Question

A single bead of mass m can slide with negligible friction on a stiff wire that has been bent into a circular loop of radius R = 0.155m. The circle is always in a vertical plane and rotates steadily about its vertical diameter with a period of T = 0.420s. 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. Hint: The bead will remain at a fixed theta for this particular value of the period T.

a) Draw a diagram of all the forces acting on the bead and decompose the forces into their vertical and horizontal components.

b) Apply Newton's second law to the vertical and horizontal components of the forces (write the equations). At what angle can the bread stay motionless relative to the turning circle?

c) When the bead is at the fixed angle does the bead have an acceleration? if the acceleration is non-zero, what is its value?

Answer 1