How a cone shape would roll?

[wazzup]

I do not know if this is the correct section? sorry if not and could you please tell me what branch i need.

I have many "pellets" which are cone shaped. the rear is always 6mm in dia ,the front is 4.5mm.

This 4.5mm size varies slightly in manufacture.

it is very time consuming measuring with a digital caliper. i have seen a video on YT of a guy using a great method. the video is not great quality with no sound.

what he uses is a raised piece of wood to form a ramp. he puts a pellet at the top corner and lets go.

the pellet rolls in a arc. the pellets roll in different arcs depending on the size. he made little pots along the board edge to catch the pellet sizes.

What i do not understand is....... is there a calculation of the arc using the 2 dia sizes of the pellet

does the height of the slope effect the way any pellet rolls

hope that make sense,thank you

[Genady]

1 hour ago, wazzup said:

is there a calculation of the arc using the 2 dia sizes of the pellet

You also need the length of the pellet.

[sethoflagos]

The.ramp slope should be no more than what is needed to get the pellet rolling. Too steep and the pellet will slide rather than roll smoothly.

Assuming a true conical profile, the pellet will follow a track bounded by two circular arcs of radius length x 6 / (6 - 4.5) mm and length x 4.5 / (6 - 4.5) mm.

You might consider embedding photo detectors.in the ramp just outside these bounds to detect out of tolerance pellets coupled to a deflector arm or similar to dispose of them.

[KJW]

Thank you! You have created another analogy for how gravitational time dilation causes gravity in the "What is gravity?" thread. In that thread, I created the analogy of a slinky as well providing a formula that relates time dilation to acceleration. This formula is based on a geometric principle that I also applied to a disc. It also applies to your problem.

 

Let [math]D_L[/math] be the large diameter, [math]D_S[/math] be the small diameter, and [math]X[/math] be the length of the axle between them. Then the radius of the curvature of the roll of the large diameter, [math]R_L[/math] is given by:

[math]\dfrac{1}{R_L} = \dfrac{1}{D_L} \dfrac{D_L - D_S}{X}[/math]

 

 

Edited March 4 by KJW

[CharonY]

On 3/4/2024 at 4:28 PM, KJW said:

Thank you! You have created another analogy for how gravitational time dilation causes gravity in the "What is gravity?" thread. In that thread, I created the analogy of a slinky as well providing a formula that relates time dilation to acceleration. This formula is based on a geometric principle that I also applied to a disc. It also applies to your problem.

 

 

!

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