . In the limit that R 0, what is 2? Does this make sense?

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