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.

Hint 1, Hint 2, Hint 3, Hint 4, Best solutions and final results

Chinese translation of problem 1 (中文)

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