(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A bead, under the influence of gravity, slides along a frictionless wire whose height is given by the function y(x). Assume that at position (x,y) = (0,0), the wire is horizontal and the bead passes this point with a given speed v_{0}to the right. What should the shape of the wire be (that is, what is y as a function of x) so that the horizontal speed remains v_{0}at all times? One solution is simply y = 0. Find the other.

2. Relevant equations

3. The attempt at a solution

I started out this problem by considering the initial and final energies of the bead, [itex]E_{i} = \frac{1}{2}mv^{2}_{0}[/itex] and [itex]E_{f} = mgy + \frac{1}{2}mv^{2}[/itex]. From there, I can find the velocity of the bead at a point on the wire to be [itex]v = \sqrt{v^{2}_{0} - 2gy}[/itex]. This is the part where I start to get tripped up. I know that the horizontal component of the velocity (v_{0}) would be equal to [itex]v\cos{\theta}[/itex]. I already have an expression for v, but I'm not quite sure how to represent the cosine in terms of variables I already have. Once I have that, I'm pretty sure I'd be in the clear for solving this one. Any help would be appreciated! Thanks.

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# Homework Help: Bead on wire with constant velocity

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