For those of you weren't aware, I am a huge klutz. Because of this, the Colgate campus can be a dangerous place for me in the wintertime... let's just say that I have a very familiar yet strained relationship with ice. This past spring, I was trying to avoid falling on some black ice on one of the pathways on campus (the hill behind Lathrop/Lawrence going down towards the Office of Admission), and I underestimated the slipperiness of the grass. I proceeded to fall, hit a tree, and break my leg (my tibia to be exact). People kept asking how I broke my leg and, well... it was hard to explain because it wasn't a far fall. So using my physics knowledge, I wanted to calculate all the fun physics about my broken leg!
The first thing I wanted to do was find the force at which I hit the tree. After a quick search online, I was able to find that the force needed to break a tibia is 4000 N, and I was able to use that to calculate the speed at which I hit the tree:
F = ma
4000 N = 65kg*a
a = -61.54 m/s2
vf = vo + at
0 m/s = vo + ( -61.54 m/s2 * 0.25 s)
vo = 15.4 m/s
I also was interested in finding out the strain on my bone which caused it to break. I was able to find that A = 0.08 m2:
F/A = E*(△L/Lo)
stress = strain
(4000 N/0.08 m2) = strain
strain = 50,000 N/m2
While there are a ton of other things I could calculate about my fall, I decided to call it and focus on avoiding falling down the hill again!