Right. What's this? Chapter nine Problems 79. Um, if we look here to read the problem, it's a bit of a long one. I'm going to assume you have the book with you on this one in the interest of time Problem nine Problem 79 in chapter nine. I should say, uh, essentially, we have a We have, uh, an adventurer going using a mountain climbing technique. And they need to get past a music, traverse a deep chasm. And essentially, we want to see if the rope that they're going to use to traverse between this chasm you're going to break or not based off of the tension in the rope. This is very similar to two problems before to our problems before Schefter Chapter nine. Problem 75. Uh, in that you can you just need to do the sum of the forces. So we're looking for X here. We want to see how far it's sagging and then based off of how far it sags. We also want to see what the tension in the rope is. And if it's gonna break or not, Right. So let's calculate all these things we can use the mutant. Second long. This will tell us everything we need to know. So first, of course, as we always do with force with forces. Let's drop free body diagram. Let's go look something like this and equip it. Remember our vector signs. So 2025 meters both ways. We have angles there at the top ex, the ex distance. We don't know what Saget is for the person. They're obviously being affected by gravity. They have mass. And there's tension pulling them in both ways as the rope is tied into the trees. Um, yes. So to include the safety factor, the tension must be less than or equal to 2900 Nugent's, that is to say, Yeah, but the tension must be no more than 2900 means. And so we have the exact same equation from problem 75 to times the, uh why component of the tension, which is just ft attention for its multiplied by sine data. It's attracted by energy, is equal to zero. And with that, if we have the maximum force possible there, which was just calling 2900 for now, then say that would be ah, well, you have all these numbers, right? G is 9.1 massive 75 kilograms and the FT max is 2900 news. You can calculate fatal minimum to be seven degrees at most. So this means weaken more or less interchange, sign and tangent as before. Small angle approximation. Um, but also from the triangle that we see on the left side of the road by Bagram. Well, it could be the left or the right. Let's just say neither triangle we can use are triggered. No metric, uh, brain, too. So this problem So you say tangent data. It was attention. Data man is equal to X men over 12.5 meters. We can calculate the distance the minimum distance needed to have for there to be a sag. And as we can see, we are too calculated the angle needed so we can just plug that in, multiply by 12.5 and we find that be sag, you're going to be 1.6 meters. That's to say the minimum distance the rope must sag based off of the maximum force is going to be 2900. It's gonna be 1.6 meters now taking that sag and multiplying it by 1/4. Let's look at if the Tyrolean traverse is set up incorrectly so that the rope sags by only 1/4 the distance found. What's the tension? Then we want to say, OK, let's multiply at 1.6 my fourth, so it's gonna be about 0.4. But let's do it exactly. It'll be 0.3992 meters. We can use this distance to find out what the tension on the rope is by working backwards. So what we can do here We were the next page. So, as I said the most by by 1/4 to get 0.3992 Use that distance. Find the tension. And so essentially, we flip around the changing equation and take the arq Tana both sides to cancel out the changing on the left. To get the angle we plug in our new distance rather than 1.6. Now it will be a 0.3992 meters, uh, calculator angle. Our new angle is going to be 1.8 to 9 degrees, which we can then plug into the sign below the sign of the equation below and mg over to science data will give us the tension with with all of our numbers plugged in should be about 12,000 Newtons more exactly. It'll be 11,512 neuters, um, and with this the rope line on break. But, uh, rather than the safety factor being 10 it's only going to be four. Because if you divide 12,000 by four, you should get about 3000. Which is what our, uh, forces here. Right there's about 5900. Just $100. This is 500 off, but still pretty close to 12. So that's a factor of 10. Would have had a 29 killer Newton attention.