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Numerade Educator

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Problem 19 Hard Difficulty

A metal plate was found submerged vertically in seawater, which has density $ 64 lb/ft^3 $. Measurements of the width of the plate were taken at the indicated depths. Use Simpson's Rule to estimate the force of the water against the plate.

Answer

4148 $\mathrm{lbs}$

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Video Transcript

in this trouble were given a table that shows a change in with often object as a function of depth and where else are given weight and still fulfill it, that this object is submerged into another £64 per feeding tube. And where has to find total hydrostatic force on this object? Using Simpsons rule in order and total horse is because to inter go from A to B, so that is the limits of the object and or the changing BEP. That would be 7 to 9.4 Row 10 g temps Death Times The Web is a function of dub times, the X that is the thickness or the hide off a need for municipal strip. Now we know what Rogie is because given done, that it's 64 So we can I write this one as 64 times eight to be where the limits are from 7 to 9.4. So 7 to 9.4 we have ex temps w X, the X now in or defuse a Simpsons rule. We would first need to know the, um, spacing or Delta X. And as you can see, that or the increment in depth this point for. So it means that Delta X is equal to point for Let's use the Simpson troll. We know that force will let me go to 64 is a constant that come from here times. Here's a sip. Central Del Tax or three times seven times W seven plus 4 7.4 Devil 7.4 plus two time. 7.8 times W 7.8 plus 4 8.2 times W 8.2 plus two 8.6 times W 8.6 plus four times nine times Devil Ooh, nine plus 9.4 Devon Do 9.4. All right, let's close the parentheses. Now we know. W seven Double 74 and 47.88 point to 8.6 nine and 9.4 Those air given here These are values. So if you pluck those in and if you do this calculation, we see that D total fours F is equal to 64 over three 64 over three. Delta X ray noted this point for missing in calculation is 486 points 04 and total force acting on the subject is then 4000 148 bounce. All right,