Physics Cup – TalTech 2021 – Problem 1

by Jaan Kalda (TalTech).

Two hollow spheres of radius R=10\,\mathrm{cm} are made of copper and connected with a cylindrical copper rod of length L=1\,\mathrm{m} and radius r=1\,\mathrm{mm}. The total mass of this dumbbell-like system is m=150\,\mathrm{g}. The entire system is in a very strong magnetic field B=2\,\mathrm{MT} which is perpendicular to the rod. This “dumbbell” is given an initial velocity v=1\,\mathrm{m/s} which is parallel to the direction of the rod. However, this orientation is unstable: the “dumbbell” will start oscillating; eventually, these oscillations decay so that the “dumbbell” will take a stable orientation and a new final speed u. Find an expression for this terminal speed u analytically and evaluate it numerically. The “dumbbell” moves in weightlessness in a total vacuum.

Chinese translation of problem 1 (中文)

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