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, \(x\) and \(y\) are related by \(y=x^2\). The wire starts accelerating to the right with acceleration \(\mathbf{a}\). Suppose the value of \(x_\textrm{ss}\), the steady state location of the bead in the coordinates of the wire, is \(-\SI{30}{\centi\meter}\).

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

Details and Assumptions:

  • \(g = \SI[per-mode=symbol]{10}{\meter\per\second\squared}\).
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