Find Function R(z) for Coin Rolling in Funnel

  • Thread starter jaykay99
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In summary, the problem involves a coin with a homogeneous mass distribution rolling in a funnel with only horizontal speed and maintaining a constant altitude. The task is to find a function R(z) that describes the shape of the funnel, with R>>r and z representing the altitude of the funnel. The equation \tan\alpha=\frac{v^2}{r\cdot g} is suggested, but it must be a function of z, not r. However, in a real-world experiment, the coin may not behave as expected due to the gyroscope behavior caused by the precession of its axis. This may result in an erratic path or the coin falling. The question remains as to what form the funnel must have and whether it is too
  • #1
jaykay99
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Homework Statement


A coin(radius=r) rolls in a funnel only with a horizontal speed v. The coin always stays at his altitude.
The coin has a homogen mass distribution and it only rolls! So it has a translational motion and a rotation motion.
Find a function R(z) whitch discribes the form of the funnel!
R>>r and z is the altitude of the funnel. the z-coordinate of the coin is changeless.

Homework Equations



I thougth it must be [tex] \tan\alpha=\frac{v^2}{r\cdot g}[/tex]

But then i tought the speed at all parts of the coin isn't the same.

If there are any questions in understand my problem, ask!
I made a drawing of that:
attachment.php?attachmentid=29220&stc=1&d=1287583375.jpg


Can u pls help me?
Thank you
 

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  • #2
But then i tought the speed at all parts of the coin isn't the same.

Every wheel that rolls on a surface behaves like that and its velocity is the velocity of the center.
Your equation is ok, but the problem asks to have it as a function of z, not of the radious (r).

But anyway I think in a real world experiment, it will not work, can you see why ? (tell your professor!)
 
  • #3
If there is no friction, it could work.

Because the speed is not constant the F_z also is not constant. So it would be more difficult.

Or other question:
What is the difference between a pointmass and a coin rolling like this?

When a point rolls like this it is quite easy to get R(z) or Z(r) cause they are inverse functions.
 
  • #4
is it too difficult?
Should i put in advanced physics?
 
  • #5
jaykay99 said:
If there is no friction, it could work.

Because the speed is not constant the F_z also is not constant. So it would be more difficult.

Or other question:
What is the difference between a pointmass and a coin rolling like this?

When a point rolls like this it is quite easy to get R(z) or Z(r) cause they are inverse functions.

No, it's not a problem of friction.
If you think the coin as a flat cylinder, the axis of the cylinder will have to rotate in order to form always the same angle with the surface of the funnell.

The coin rolls about his axis, but the axis must make a precession like movement (as if it was a spinning top).
It will behave like a gyroscope.
If the precession velocity of the gyroscope is not the same of the angular velocity of the coin around the funnell, then the coin will finally fall or follow an erratic path.

For your problem you are ok, the answer you gave is correct, I think that the gyrscope behaviour is advanced for your class.
In real world that coin would make an erratic path.
 
Last edited:
  • #6
Thank you for your answer.
I found a nice vid on youtube: https://www.youtube.com/watch?v=http://www.youtube.com/watch?v=rfyng8f-bOA&feature=related

What form must the funnel have?
Is it really to complicated to calculate with the gyrscope behaviour?
 
Last edited:

1. What is the purpose of finding the function R(z) for coin rolling in a funnel?

The function R(z) for coin rolling in a funnel is used to mathematically describe the relationship between the height of a coin (z) and its rolling distance (R) when rolled down a funnel. This can be useful in understanding the physics behind coin rolling and predicting the behavior of coins in a funnel.

2. How do you calculate the function R(z) for coin rolling in a funnel?

The function R(z) can be calculated by conducting experiments where a coin is rolled down a funnel at different heights and measuring the corresponding rolling distance. These data points can then be plotted on a graph and a curve can be fitted to find the function R(z).

3. What factors can affect the function R(z) for coin rolling in a funnel?

Some factors that can affect the function R(z) for coin rolling in a funnel include the shape and size of the funnel, the material of the funnel, the surface of the coin, and the starting position of the coin in the funnel. Other factors such as air resistance and friction can also play a role in the coin's rolling distance.

4. Can the function R(z) for coin rolling in a funnel be used for any type of coin?

The function R(z) can be used for any type of coin as long as the experiment is conducted under the same conditions for each coin. However, the function may vary slightly for different coins due to differences in weight, size, and surface properties.

5. How is the function R(z) for coin rolling in a funnel useful in real-world applications?

The function R(z) for coin rolling in a funnel can be applied to various scenarios, such as predicting the behavior of coins in a vending machine or designing a coin-operated ride. It can also be used in studies of fluid dynamics and gravity, as well as in developing new technologies that involve rolling objects.

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