Last week when I was home over Thanksgiving break, I accidentally broke my computer screen. My laptop was lying open my couch, but it was not visible because I had previously thrown a shirt on top of it when changing. After I changed, without thinking I jumped onto the couch and landed directly on the screen of the computer causing it to shatter. Even though I was very distraught after breaking my laptop, I immediately began to consider the physics of what had just happened. First, I calculated the force exerted on the laptop by my body, using my mass (about 70 kg) and my acceleration due to gravity (my body is in free-fall after the highest point of the jump.
F = ma = (70 kg)(9.8 m/s^2) = 686 N
I was also curious about the amount of energy that my body had just before landing on the computer, so I could know the energy that was transferred into the computer causing it to break. To do so, I first calculated my final velocity (just before hitting the couch) estimating that the highest point of my jump was about 0.5m above the couch.
Vf^2 = Vo^2 + 2ad = 0 + 2(9.8 m/s^2)(0.5 m)
Vf = 3.13 m/s
Once final velocity was calculated to be 3.13m/s, the total energy transferred into the computer screen can be calculated using: Total E = KE + PE. Calling the top of the couch h=0, the potential energy at the collision is 0, so the only energy is kinetic energy.
KE = 1/2mv^2
KE = (.5)(70 kg)(3.13 m/s)^2 = 343 J
My laptop is a 12-inch Macbook weighing only 2.30 pounds, or 0.92 kg. After calculating the force acting on the laptop from my fall to be 686 N as well as the energy transferred to be 343 J, it is clear why my screen shattered the way it did. These values for force and energy are both very large in comparison to the very small size of the laptop. Weighing only 0.92 kg and being only a few millimeters thick, my Macbook’s screen stood no chance of surviving the force of my entire body falling directly onto the screen.