From: SFPhysics@aol.com
Date: Tue Jan 21 2003 - 01:27:31 PST
From: SFPhysics@aol.com Message-ID: <113.1dd26aa7.2b5e6c83@aol.com> Date: Tue, 21 Jan 2003 04:27:31 EST Subject: Objects Dropped from Tall Buildings
Hello Debbie:
I don't claim to have an absolute answer to your student's question but here
is my reasoning.
As the formula is v final = square root of (2 * gravity acceleration * delta
d), you would first have to assign a value to the building. Let us say the
building is 300 meters tall. The velocity of the penny would then be roughly
77m/s. The gram weight of a copper core penny (not the new phony ones) is
3.11grams (new phony penny is 2.5 g). Thus the kinetic energy stored in the
moving mass is good enough to do some minor damage.
Now about the question of how far the coin would penetrate, that depends on
the point of impact (soft tissue vs. thick cranium) and whether the impact is
on the edge of the penny or a flat side that would dissipate the energy over
a larger area. Assuming the human skull to be 5 mm in thickness with a
reasonable amount of cushioning hair and a small amount of fleshy overlaying
derma, the coin would likely only be a flesh wound and at worst a minor skull
fracture. The BB gun my mother warned me about could put out an eye but even
with an average muzzle velocity of 60m/s it could not penetrate most of the
human skull. Even on soft tissue the depth of penetration is rarely more
than 2 mm. This has to do with the kinetic energy in the mass of the penny
overcoming the inertia of a larger amount of mass on the body. The question
is then 3.11 g moving at 77m/s will move how much of the mass it strikes?
The elasticity of the tissue just will absorb the energy quickly and a human
weighing many kilograms is not all that vulnerable. I am still cogitating on
how one would more accurately compute object penetration of the body by a
falling object but I bet Ron Wong would have a good answer.
IMHO - The junk science Urban Legend that coins thrown off the Empire State
Building would go through car hoods, and through people, is highly unlikely.
That seems especially reasonable when air resistance is added into the logic
stream.
As always, check my logic and math for errors. I am often wrong and love it
when shown the correct answer.
Al Sefl
Either I'm doing life long learning or I'm so old I'm forgetting everything
and starting over...
PS: Why my postings last week were doubled and in HTML is beyond me. I have
all that turned off and hope this one comes though using minimum bandwidth.
This archive was generated by hypermail 2.1.3 : Mon Aug 04 2003 - 16:18:11 PDT