When I get incredibly stressed, like the past two weeks, I become restless in bed, meaning I toss and turn all night long. It was only a matter of time before one day I would just so slightly toss a little too far and fall out of bed onto the ground. So, low and behold, I fell. As I was falling, my first thought was obviously the physics of the event. If we call the top of my bed the max height and using my mass we can calculate my potential energy just before falling.
Coincidentally my potential energy at the top of my fall is equal to the work done by gravity during my fall (assuming I live in a vacuum of course). Next, as I fell I thought about all of that potential energy that was being converted to kinetic energy, and thought to myself, “I wonder how fast I’ll be going when I hit the ground”. Luckily for me, there is an easy way to find that using the principles of the conversation of energy.
mgh1 + 1/2mv21= mgh2 + 1/2mv22
500J + ½(68)(0)=68(0)(9.8)+1/2(68)v2
Then at the point right before I hit the ground, my mind went where most people’s minds would go, “What is my momentum at this point”. Once again, my physics training had enabled me to find this
mv= 68(-3.8)= -260 kg*m/s
Then as the ground caught me, I thought about how my momentum was changing and how much force I experienced as I hit the ground ( I would assume the amount of time for my body to stop falling to be 0.001s). Thus, I quickly got up off the ground and calculated the force applied by the force to stop my fall.
F=260,000 N = 58000 lbs. of force
Next, I thought about how that force would be distributed throughout my entire body so I divided the total force in pounds by my height in inches:
58000lbs./70in= 830lbs of force/Inch of John
Lastly, I thought about how quickly my velocity was changing as I came to my stop so:
a= 380 m/s/s
Luckily for me, however, is that as I fell I did not freefall nor am I an ideal atom falling in a vacuum; therefore, I did not sustain any serious injuries other than the embarrassment of falling out of my bed.