Cooridinate+Mechanics

A piece of wire is bent in the shape of a parabola whose equation is \(y=kx^2\) (\(y\)-axis veritical) with a mass \(m\) on it. At rest, it stays on lowest point of the parabola. The wire is now accelerated parallel to \(x\)-axis with \(a\). What is the distance of new equilibrium position of the mass from the \(y\)-axis, where it can stay at rest with respect to wire?

Details and assumptions:

  • Assume the system to be smooth (frictionless).

  • Acceleration \(a\) is constant.

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