Sunday, October 25, 2015

The Physics of an Achilles Tendon Rupture

Recently, I had the unfortunate experience of rupturing my Achilles tendon during an intramural soccer game. Having played competitive soccer for most of my life without experiencing any sort of significant injury, I find it very ironic that such an injury finally occurred during a noncompetitive intramural game.

My injury happened on cold fall day right after half time of the second game I was played that day. Stupidly, I did not stretch after half time and believe that while resting during half time my muscles really tightened up due to the cold weather. A few minutes in to the half, the ball was played to me and I turned with it while sprinting and changing direction. At this moment, I experienced what felt like someone kicking me as hard as they possibly could in the back of my calf. I subsequently went to ground and rather painfully noticed that my calf was cramped up and stuck all the way up below my knee. I was eventually able to pull the cramp out and hobble off the field. At first, I was convinced that someone on the other team had kicked me in the back of my leg and that had caused my cramp. However, having talked to my friends on the sidelines they said nobody was behind me so the feeling of getting kicked was due to something else. As a result of this, I thought maybe I had torn my calf or had some sort of deep tissue bruise.  Although initially I did not think my injury was too significant, I decided to go see the doctor. At the doctor's office, it took maybe 2 minutes to diagnose me with a ruptured Achilles tendon.

Ignore air Resistance

As a student of physics, I have recently spent some of my free time wondering what kind of force the ground must have exerted on my Achilles in order to tear what apparently is the strongest tendon in your body. According to my doctor, an Achilles is able to receive a load stress that is 10 times your body weight. It receives a load of 3 times your body weight while walking and 7 times your body weight while running. With this being the case, let’s try to analyze the minimum tension force that I placed on my Achilles when it tore:

Mass: 85kg

Ftotal= 10(85kg)(9.8m/s2)= 8330 N

Fx=10(85kg)(9.8m/s2)Cos(70)= 2849N

Fy=10(85kg)(9.8m/s2)Sin(70)= 7827N

Additionally, when your Achilles tendon snaps in makes a very loud sound that is similar to a gunshot. Some of my friends thought they heard a loud snapping sound when I went down on the field, but at the time did not realize where the sound was coming from. With this being the case, let’s try to estimate the velocity with which my tendon snapped:

Wnet= ΔKE

Ftotal= 10(85kg)(9.8m/s2)= 8330 N
Distance (estimate)= .25m
Mass tendon (estimate)= .2kg

Fd= ½ mv2

(8330N)(.25m)= ½ (.2kg)v2

v=144 m/s No wonder it is so loud!

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