Optimal Wire Shape for Constant Horizontal Speed | Bead under Gravity

  • Thread starter Thread starter oscar_lai_hk
  • Start date Start date
  • Tags Tags
    Constant
oscar_lai_hk
Messages
12
Reaction score
0
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?
 
Physics news on Phys.org
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?
 

Attachments

  • SDC10081.jpg
    SDC10081.jpg
    18.1 KB · Views: 573
  • SDC10082.jpg
    SDC10082.jpg
    13.2 KB · Views: 543
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
 

Thread 'Please tell me where I am going wrong in this integral'

##|\Psi|^2=\frac{1}{\sqrt{\pi b^2}}\exp(\frac{-(x-x_0)^2}{b^2}).## ##\braket{x}=\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dx\,x\exp(-\frac{(x-x_0)^2}{b^2}).## ##y=x-x_0 \quad x=y+x_0 \quad dy=dx.## The boundaries remain infinite, I believe. ##\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dy(y+x_0)\exp(\frac{-y^2}{b^2}).## ##\frac{2}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,y\exp(\frac{-y^2}{b^2})+\frac{2x_0}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,\exp(-\frac{y^2}{b^2}).## I then resolved the two...
View full post »

Thread 'Direction of the magnetic field of an oscillating charge'

Hello everyone, I’m considering a point charge q that oscillates harmonically about the origin along the z-axis, e.g. $$z_{q}(t)= A\sin(wt)$$ In a strongly simplified / quasi-instantaneous approximation I ignore retardation and take the electric field at the position ##r=(x,y,z)## simply to be the “Coulomb field at the charge’s instantaneous position”: $$E(r,t)=\frac{q}{4\pi\varepsilon_{0}}\frac{r-r_{q}(t)}{||r-r_{q}(t)||^{3}}$$ with $$r_{q}(t)=(0,0,z_{q}(t))$$ (I’m aware this isn’t...
View full post »

Thread 'Initial conditions for orbits around a wormhole'

Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
View full post »

Similar threads

Bead sliding on a wire - calculus of variations
Replies
7
Views
3K
Bead sliding along wire with constant horizontal velocity -- Shape of wire?
Replies
2
Views
1K
Motion of a bead on a rotating linear rod
Replies
7
Views
9K
Proving stable equilibrium: Rotating circular hoop
Replies
6
Views
3K
Lagrangian equations - ring which is sliding along a wire
Replies
3
Views
2K
Bead on a rotating stick and the Lagrangian
Replies
2
Views
2K
What is the Speed and Frequency of a Bead Sliding Inside a Paraboloid?
Replies
10
Views
3K
Bead on wire with constant velocity
Replies
1
Views
5K
Physics Homework: A bead on wire
Replies
8
Views
4K
Force on a bead due to a rotating wire
Replies
23
Views
5K

Hot Threads

Recent Insights

Back
Top