Question

A manufacturer of corrugated metal roofing wants to produce panels that are u = 44 in. wide and 2 in. thick by processing flat sheets of metal as shown in the figure. The profile of the roofing takes the shape of a sinewave with equation

y = sin(πx/11).Find the width w of a flat metal sheet that is needed to make a 44-inch panel.

Answer 1

I've been out of this for a while; I wanted to see what I could rememeber. Hope this helps.

So here's what I'm thinking... Your looking for the distance over a curve, so you can use the old pythagorean theorem c =√(a²+b²) to find the distance between any two points on the curve. Problem is since this is a curve, you have to find thedistance between two points that are infinately close to one another, and you have to do this over x values of 0 to 11. Here's where calc kicksin.

Integegrate the pythagorean theorem from 0 to 11. Before you do this, you'll need to eliminate the y... well the y becomes sin(πx/11) sincey=sin(πx/11). So you get a pythagorean theorem that looks like this:

c = √(x²+(sin(πx/11))²). Now integrate that right side from0 to 11; should be a lot of fun. Sorry I don'thave time to try it out; I think it'll work though.