A single bead can slide with negligible friction on a stiff wire that has been b
ID: 1354024 • Letter: A
Question
A single bead can slide with negligible friction on a stiff wire that has been bent into a circular loop of radius 13.1 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 that the radial line, from the center of the loop to the bead, makes with the vertical.
(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.)
60.8°
65.7°
0°
90°
66.7°
63.5°
(b) Repeat the problem, taking the period of the circle's rotation as 0.880 s. (Select all that apply.)
63.5°
60.8°
65.7°
90°
66.7°
0°
(c) Describe how the solution to part (b) is fundamentally different from the solution to part (a).
(d) For any period or loop size, is there always an angle at which the bead can stand still relative to the loop? Are there ever more than two angles? Arnold Arons suggested the idea for this problem.
This answer has not been graded yet.
(e) Are there ever more than two angles? Arnold Arons suggested the idea for this problem.
YesNo
Explanation / Answer
a)
here
omega = 2 * pie / T
omega = 2 * 3.14 / 0.485
omega = 12.948 rad/s
then
theta = cos^-1( g / r / omega^2)
theta = cos^-1(9.8 / 0.131 / 12.948^2)
theta = 63.5 deg
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