Can an egg be balanced on its end?

[Sutitan]

Before I ask my question, I understand its possible to balance an egg. I just went out to buy some eggs and did it. I seem to have a magic egg that literally takes me about 3 seconds to balance. (I did cheat a bit. I shook it up pretty nice to break the chalaza to lower the center of gravity.)

The question my physics teacher asked me is "Why can't an egg be stood on its end? (assuming uniform density and a ellipsoid shape)" By ellipsoid I am assuming a Prolate spheroid. I am guessing he just wants a perfect "egg shape"

from my understanding, we can. Wouldn't the center of gravity be right down the middle? the location would be the same as the center of mass because of the uniform density. And the center of mass would just be at the center of the ellipsoid. therefore, if you found the exact point of the end of the ellipsoid, you could balance it, since it would line up with the CG.

I don't know what I am missing. I think you should be able to balance an egg on its end (especially given the conditions I was given). I hope I didnt mis-understand him cause of his really heavy accent. If it helps, we are learning about static equilibrium and elasticity.

 

[Doc Al]

Sure the center of gravity can be placed over the center point...or could it? What your teacher is probably getting at is whether a perfect egg shape can be in stable equilibrium when on its point. Can it? If unstable the slightest jarring will knock it over.

 

[cjmdjm]

You have to look at what happens to the height of the center of gravity when the angle theta is changed. By theta, I mean the angle between a line shooting out of the top of the egg, and the ground. It is 90 degrees when the egg is balancing on end. Anyway, consider a small change in the angle theta (to say, 89 or 91 degrees). If such a disturbance results in the center of gravity being higher above the ground, then the egg is stable. It means that 90 degrees is the angle which minimizes the eggs gravitational potential energy. (at least, its a local minimum) If such a disturbance lowers the eggs CG, then it is unstable, because, due to gravity, it wants to get the CG as low as possible.

If it is unstable, you may get it to balance with a lot of effort, but the tiniest disturbance will cause it to fall.

So a perfect egg shape of uniform density is unstable because a small disturbance lowers it CG compared to where it was before the disturbance. Proving that a small disturbance lowers the CG is a fairly involved problem mathematically, and you would need an exact definition of a perfect egg shape.