00:02
We need to find the sag of this wire from point a to point b, which is labeled in our diagram as this length of h.
00:11
And we also need to find the mass of this cable, which we can find by first finding the weight per unit length of that cable.
00:21
So before we start the problem, we need to find these unknown values.
00:26
So the length from b to c, we're given that the length from a to b is 90.
00:34
So to get the length from b to c, we just do 90 divided by 2 to give us a value of 45 meters.
00:41
And we do the same thing for the length in the x direction from point b to c.
00:46
So we use the given length of 60 divided by 2, and we'll get a length of 30 meters from b to c.
00:53
And we're also given that the tension, the maximum tension of the cable is 300 nanos.
01:00
So we're going to first start by finding the length of the sag.
01:12
So i'll start by writing out the following equation.
01:16
So the length of the cable from point b to point c is going to be equal to c times the hyperbolic sign of x of b .c divide by c.
01:35
And we know what s of b .c is.
01:39
C is our unknown.
01:42
And we know what x of bc is.
01:47
So we can take this equation and solve for the unknown value of c.
01:52
So we'll get that c is equal to 8.
01:58
18 .45 meters.
02:05
And now the equation for y of b, that's going to be c times the hyperbolic cosine of x of b c, divide by c...