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Old Jun 17th 2011, 11:51 PM   #1
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Angular Energy and Falling Dominoes

First of all, hi! I'm new here.

1. The problem statement, all variables and given/known data
Rather than a specific problem, my friend and I are doing an Extended Experimental Investigation on the energy transfer of dominoes for our grade 12 assignment.


2. The attempt at a solution

We have approached it using loss of gravitational potential energy (Ug) and then comparing that with rotational kinetic energy determined by the theta: Theta is the angle from the vertical to the point as where it has fallen.

Assumptions:
Gravitational energy becomes rotational energy.
The domino's leading edge that it rotates around does not slide
The domino has a toppling point, and its velocity at this toppling point is 0m/s

We then aim to compare these two values with experimental data gathered with a camera.

Here's what we have done (equation number):

To find the gravitational potential energy, we calculated the height of the center of gravity at the toppling point* (1), found Ug at this point, then calculated Ug at the end point in the same method (2).
The difference was found, and hence the loss of gravitational energy, which should have been converted into rotational kinetic energy.

*The toppling point is when the point of the center of gravity of the domino is outside the vertical of the axis of rotation. I.e, draw a diagonal from the edge the domino is rotating on to the opposite corner (this line will pass through the center of gravity) and when that diagonal line passes vertical, the domino starts to fall due to gravity. If the diagonal is not past the vertical, it will fall back to an upright position.

To find the rotational kinetic energy theoretically we did the following:

The Domino's velocity is 0 at the toppling point, at which the angle is dependent on the height (3).
The acceleration of the domino is not constant, however is can be modeled. As the angle of fall increases (theta), the component of gravity actually affecting the domino increases, hence the acceleration increases(4). Thus by integrating the acceleration, one can find the velocity (i say velocity here, but it is more the speed of the domino) of the domino due to the falling angle (5).

Once this velocity is acquired, it was used to find the rotational velocity (omega) (6). Using the mass moment of inertia (7) and the rotational velocity, the rotational energy was found (8).

3. Relevant equations

refer to the attached image

Summary

Basically, the calculated change in Ug and Ekr does not match, they are out by about a factor of 7. I have attached my spreadsheets if you want to look at exact calculations, however, because the formulas derived are dependant on height as well as theta, in the rotational energy spreadsheet columns E, F, G, H, and K are all for the height of 0.05m. The rotational energy calculated is at a theta value of 1.42 i think - Pretty much the last cell in the bottom right.

Any help is greatly appreciated, thanks!
Attached Thumbnails
Angular Energy and Falling Dominoes-equations.jpg  
Attached Files
File Type: xls Gravitational Calculations upload.xls (23.5 KB, 3 views)
File Type: xls Rotational Calculations upload.xls (67.0 KB, 3 views)
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Old Jun 20th 2011, 08:46 AM   #2
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Originally Posted by SaminS View Post
First of all, hi! I'm new here.

1. The problem statement, all variables and given/known data
Rather than a specific problem, my friend and I are doing an Extended Experimental Investigation on the energy transfer of dominoes for our grade 12 assignment.
If you are talking about the energy transfer between dominoes as a row of dominoes topples in sequence you have a problem, you cannot isolate individual dominoes. Any domino other than the first is always in contact with one or more other dominoes, though that hasn't stopped others from assuming isolated dominoes.

Also, unless you have access to a high speed camera you might find measuring anything useful off of a video difficult.

Have you looked at "Towing Icebergs, Falling Dominoes, and Other Adventures in Applied Mathematics" by Banks? This is of interest despite the mistakes in the asymptotic analysis.

Z

Last edited by zedd; Jun 20th 2011 at 08:50 AM.
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