DUI: Decorating Under the Influence

According to various studies, emergency room visits rise during the holidays due to season-specific activities gone wrong. These can include cooking, decorating, trees catching on fire, etc. However, a rising number of these ER visits seem to be coming from people decorating under the influence when they are filled with overwhelming joy and holiday spirit. When considering the most dangerous situations that this phenomenon can present, stringing lights came to mind first. 

I first considered the forces that would be involved in a fall from the top of a two-story house. 

ΔKE + ΔPE = W_NC

ΔKE + ΔPE = 0 J

½m(v_f² – v₀²) + mg(h_f – h₀) = 0 J

½(70 kg)(v_f²) + (70 kg)(9.8 m/s²)(0 m – 7.26 m) = 0 J

v_f = 11.9 m/s

If we assume that the height of a two-story house is approximately 25 ft, or 7.26 m, the velocity of the person just before they hit the ground will be 11.9 m/s.

p = mv = (70 kg)(11.9 m/s) = 833 kg m/s

 ΣF = Δp/Δt = (0 kgm/s + 833 kgm/s) / (0.001 s) = 8.33 x 10⁵ N

By using momentum and up as positive, we calculate that the sum of the forces acting on the person when they stop to be 8.33 x 10⁵ N. Assuming that this force is distributed over two legs, each leg would experience 4.17 x 10⁵ N of force.

4.17 x 10⁵ N / (π(.0127 m)²) = 8.22 x 10⁸ N/m²

Assuming this force is distributed directly to the tibia, the force can be written as . Since the ultimate compressive strength of bone is 8.22 x 10⁸ N/m², the person will most likely suffer some injuries and end up in the hospital for the holidays.