Re: Help on Radius of Arc

[Bob Sciamanda <sciamanda@worldnet.att.net>]

Bill Cheesman wrote:
> I am having my students design model roller coasters.  Is there a way we
> can determine the radius of an arc if we know the length of the arc and
> the length of the cord of that arc?
>
> Bill Cheesman
> Fairport High School
Hi Bill,
	There may be an easier way, but from the geometry, I get the two
equations:
h/(2r)=sin(T/2) and s/r=T,  where h=chord length, s=arc length,
T=subtended angle.
Given h and s, these are two equations in the two unknowns, r and T.
Eliminating r yields:
		{sin(T/2)/(T/2)} = h/s  must be solved numerically (use Mathcad, if
available).

If your students have never had to solve an equation numerically, this
will give them a new and valuable experience.

Hope this helps.
-Bob
-- 

Bob Sciamanda				sciamanda@edinboro.edu
Dept of Physics				sciamanda@worldnet.att.net
Edinboro Univ of PA			http://www.edinboro.edu/~sciamanda/home.html
Edinboro, PA				(814)838-7185

You never did anything until the first time you did it.
-Me, here, now.