Friday, November 24, 2017

The Physics Behind Winning the Wishbone Breaking Contest

Every year, after my family pigs out on a Thanksgiving feast, we have two people face off for the bigger half of the wishbone. You make a wish, and each take an end of the wishbone and pull. Legend says whoever pulls the bigger half has their wish come true. This year was my turn against my aunt, and stakes were high. I turned to physics to maximize my chances of winning, and I actually succeeded. Logically, I assumed that the person who exerted more force would be more likely to break the bone.
To figure this out, I used the torque formula, T=rFsinΘ. To find the force (F), I used the formula stress=force/area. After doing research, I found the bird bone's ultimate strength to be 96 MPa, or 9.6 x 10^7 Pa (note: this is the ultimate strength of a chicken bone, I couldn't find the value of a turkey bone.. so this estimation isn't quite exact). I assumed the diameter to .75 cm, radius=.375. Using A= πr^2, I calculated an area of 4.4 x 10^-5 m^2. Using this information, F= (4.4 x 10^-5 m^2)(9.6 x 10^7 Pa)= 4241 N. Thus, 4241 N of force is required to break the wishbone. I then assumed the angle of the wishbone to be about 40 degrees. Following this, I plugged this information and varying r values into the torque formula to see how torque would change. I ultimately found that the higher the r value, the higher the torque, making the person more likely to break the bone. By holding the bone closer to its center, it will be more difficult to break your side of the bone. Thus, you can gain some control as to whether your side of the bone breaks depending on where you position your hand in relation to the bone's center.
In addition to this, another advantage in winning the wishbone competition is choosing the thicker side of the bone (if you could get away with it!). The thicker side of the bone has a larger cross sectional area, thereby reducing the stress created by a certain force.. making it less likely to break.
With these physics ideas in hand, I was able to beat my Aunt Rose in the wishbone breaking contest!