From: timr@sco.COM (Tim Ruckle)
Subject: Re: Physics and Football (was Re: Packer depth chart starters)
Organization: The Differently Clued
Date: Mon, 10 Aug 1992 07:57:52 GMT
Summary: okay, I screwed up
Keywords: Power, Force, Energy, Momentum, Velocity, Mass, Fuckup


Va negvpyr <l84sdbINNq3m@saltillo.cs.utexas.edu>
goolsbey@cs.utexas.edu (Keith Goolsbey) jevgrf:
} In article <1992Aug06.073807.3463@sco.com> timr@sco.COM (Tim Ruckle) writes:
} >
} >Power = Work/Time
} >
} >Work = Force X Distance
} >
} >So, (320lb)(120ft)/4.7s = 8,170 ft-lb/s
} >
} >Now 1 Horse Power = 550 ft-lb/s, so a theoretical sprinting Mandarich
} >packs about 15 HP under the hood...
} 
} [BZZZZT!]
} 
} This is completely bogus.

Quite possibly--dunno if you caught the reference in the header,
but I quite clearly labelled myself as a *failed* physics major.
It's been a helluva long time since I tackled even the simplest
of word problems, so I was hoping I'd be cut just a little slack...

} You are not doing vector calculations.  The runner is running
} *horizontally* and the force on him, his own weight of 320lb,
} is acting *vertically*.

Sure sure.  The runner is starting at rest, and has to exert a
force to get his mass up to that speed.  And I screwed up by using
the weight as the horizontal component of the force--so how do we
calculate the force necessary to accelerate a 320lb runner up to
25.5 ft/s?

} Also, the constant acceleration hypothesis is clearly bullshit.
} No human accelerates at a constant rate when running the 40,
} they accelerate very quickly up to top speed and stay there.

Y'know, we used to joke about our physics instructors having a
garage full of frictionless pulleys and massless ladders...

But ya, you are of course correct, and the assumption does make a
big difference--once he stops accelerating there's no more net
force on the runner, right?  (or has my physics atrophied beyond
all possible repair...)  Anyways, the crux of the matter would
seem to hinge on just how quickly that 300+ pound person does
accelerate to top speed.

} [...]
} 15 horsepower is *superhuman*.  *No human* can come close to a horse,
} much less a team of 15.

It's *amazing* what they can do with "vitamins" these days, eh?  ;^)

I should have noticed that this was not a reasonable result.  And
while it's perhaps the height of hubris, I will try giving it another
shot in hopes of getting it right this time.  (please hold on while I 
go dig up an old physics textbook so as to try and not embarrass myself
once again)

Okay, we have a 320lb person who's run 120ft in 4.7s.  I'm going
to convert to metric here to try and make it a little saner.

Question: what is the power output of a 145Kg runner who goes 36.58m
in 4.7s?  Assume a constant acceleration of the runner for half that
time, after which top speed is reached and maintained.

F=ma =m(dv/dt)= (145Kg)[(7.78m/s)/(2.35s)]
              = 480 Newtons

W=FD

Now, assuming the acceleration is constant, and the initial velocity
and position are zero, the book says that the displacement is equal to:

1/2(a)(t^2)= 1/2(3.31)(2.35^2)= 1/2(3.31)(5.52)= 9.14 meters

Is this reasonable?  Seems like it to me, if not a bit conservative.
(If anything, I'd think that a big person like that would still be
accelerating after the first ten yards of the forty). So:

W=FD =(480 N)(9.14m) = 4,387 Joules

And again, Power is the work done per unit time, so:

P=W/t =4,387J/2.35s = 1,867 WATTs

Hmmm, that comes to 2.5 Horse Power for that theoretical Mandarich.
Is this reasonable?  Oh hell, I don't know.  I probably screwed up
the calculation again, or else made a bad assumption.  Perhaps a
person who really knows their physics can give a tutorial on the
subject?

But it does occur to me that some of these fellows they're building
nowadays *are* superhuman.  Maybe they really are as strong as a
horse, and then some...

-timr

Special to Mr. Cho: check the attributions--it was my mistake, and not
John Heim's.  I did have some clue as as to what I was calculating, but
was apparently clueless (or as we say in California, "differently clued")
as to how to properly handle the calculations.

--

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