Optimal Wire Shape for Constant Horizontal Speed | Bead under Gravity

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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 9x,y) = (0,0), the wire is horizontal and the bead passes this point with a given speed v 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 remain v at all the times ? One solution is simply y = 0. Find the other.

I don't know how to solve this problem by using which physics equation?
 
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oscar_lai_hk said:
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 9x,y) = (0,0), the wire is horizontal and the bead passes this point with a given speed v 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 remain v at all the times ? One solution is simply y = 0. Find the other.

I don't know how to solve this problem by using which physics equation?

Hi oscar_lai_hk! :smile:

Start with KE + PE = 0.
 
tiny-tim said:
Hi oscar_lai_hk! :smile:

Start with KE + PE = 0.

I try to solve this problem of conservation energy.but why the answer not include y = 0?
 

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Hi oscar_lai_hk!

Are those two jpg's your answer?

It will take hours before they're approved.

Please type your answer so that we can se it now. :smile:
 
tiny-tim said:
Hi oscar_lai_hk!

Are those two jpg's your answer?

It will take hours before they're approved.

Please type your answer so that we can se it now. :smile:

The answer is :
y = (square root(mg) ) X /v
 
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