00:01
So we have a non -uniform cable that's hanging under its own weight, and i've really exaggerated the difference in diameters here.
00:09
Okay.
00:10
We want the stress to be a constant, which is the tension divided by the area at any given y.
00:17
So it's t of y divided by a of y.
00:25
And of course, the area as a function of y is pi over 4.
00:36
Times the diameter, which is a function of y, quantity squared.
00:46
Okay.
00:46
And then the tension is equal to the mass below the mass, which is a function of y times g.
01:01
Because basically the weight of what's down here is pulling on the wire, and that's what the tension is at this point.
01:14
And then the mass at y, we can figure that out like this, is going to be an integral of the density, which is going to be constant times the thickness.
01:45
If i take a narrow slice here, so it's pi times d of y squared times the thickness.
02:00
D .y.
02:01
So let's make this capital d instead of little d.
02:07
That'll be less confusing as far as so...