A single bead can slide with negligible friction on a stiff wire that has been b

Question

A single bead can slide with negligible friction on a stiff wire that has been bent into a circular loop of radius 15.7 cm, as in the figure below. The circle is always in a vertical plane and rotates steadily about its vertical diameter with a period of 0.485 s. The position of the bead is described by the angle theta that the radial line, from the center of the loop to the bead, makes with the vertical. (See http://i45.tinypic.com/2jcf0iw.gif) (a) At what angle(s) up from the bottom of the circle can the bead stay motionless relative to the turning circle? (Select all that apply.) 0

Explanation / Answer

This is a complicated problem that requires several steps.First, note that the bead turns in a horizontal circle when thehoop spins. The radius of this horiz circle is r = 0.11 *sin? The bead moves at speed = distance / time = 2?r / T = 2?r / 0.470 = 13.369 r Now... horizontal and vertical forces acting on thebead: horizontal: normal* sin? = m v2 / r vertical: normal * cos? = mg divide these equations sin? / cos

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