Question

A bread of mass m is located on a parabolic wire with its axis vertical and vertex directed towards downward as shown in the attachment and whose equation is x² = ay. If the Coefficient of friction is (μ), the highest distance above the x - axis at which the particle will be in equilibrium.

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Answer 1

$\huge \bf \pink{Aηswer}$

At highest point, frictional force =mg sin θ

Mg cos θμ = Mg sin θ

μ=tanθ

tanθ=dx/dy = slope =2x/a

x2=ay

y=y²/a

dx/dy = 2x/a

μ=2x/a

x= μa/2

y=x2/a = μ²a2²/4a = μ²a/4

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