Subject: Re: catenaries vs. parabolas
From: Alan Wilson (awilson@accessus.net)
Date: Tue May 02 2000 - 11:52:50 EDT
A similar problem (not mine) is to ask the students to approximate the St.
Louis arch with a parabola and answer questions similar to those below for
their approximation. Particularly nice as we live close to the arch.
On Tue, 2 May 2000, Bret Taylor wrote:
> A little problem I like to give my calc students:
>
> A suspension bridge is 300 ft long. At the ends, the cable supporting it is
> 100 feet above the road. In the center it is 40 feet above the road. A
> power line is also spanning the river. It just so happens it "parallels"
> the cable - 100 feet above the road at the ends, and 40 feet above the road
> in the center.
>
> Which hangs in the shape of a catenary and which in the shape of a parobola?
> Which one is longer? How much longer?
>
> (Neat thing to do with graphing calculators. Try and get an appropriate
> window that shows both cables completely.)
>
> Second question (fun question - makes them think - I usually just use it as
> a discussion question in class):
>
> A telephone comany needs to string 50 miles of line. We know these lines
> expand in the summer and contract in the winner. Assume the line needs
> "hang" 5 feet in the summer and it will contract to 2 feet of hang in the
> winter. (If it hangs less than 5 feet on the hottest day of summer, it will
> contract too much in the winter and be too tight between the poles.) How
> much less line would the company use by stringing it in the winter rather
> than the summer? How much money would they save? Is this reasonable or is
> there a fallacy in our logic to even be discussing this?
>
>
>
> Bret Taylor Lake-Sumter Community College Leesburg, FL John 3:30
>
> It matters not the subject taught, nor all the books on all the shelves.
> What matters more, yes, most of all, is what the teachers are themselves.
> John Wooden, UCLA
>
>
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