Extremum Accelerometer

A smooth wire is bent into the shape of a parabola. If the origin is taken to be the lowest point on the wire, xx and yy are related by y=x2y=x^2. The wire starts accelerating to the right with acceleration a\mathbf{a}. Suppose the value of xssx_\textrm{ss}, the steady state location of the bead in the coordinates of the wire, is 30 cm-\SI{30}{\centi\meter}.

Find the acceleration a\mathbf{a} (in m/s2\si[per-mode=symbol]{\meter\per\second\squared}) of the wire toward the right.

Details and Assumptions:

  • g=10 m/s2g = \SI[per-mode=symbol]{10}{\meter\per\second\squared}.
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