Physics Behind Weebles: Can You Build One?

[RMV]

Weebles wobble but they don't fall. I came to know that they wobble and come back to position since the center of mass lies close to the bottom.
Can I apply the formula for center of mass and do a human weeble as in

In that case if I consider a hemisphere of radius 60 cm and the average weight of a person as 70 Kg (M2) and height of the person as 175 cm. The center of mass of the person is at his middle at 87.5 cm (R2) from the top of the hemisphere. My aim is to find the mass (M1) to put at the bottom for it to act as a weeble. The center of mass of the system must be at the bottom say 30 cm (R1) from the ground into the hemisphere.
By considering a coordinate system with COM at (0,0), M1 at R1 (- 30,0) and M2 at (117.5,0)
M1 =( M2* R2) / R1
M1 = 70 * 117.5/ 30 = 274.2 kg

But this seems very large! Is it right?
Will I be able to build one?

 

[Khashishi]

Sounds like a cool project. Is the person standing on top of the hemisphere? You could have the person countersunk into the hemisphere to reduce the center of mass. If you want the center of mass to be 30 cm above the bottom of the hemisphere, then you can't have M1 at (-30,0) since that's the bottom of the hemisphere. The mass has some size, so it would probably be somewhere like (-15,0). Maybe you could make the base out of lead. Concrete might not be dense enough.

 

[RMV]

This is the model.

If you want the center of mass to be 30 cm above the bottom of the hemisphere, then you can't have M1 at (-30,0) since that's the bottom of the hemisphere. The mass has some size, so it would probably be somewhere like (-15,0).

Yes, I should have used something around (-15,0).Thanks!
In that case the mass goes to 500 kg ! Is it right? Its hard to believe we need 500 kg to balance 75 kg.

 

[shihab-kol]

Wow.Thats great.

 

[hassan]

hi there can you please send me the mathematical model of weeble mechanism