00:01
All right, so let's say we have a restrainer of some kind with a cable tied to it, and a slider is dropped from a height.
00:11
Let's see, we'll just call this h, but it's one meter.
00:15
And the slider has a mass of 35 kilograms.
00:20
And we're told that young's modules for this particular cable is, let's see, 130 gigapascals.
00:27
And the cable itself has a cross -section area of 40 square millimeters.
00:33
So we want to know what's the minimum length of the cable that will allow it to withstand a critical stress of 500 million pascals.
00:42
So the idea here is that when this falls and strikes the container, all that kinetic energy is going to be transferred over a small deformation in the length of this cable.
00:54
And so what we'll have is like, you know, the change in kinetic energy is equal to the negative change in potential energy as this falls.
01:06
And from our old kinematic equations, we kind of know that like the velocity squared, the final velocity is here.
01:14
The velocity is going to equal two times the acceleration times the distance over which it stops, which is like the change in length of the cable.
01:22
And a here is going to be the force divided by the mass.
01:26
And the force here, presumably, is going to be the maximum permissible load times the area of this cable, because this is like our critical acceleration that will cause this.
01:36
We want to find the deformation that will cause, that results from this critical stress being applied.
01:43
Okay.
01:44
And so what we'll have is like 2 times sigma times a over, or sorry, over m, times delta l is equal to, v squared...