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Sk.imming pool 40 t wlde and 86 Iana and IEs bottot an Inclined deep *nd, AGTn pialie, rne shallow wad navina depth 04 ft 20 the pool /5 %4 mater (Round vour 3nslai...

Question

Sk.imming pool 40 t wlde and 86 Iana and IEs bottot an Inclined deep *nd, AGTn pialie, rne shallow wad navina depth 04 ft 20 the pool /5 %4 mater (Round vour 3nslaig (0 trie nearst whola number Racall thjt denslcy Iha Woinht walei is 62.5 Ib/l ) Estimsto tbe hydroseatic Iorce on the #tallow end(0) Exllmate_Ine hydrostatic torce 9n th" daco And(9) Eatluato thathrdro Latic (oica On Ono ttu eIdasLEeuinacohydrontatlc loteo 0n1 Uie DaltomRecd Hele?

sk.imming pool 40 t wlde and 86 Iana and IEs bottot an Inclined deep *nd, AGTn pialie, rne shallow wad navina depth 04 ft 20 the pool /5 %4 mater (Round vour 3nslaig (0 trie nearst whola number Racall thjt denslcy Iha Woinht walei is 62.5 Ib/l ) Estimsto tbe hydroseatic Iorce on the #tallow end (0) Exllmate_Ine hydrostatic torce 9n th" daco And (9) Eatluato thathrdro Latic (oica On Ono ttu eIdas LEeuinaco hydrontatlc loteo 0n1 Uie Daltom Recd Hele?



Answers

A swimming pool is 20 ft wide and 40 ft long and its bottom is an inclined plane, the shallow end having a depth of 3 $\mathrm{ft}$ and the deep end, 9 $\mathrm{ft}$ . If the pool is full of water, estimate the hydrostatic force on (a) the shallow end, (b) the deep end, (c) one of the sides, and (d) the bottom of the pool.

Mhm. Okay. The final problem, we are asked to find the force that's going to be based on the hydrostatic force is gonna be on the show on the deep end one of the sides and the bottom of the pool. Mhm. Well, we know that the deeper we go um there's going to be greater hydrostatic force because there's going to be a higher amount of pressure. Remember that pressure is equal to force over the area. In that case we know the force or we're trying to find the force, knowing what we have already about the pressure. So what this is going to look like is we're going to find the force, the hydrostatic force. And at the shallow end we're going to get 5.63, I'm 10 to the 3rd lbs. Then we're going to get 5.06 times 10 to the 4th lbs. That's going to be um at the deep end and then 4.88 times 10 to the 4th, that's gonna be um at one of the sides. And then lastly, we'll have the bottom of the pool which will be 3.3 times 10 to £15

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'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's. This would be your answer for part B. That is the end of the solution. Thank you for

Uh huh. I mean this question we have. That's cool. Mhm. The depth of which variation family from one m 25. Mhm. Filled with water. I have to find a pressure at bay shadow end and then it's in here. We know that the pressure will be due to the pressure of the workers as well as a special youtube. We have an issue. No, I welcome to three pressure. Is this in Alaska? I mean uh fresh up. They won't have tea as the incident gravity times height. This is for water is starting programs cubic meter and gravity It's 9 8. It is the I think it's great. So then the pressure at a. Mhm. The pressure A. Is G. H. The last year. Not. And put in this where the height is one m. So putting all this and we're going to have 1009 point. It doesn't work here. One. And thinking about All right. That is 112 date with pasqua. Similarly the pressure of the should be. And the height. He do not hide this fine. And seeing about two shots. 1 18. I was in Alaska. Next we have to find the average for the bottom of the pool. But the average force force average. Should we go to area of the boat and average treasure. Now the area is Length times it is eight with 35. And the average pressure S. P. A. Was a baby. All about two. Yes. 1 80,400. That's good. So our average was there is it going through the 1 50 400 past 12 comes eight times. That's fine. Okay. 36 512. Okay. That is all for this question. Thank you so much.

Can this problem were given a table that shows the depth of a pool at certain places in the pool. So in the first, um, square that we've made here, the depth is too. And the next squares 34 etcetera. Can. The question is to find the volume of the pool. And remember these air just rectangles that I have made here sort of find the volume of a rectangle. You just multiply the length times the width, times the depth here in this one. So the volume of the first rectangle rectangular, rectangular prism would be, um, the length, which is from zero out here to five. So five the width, which is from 0 to 5 times to depth, which is too. So that makes 50 there. And then in the second one, it's gonna be five times five times three. And that's gonna be 75 etcetera. So why don't we just do this? Volume will be the length of each rectangle. Rectangular prisoners, five. The width of each rectangular prism is five. And then, if we add up all the depths two plus three plus dot, dot, dot plus four, that will be our estimate for the width here. Okay. So 2468 10 36 10 15 for 10 2022 13 23 28 15 25 31 34 18 30 38 42 16 26 30 37. I don't know why I didn't write him in a column. Maybe I'll just keep doing this. So 25 50 um, 76 37. So 75 76. 11 14 15 37 81 88. So five times. Five times 1 88. So 188 times. 25 04449061 71 3. So our estimate is gonna be 40. 700 cubic. Seen is the volume okay? If I would have had a calculator, that might have been faster. Easier way to add those up. Maybe 4700 cubic feet.


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