Optimal Wire Shape for Constant Horizontal Speed | Bead under Gravity

[oscar_lai_hk]

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?

 

[tiny-tim]

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!

Start with KE + PE = 0.

 

[oscar_lai_hk]

Hi oscar_lai_hk!

Start with KE + PE = 0.

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

 

[tiny-tim]

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.

 

[oscar_lai_hk]

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.

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