find-the-force-on-the-lower-half-of-the-wall-at-the-deep-end-of-the-swimming-pool-in-exercise-25-2

Name: find the force on the lower half of the wall at the deep end of the swimming pool in exercise 25 2
Uploaded: 2021-12-10
Duration: 2 min 54 s
Channel: Numerade
Description: Find the force on the lower half of the wall at the deep end of the swimming pool in Exercise 25.

Question

Find the force on the lower half of the wall at the deep end of the swimming pool in Exercise 25.

Stanley Enemuo · Accepted Answer

we need to find the distance traveled by the socket from a crazy go through one km 3 km um function the patent described by the locket is the function why is equal to 2 32/3 times X squared minus one so that we have and as we know by now the length of the curve the hard planes given that executes even the X. Is equal to A and X is equal to be equal to as the integral of a. B. Time. That description of one post the Y. With the X square. Yeah. First we need to calculate the distance traveled by the D. By the rockets. I put in these values into the equation of our our clothes. To solve this music, the friendship of the idea. Again using the chain rule we can evaluate the derivative of Y. So dy dx over the X. Gives this two X times X squared minus more. Now you can input your dy over D. X. Into this equation to find the distance traveled. So the this is travel is equal to the integral of a B A. S. one. These three you have the interval of the square root of one plus to access times X squared minus one the X. So we got three .33 km

Averell Hause · Answer

so here for a party, we can say the weight of the water would be equaling the density times G times be and so the mass would be the density times of volume. And then, uh, the mass times acceleration due to gravity would give us the weight and so this would be equal to the density of water. 1000 kilograms per cubic meter multiplied by 9.80 meters per second squared. This would be multiplied by the volume 5.0 meters multiplied by 4.0 meters times 3.0 Brother being the same multiplied 3.0 meters and this would equal 5.9 times 10 to the fifth Newton&#x27;s. This would be the weight of the water. Now for part B. Integration gives the expected result that the force is what it would be if the pressure were uniform and equal to the pressure at the midpoint. So essentially we could find the force. This would be equaling the density times acceleration due to gravity times. The area multiplied by D over too. And so we find that this is equaling 1000 kilograms per cubic meter multiplied by 9.8 zero meters per second. Squared multiplied. Rather, we can say for 0.0 meters multiplied by 3.0 meters multiplied by D over too 1.50 meters. And we find that the force is equaling 1.76 times 10 to the fifth Newton&#x27;s. This would be your answer for part B. That is the end of the solution. Thank you for

Samuel Coplin · Answer

Okay, so let&#x27;s start this question by drawing a sketch. So a diving pools four meters deep and reviewing window on one of its vertical walls. But we know the square 0.5 meters in the side. All right, so let&#x27;s draw our tank of water. Here&#x27;s your tank. And we&#x27;re also add in our ex and or stare. Why? And now X axes, um, and are square is 0.5 meters long. Let&#x27;s 0.5 meters. And this is for meters. Okay, so this for this question, we&#x27;re not gonna be doing anything too difficult. What is gonna be using this equation, which you may be familiar with by now? Um, from a to B the density of water multiplied by the gravitational constant that is multiplied by, uh, the area of which the window extends in the length of the window. So that&#x27;s a minus y in the length represented by W of why. And of course, that is with respect to why so we have our area would be four minus. Why? Because we Because the pool is four meters deep, so a minus why is equivalent to four Myers, Why w of why is going to be 0.5, and I make sense because the window has a side length 0.5 and now the rest row in the gravitational constant are both. Constance Row is 1000 the gravitational constants about 9.81 and we&#x27;re gonna be overlooking or have a boundary of 2.5 as that is the length of this window. Let&#x27;s plug in what we know. We could just pull our row in our gravitational constant out, and also we could pull out our 0.5. Make sure that just separate your 0.5. And now the only thing we have to integrate is the four minus. Why? So that would be four y minus y squared over two. And that&#x27;s from 2.5. And we have a 0.5 row gravitational constant plugging in 0.5. I could probably do this in our head four times. 40.5 is, too. 0.5 squared. Let&#x27;s double check that on a calculator. 0.5 times 0.5 is 0.25 Even if you think you know what, Sometimes with these decimals that could get kind of confusing. You just want to double check 0.2 5/2, Um, and that is multiplied by 0.5 row G. And now let&#x27;s combine everything together. So we have 0.2 5/2 is 0.1 to 5 to minus 50.1 to 5, one 0.875 multiplied by 0.5 multiplied by 1000 that&#x27;s in place of the row is a density of water is 1000 kilograms per meter, cubed multiplied by nine 0.81 If you plug that into you a calculator, you will get a value of approximately 9187.5, and we&#x27;re looking for a force here, and that would give you a unit of Newton&#x27;s.

Tony Cheung · Answer

for this question were given when a square window that is submerged under water where it&#x27;s bottom is one meter from the bottom of a four meter depth and were asked to find the force on the window. So for these having problems we have we can use the formula f equals integral from zero to a road G A minus Y b minus Y w of why do you Why, um however, you do need to understand how this form of the works this from zero to a refers to the shape of of, um, the height of the window because it refers to how many wrecked Almony rectangles we need. Teoh stack up to Philip this rectangle, whereas this a minus wife refers to that depth that the window has to go up. And so in this case, this a value should be 0.5. Whereas this a minus, Why should be, um so it depends on how we orient our X and Y coordinates. So I see that for this one, there&#x27;s one meter here and four meters there. Instead of doing that, I could just make this 40.0 line, in which case I am going from zero all the way up to buy three meters. So this would just be three minus. Why? When w of why it is what we would typically do now if we re aren&#x27;t we&#x27;ve we reorient our X y cornet system, but we can actually just see it from here for this one If Why? This is where my eyes, they&#x27;re all most of in my X axis is, um where Why you? Cause they&#x27;re always and then I&#x27;m going up. I see that for this shape, this is just a square. My shape has a width of 0.5. It is a constant of 0.5. So this is just their 0.5. So my integral would be f equals integral from 0 to 0.5. So that&#x27;s the height of the window. 1000 for row, 9.8 for gravity and a minus y would be three minus y. And this is a constant of 0.5 do you want so I can move all the constants to the other side and I can actually just multiply it. So 9.8 times 1000 is 9800 times 98000.5 would be 4900. So 4900 into grow from 0 to 0.5. And I&#x27;m just left with three miners. Why do you? Why? Which would give me 4900 times three y minus Y squared over 21 to take the integral. You violated from 0 to 0.5. Ah, this gives me. Actually, I would just punch this in the calculator. This would just give me 6000 737.5 new tints, and that&#x27;s all.

Samuel Coplin · Answer

Okay, let&#x27;s start out by drawing a picture of this scenario. So a diving poor that is four meters deep and full of water has a viewing window on one of its vertical walls, and the window has a radius of 0.5 meters. Let&#x27;s draw this. Here&#x27;s your pool and will draw. Are why axes make that more centered. Why axes your ex axes and here&#x27;s you&#x27;re circular window. And that window has a radius 0.5 and will make this at four meters. Okay. All right. So the equation we&#x27;re gonna use to figure out the amount of force is the density multiplied by the gravitational constant multiplied by cross sectional area. And that&#x27;s multiplied by W. Why? Which is equivalent to, um, the length of the window at a specific height? That&#x27;s do you. Why so for the w why we know what the range is. Zero 21 And that&#x27;s because the circle has a radius of 0.5. So its diameter is one. The formula for the circle itself is negative. Why? Minus point 05 And keep in mind what is rearranging the Y squared. Plus X squared equals R squared equation. We&#x27;re just plugging in our knowns, and that is how we get this. If we rearrange that by solving for X, we will acquire a value of radical point five squared minus why minus point five and that is all squared. In other words, why would equal to radical why minus Why squared? And the reason you have to multiply it by two is because you have to, um, account for the two halfs two halves of the circle. This equation breaks it up into 1/2 breaks up into problems with the multiplied by two to get the full circle. And, of course, our A minus y value before minus. Why, since that is the height of the tank of water? So let&#x27;s set this up so we have from 0 to 1 p or state row G four minus y, and we multiply that by two 0.5 squared minus. Why my point? Oh, five squared? That&#x27;s acting. Why, Okay, so this integral looks a bit overwhelming, but let&#x27;s do a little bit of substitution that is saying, let&#x27;s do X equals Why minus 0.5, and we could plug this in place of the wind minus 0.5 and that could also be substituted into the four minus y. So if we plug that in, we would have first of our boundaries would change. They would change too. Negative 0.5 and 0.5 because you&#x27;re gonna take one and you&#x27;re going to subtract 0.5 and your intake zero and then subtract 00.5 again. And then we would have 3.5. You could bring this to bro g up to the front for the time being. And then we could do 0.5 squared and that would be minus X squared in that 3.5 again comes from setting four minus y and, yes, setting for minus wine. Why minus 0.5 equal tor another. Um, okay. And we&#x27;ll get Do you have X and that would be subtracted then. Reese attract five 0.5. And if you solve this integral out, you will acquire value two p of two row G. You&#x27;re gonna get a value of about 1.3 seven. And if you want to buy those two together knowing that row is 1000 in the gravitational constants 9.1, you will get a value of approximately to seven 27,000 Newtons in. That is how you go about this problem

Protim Das · Answer

from this problem. We have a square plate off 1 m on and both the square plate is under the full surface, just 1 m below. So this is our first case, and this is over. Second guess. Okay, Now we know that hydrostatic pressure grows as Deb Growth. Right? So in the first figure, the idea under the pool surface is greater than the area under the second service two year. So what is the conclusion? First conclusion is the forces that if for first he&#x27;s greater, then there if off singing because no idea. Flushed, scraped up, then media singing. This is underwater. Okay, so the area under the water for first finger is greater. So the hydrostatic force also greater for that first figure. Okay, Now we consider the first river. If we just rika lying here. So the four first finger If you just are, take that. This is a zero point. And if you just come out and this is stool, this is cool. And this is how old then area extends are vertically over his minus off wrote over two white zero because my nestle fruit over two way, because you know what? Please a diagonal first. Quit. Right. So this is the vertical extension off area. So what is the Are 80 year bounded by the car? So if we just take the square so what? The car. So one is how this line is the first land. This is the second line on another two line is here and here. Right? So we just trained on the creation. So for the area bounded by the car, the first equation is the white will be explicit record weeks. Another is why called O minus six Partick Question is why Quarto Hicks minus Look at what Duke? And the Fort equation is minus six miners off door. So these are the four equations for area of owned by the car. Now I point way lend off the horizontal line inside the boundary. It was for the violence that is minus two minus off local work toe. Why? Between minus off over to my way for this region, we considered the this region Okay, so there is not white. This is our two for minus off Cocteau. So this is the region we considered and we caught the width equation in like that are two y plus go off. So this is the word equation. This is the would be question for us for this region. And if we just take another reason for my next go, go. What do my wife, Tzeitel, then? The question is why minus minus off white like so if you just extremely so this is our main regions, like minus recover toe y zero. And this is the four equations. If we just swapped the equation, we get a wind equation like this for that greedy in. Now, if we use the Formula Four force that is integral a tow B through G H miners. Why the blue off? Why the right? So what is the what is he? He Toby is the heights of water, which the triangle extents and a blue is the length off the window at height white. So we just stop with the values here. So we take the integral from minus toward to minus off. So pregnant, it&#x27;ll in tow. Troopers road G one minus y. The question is to why plus Rocca Work Goal de y, plus the second from minors Off hook over toe. Zito, your G one minus who I on the equation off with these minus two. Why the white? And if we just put the value that help, will it? We have 16 seven door, nine point 64 nuclear. Now we come through. How? Second pot? There is a second period for second period. There is no such complexity. If we don&#x27;t know Force a question directly, that is, It&#x27;s from simply 0 to 1. Brody. Okay, now from Rectal Delegate. So that Zito, this is stool. This is bull the system. So wrong. Graphical easily take these values on. The question is to hide his to and there is no preparations of this is white and this is doing we just simply pointed available. So it is 14700 Newton he sees oh, answer. And the Caesar singing, Dancing One thing you always are the brain that density is nothing but 1000. Katie, when we take you and Jesus 9.8. It is the common values for everyone

Problem

A small dam is in the shape of the area bounded b…

Problem 26 Easy Difficulty

Find the force on the lower half of the wall at the deep end of the swimming pool in Exercise 25.

Answer

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Allyn J. Washington, Richard S. Evans

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Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

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