The Physics of A Glass Starfish Falling on Your Toe

The Physics of A Glass Starfish Falling on Your Toe
by: Dani Glassman

The summer going into my freshman year of college, I went to Pier1 Imports with my dad to buy a chair for my room. While I was there a freak accident occurred, where my knee knocked a loose shelf causing the shelf to collapse. The shelf was holding a giant blue and cream glass centerpiece starfish on it. The starfish fell directly onto my big toe, splitting it open and cutting my ligament. I had to go to the ER to get stitches. This all occurred a week before I planned on leaving for Colgate, so I had to go to college in a booty for the first 2 weeks. I never considered the physics behind the incident until now...

A) I calculated the force that the starfish hit my toe with [note- because it was the summer I was wearing flip-flops so it hit directly onto my skin).

F=ma
m starfish= 1.5 lbs or 0.68 kg [I looked at glass centerpiece starfish online and choose mass of similar one, the actual starfish that fell on me is no longer made and I could not find it online anywhere]

F= (0.68kg)(9.8m/s^2)
F=6.66N
So, my toe felt 6.66 N from the starfish falling on it.

B) I calculated the velocity that the starfish hit my toe, assuming that the shelf was around the height of my knee, 0.5m tall.

Vf^2=V0^2 + 2a(Δy)
Vf^2= 0m/s + 2(-9.8)(-0.5m)
Vf^2= 3.13 m/s

can also do this calculation with energy, assuming no Wnc
-ΔPE= ΔKE
-mgΔh = 1/2 mV^2
-(9.8)(-0.5)=1/2)(Vf-0m/s)^2
9.8=Vf^2
Vf= 3.13 m/s

3.13m/s = 6.99 mi/h
So, the starfish hit my toe with a significant amount of speed!

C) I calculated the time in which it took the starfish to fall off the shelf and strike my toe.

Vf= Vo + at
3.13 m/s = 0m/s + (9.8)t
t= 0.32 seconds

The typical human reaction time is around 0.2 to 0.3 seconds, where 0.2 seconds is considered an excellent reaction time. To give some reference point, the reaction time for a sprinter it is around 0.1 seconds. I estimated my reaction time to be 0.3 seconds. Therefore, I technically could have moved my foot out of the way in time to avoid being struck by the starfish. However, the counter that I was standing at extended out horizontally, so I was unable to see the shelf bellow. Thus, I could not react to the falling of the starfish because the I could not see it. The only thing, that could have caused me to react would be the feeling of my knee grazing the shelf.

In the end, my mom got very mad at me because I was wearing flip-flops and had no protection against the falling object. In thinking about changes in force and how it could have impacted my injury, I thought about my toe in terms of using a helmet when riding a bike. In this scenario  it is parallel to crashing your bike and hitting your head without wearing a helmet. In this case, the "helmet" would be equated to wearing closed toed shoes. Therefore, if I had been wearing closed toed shoes, it would have provided a cushion and increased the distance and subsequently the time in which the starfish was falling, thus decreasing the force that my toe would feel with the same velocity. Without the helmet, my toe felt the entire force of the starfish, where assuming no Wnc, all of KE the the starfish had gained during the fall (equal to its initial PE). Although my mom did not know the physics behind the accident, she was right to be upset that I was wearing flip-flops.

The moral of the story is don't wear flip-flops when furniture shopping because you never know if a giant glass starfish is going to fall off a shelf and shatter on your toe. Although I now have scar on my toe, the good part to the story is that it was a great ice breaker for making friends freshman year!

NOTE- pictures of starfish replica and of my toe (at various stages) will be included if chosen as blog of the week! They make the story...