A small massive bead can slide without friction along a wire ring of radius R mounted in the vertical plane. A light elastic cord is attached to the top of the ring and to the bead. Initially, the bead is at rest at the bottom of the ring, and the force exerted on the bead by the ring is twice the bead's weight.
After a small disturbance, the bead begins to slide upward along the ring, reaching its maximum velocity at the moment it covers one-third of the ring's circumference. What is the length of the relaxed cord?
We received many solutions to our September Challenge, Let's Rock-n-Roll! Many of the solutions came from students – a welcome change despite the fact that some of their solutions were not quite correct. We hope that the teachers will continue to encourage their students to challenge themselves.
We are pleased to...