On my way to my last Latin class of the semester this morning, I observed a very large block of frozen snow that had broken off in the doorway roof of Lawrence Hall fall with a very heavy thud right besides me. For a moment, I reminisced about the past times when random falling chunks of frozen snow ended up on my neck, quickly melting into ice-cold water and flowing down my back underneath my layered clothes. I wondered if I had stood at that very spot when the ice fell around what force would I have been struck with how much work would have been done in the process. Force and work due to gravity being F=mg and W=mgh respectively, this was not too difficult to estimate. Assuming the height of the doorway roof to be around 3m, my height 1.8m, and the mass of the chunk of ice around 1.5 kg, I calculated as follows.
(1.5 kg) * (9.8 m/s2) = 15 N
(1.5 kg) * (9.8 m/s2) * (3-1.8m) = 18 J
15 N being the force around holding a large book in the air, it did not seem that the falling block of ice would pose an immediate risk. However, it also occurred to me that a greater inconvenience would come from the piece of ice, if for some unfortunate circumstances it were to have lodged inside clothing and began to melt. Realistically assuming that the block of frozen snow would break on impact and perhaps only a fourth would end up in my neck, I could calculate the theoretical temperature change on my body temperature effected by the ice not accounting for the heat generated to counter the ice’s effect. The mass of me and the ice was estimated at 70 kg and 0.25 kg, respectively. The human specific heat was estimated at 3470 J/kg (http://www.engineeringtoolbox.com/human-body-specific-heat-d_393.html).
mLice+mcice ΔT=mcbody ΔT
0.25kg*3.33*105 J/kg+0.25Kg*4186 (J/kg) *t=70kg*3470J/kg*(273+36-t)
t=307.3 K, 1.7 K decrease
Theoretically, if the body did not do heat regulation via homeostasis, the ice would decrease the body’s internal temperature by 1.7 C or K, which would be around 34.3 C, below the typical diagnosis for hypothermia.
Of course, as an endotherm mammal, homeostasis would ensure that my body generates heat to maintain body temperature at 36 C. However, if my body was not able to do so, that would result in hypothermia.