Particle on a Helical Wire A smooth wire is bent into the shape of a helix5.with cylindrical polar coordinates p= R and : = dó, where R and A are constants andthe z axis is vertically up (and gravity vertically down). Using z as your generalizedcoordinate, write down the Lagrangian for a bead of mass m threaded on the wire. Findthe Lagrange equation and hence the bead's vertical acceleration . In the limit thatR 0, what is 2? Does this make sense?

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Asked Nov 4, 2019
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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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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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Expert Answer

Step 1

Write an expression for Lagrangian in terms of cylindrical polar co-ordinates

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L-T-V m(R° -mg 1 - mg mR -mg

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Step 2

Write the Euler-Lagrange equation and substitute the Lagrangian

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dt =-mg dt +1 | =-mg m =-{1-

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Step 3

Write the limiting case when t...

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lim R0 02 -g b

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