Mathematics, 20.06.2021 14:00 eyanil17

A bead P of mass m slides down a smooth wire fixed in a vertical plane, which is bent into the form of the catenary S= c tanψ, with its axis is vertical and its vertex at its lowest point. The bead is given a velocity along the tangent when at its highest point. Prove that the velocity of the bead is given by $v^{2} = \frac1{2} ga (4sec(ψ) - 3)$ and the bead will leaves the wire when cos ψ = 2/3

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A bead P of mass m slides down a smooth wire fixed in a vertical plane, which is bent into the form...