A bead slides on a circular wire

Thread starter minmm
Start date Jan 17, 2012
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Bead Circular Wire

AI Thread Summary

The problem involves a bead sliding on a smooth circular wire in a vertical plane, starting from rest at a level position with the hoop's center. The initial potential energy is calculated as U=mgb, while the kinetic energy at the bottom is KE=mv²/2, with v determined to be (2bg)¹/². The main challenge is to find the time it takes for the bead to reach the bottom of the hoop. The discussion highlights the need to relate the bead's motion to time, suggesting further analysis is required to derive the time equation. A complete solution will involve integrating the motion equations to find the desired time.

Jan 17, 2012

minmm

Homework Statement

A bead slides on a smooth circular wire of radius b which lies in a vertical plane. The bead starts from rest at a point that is level with the center of the hoop.
Find the time it takes for the bead to slide to the bottom of the hoop.

The attempt at a solution
at t=0
U=mgb, KE=0

at the bottom
U=0, KE=mv²/2, v=(2bg)^1/2

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Jan 18, 2012

LawrenceC

What about the time?

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