Wednesday, November 27, 2013

What is the force required to break a wishbone?

 A Thanksgiving tradition is breaking the turkey’s wishbone for good luck. Two people pull on the bone and whoever gets the larger piece is supposed to have good luck. I asked, what force is required to break a wishbone?

After some research, I found the ultimate strength of a bird bone is about 31 MPa. I converted this to Pa using: 31 MPa *  (1,000,000 Pa/1 MPa). Therefore, the bone has an ultimate strength of about 3.1*107 N/m2. Note that this is less than a human bone’s ultimate strength, which is about 1.3*108 N/m2.

I calculated the force needed to break the wishbone using F/A=ultimate strength. I assumed the diameter of a wishbone was about 0.5 cm, so it’s radius was about 0.25 cm or 0.0025 m. I calculated the area using A=πr2. The area was 2.0*10-5 m2.

I calculated F= (3.1*107 N/m2)(2.0*10-5 m2). The force required to break the bone is 620 N.

I then asked whether a person could make the bone break in their favor (so they would get the larger piece of the bone). I used to equation torque = rFsinθ. I assumed the wishbone was an isosceles triangle and the angle was 30°.

If a person held the bone about 5 cm or 0.05 m away from the center, the torque = (0.05 m)(620 N)sin(30) = 15.5 Nm. If a person holds the bone closer, for instance at 3 cm or 0.03 m, then torque = (0.03 m)(620 N)sin(30) = 9.3 Nm. The person at a longer distance will exert more force so they will probably break the bone. A person could make the bone break in their favor by holding the bone closer to its center. Happy Thanksgiving!

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