From: Ronald Wong (ronwong@inreach.com)
Date: Thu Jan 23 2003 - 01:01:25 PST
Message-Id: <l03102800ba52c643aefd@[209.209.18.94]> Date: Thu, 23 Jan 2003 01:01:25 -0800 From: Ronald Wong <ronwong@inreach.com> Subject: Objects Dropped from Tall Buildings
>I have a physics problem and I'm at a loss for how to solve it. I really
>want to solve it, though, since a student asked it and
>it's the first time I've ever seen this student pumped
>about anything even remotely academic. We imagined a
>penny dropped from a sky scraper and ignored air
>resistance (I know, I know). This student wants to
>know how far the penny would...
Debbie:
A few more things to add to Al's response to your question:
1. First of all, your student might have a particular building in mind.
Whether or not that is so, the following website should prove useful since
it gives you "real world" values for 419 structures ranging from the
Brandenburger Tor in Berlin to the CN building in Toronto. The latter is
currently the tallest structure in the world.
http://www.aviewoncities.com/building/_buildingsbyheight1.htm
2. Currently, the tallest building in the US is the Sears building in
Chicago (see above URL). Using the formula supplied by Al, you get a final
speed of around 93.2 m/s after falling from the top of the Sears building
(443 m). Using his value for the mass of a common penny (2.5 grams), you'll
find the kinetic energy is around 11 J.
A typical 0.177 caliber airgun (the type that uses CO2 cartridges as a
"propellant") can fire pellets with kinetic energies that range from
around 4 J to 30 J depending on the muzzle velocity.
To get some idea as to how dangerous the penny's 11 joules of energy can be
consider the fact that one gun dealer who was selling airguns that were
made to look exactly like a couple of popular handguns said this about them:
DANGER: THESE ARE NOT TOYS. Available in-store only.........
WARNING: These air guns are not toys, Adult supervision is
required. Misuse or careless use could cause serious injury
or even death, can be dangerous up to 333 yards (305 metres).
The pellets in this case had a muzzle velocity that gave them approximately
3.7 J of energy - about a 3rd of what the penny would have upon hitting the
ground after falling 443 m (in a vacuum).
Sounds potentially fatal to me.
3. In reality there is air friction of course and, using a classical
equation - and some simplifying assumptions - the terminal velocity of this
penny turns out to be somewhere between 8 and 16 m/s (16 m/s being the
terminal velocity of a sphere). This puts the penny somewhere between that
of a raindrop and a small hail stone.
In reality, it shouldn't be a serious problem - unless you happen to be
looking up and it hits you in the eye.
With that in mind, I remain cheerfully yours,
ron
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