Balancing bird

Work to be developed

Explain the functioning of the Balancing Bird.

What is the Balancing Bird?

The Balancing Bird is a geometric figure that is similar to a bird, built in a way that when it is supported on its beak it is in equilibrium.

The design and construction of a Balancing Bird obeys to Physics concepts such as the centre of mass and the balance of forces and moments.

In the shops we can find many types of Balancing Bird, with varied colours and formats.

The Balancing Bird can serve as a toy and as decoration of homes and gardens. It can also be used as support material in classes of various subjects, to illustrate concepts of Physics and Engineering.

http://pbskids.org/sid/balancingact.html

http://www.youtube.com/watch?v=L5vnpg8NhBE&NR=1&feature=endscreen

http://www.youtube.com/watch?feature=endscreen&NR=1&v=CgvDrzSMaIQ

http://video.in.msn.com/watch/video/the-ultimate-toothpick-trick/1ju9u725c?cpkey=12f5e616-f769-45cb-9f4b-1387223fd883%7c%7c%7c%7c

Theoretical Rationale

The Balancing Bird will only be in equilibrium, in relation to its beak, if there is a balance of the moments caused by the mass of the wings, the body and the tail, with respect to the point where the beak is.

Thus, through the generic expression of the equilibrium of moments;

[pic]g [pic] + [pic]g [pic]g [pic] = [pic] [pic]

Putting g on evidence,

g ([pic] [pic] + [pic] [pic] [pic] ) =g [pic] [pic]

and dividing the whole equation for g, we get;

[pic] [pic] + [pic] [pic] [pic] = [pic] [pic]

This means, [pic] = [pic] [pic]

where, [pic] (1)

On the other hand, considering that the material is homogeneous and of uniform thickness, being m = V e V= AƐ (where Ɛ is the thickness), we can write m= AƐ and substituting in (1) we obtain

[pic] or [pic]

Cancelling [pic]we obtain [pic]

In the same way we can calculate[pic],