the-rate-of-change-of-the-vertical-deflection-y-with-respect-to-the-horizontal-distance-x-from-one-3

Name: the rate of change of the vertical deflection y with respect to the horizontal distance x from one 3
Uploaded: 2021-06-09
Duration: 3 min 8 s
Channel: Numerade
Description: The rate of change of the vertical deflection $y$ with respect to the horizontal distance $x$ from one end of a beam is a function of $x$ For a particular beam, the function is $k\left(x^{5}+1350 x^{3}-7000 x^{2}\right)$ where $k$ is a constant. Find $y$ as a function of $x$ if $y=0$ when $x=0$

Question

The rate of change of the vertical deflection $y$ with respect to the horizontal distance $x$ from one end of a beam is a function of $x$ For a particular beam, the function is $k\left(x^{5}+1350 x^{3}-7000 x^{2}\right)$ where $k$ is a constant. Find $y$ as a function of $x$ if $y=0$ when $x=0$

Kian Manafi · Accepted Answer

Okay, so we&#x27;re told that dy dx is equal to k, multiplied by X. To the fifth plus 13 50 times X. To the third minus 7000 times X squared. And we want to find a function for why given that Y is equal to zero when X is equal to zero. So what we can do is we can just integrate both sides. Here can say the integral of the Y is equal to the integral of K. X. to the 5th plus 13 50 time six, third minus 7000 times X squared dx. So now we can just find this integral. So we can take our constant K out. So you&#x27;d have this is equal to K multiplied by the integral fix. The fifth plus 13 50 Times X to the 3rd minus 7000 times X squared. And this is all multiplied by dx. And so now we can do is we can find the integral of each of these terms. Um And so we would have, this is equal to k. Multiplied by X to the 6th, divided by six. We just add one to the exponents and divide by that exponents. We&#x27;re gonna do the same thing here. We can treat 1350 as a constant, so we won&#x27;t change that, we still have 1350 And this is multiplied now by X to the 4th and divided by four. And we have again we can do the same thing here. So we have we keep our constant 7000. We raise our exponent one and we divide by the resulting exponent and then we also have to remember plus C. So now we have why is equal to K Multiplied by X. The 6th, guided by six plus 13 50 Times X. To the 4th, divided by four minus 7000 times X to the third, divided by three plus C. So this is equal to y. So now we can use the fact that when X is equal to zero, Y is equal to zero. To figure out what C. Is equal to. So we have zero, it&#x27;s equal to k. Multiplied by 0-6, divided by six is just zero, And then 0 to the 4th Multiplied by 1315, divided by force also zero. And this term is also going to go to zero and X equal to zero suite of K multiplied by zero plus zero minus zero plus C. So then zero is equal to K. Multiplied by C. So then C. is equal to zero. So now we have our equation for why which is equal to K. Multiplied by X to the 6th, divided by six plus 13 50 Multiplied by X. to the 4th, divided by four In -7000 times X. To the third, divided by three.

Ankit Gupta · Answer

the beam deflection. Why is given as one developed but 14 off X Q. Minus one divided by 40? No, it&#x27;s that will people toe x four multiplied by one Do adverts are 10 X squared minus one. The wide right. 14 So clearly when why equal to zero x will be zero. Another factor. One. Divide by 14 It&#x27;s Esquire Menace one divided by port in will be zero, which will give 14 x X squared minus 13 equal to zero. Or we can. That excess crab will do heart in the right invite 14. So two possible value came up acceptable toe plus off routine that start in 2014 x equal to minus approval hurt in my reporting. But Lord, that we have so find out X in the interval of zero toe to inclusive so possible values under the intervals, you know to inclusive for the polynomial odd zero and another tough start in divided by 14

Isabella Leite · Answer

So here you have a question where we have to figure out the variation equation in the constant variation. And we&#x27;re told that the way of a load varies jointly as the whiff of a beam, the square of its height and also inversely as a length. So let&#x27;s assign variable. So all of these, I&#x27;ll say capital L w each lucky so And if we put these together in an equation, we get l equals the constant K times w Now we&#x27;re using the swear of the height. So each squared times eight squared and we&#x27;re using the in verse of the length So one over L not the Silver K. We just have to plug in this data that they gave us. So one ton lewd as he who too k times with of four inches a in just hall and one over that the length is given in feet. So I&#x27;ll just convert that two inches 12 feet times 12 inches per feet. That&#x27;s equal to 144 inches. And if you saw for K here, you get okay equals 0.56 25 Well, if you know it&#x27;s tons per injures squared So our overall equation is l equals 0.56 to 5 tons. Her interest squared, W H squared times one over elk. Now, the question also asked what would happen if you increase the hi to 10 inches so we can just plug it again? L equals point 56 to five tons per interest squared times four inches times 10 and juice squared times one over 1 44 inches and you get l equals one point by six tons.

Isabella Leite · Answer

so in this problem were given an equation from a previous problem, which was M equals 30 w h squared over l for a 10 foot beam. And we have to find M if w equals six inches and h equals four inches so we can just plug in, um equals already. Time. Six inches times four inches squared in an to 10 foot beams. We put 10 feet for L, and that is equal to £288 for the maximum load. Now asked, What is the maximum lewd If h equal six inches and W equals four inches again, we could just plug in so M equals 30 times four inches time six and just squared over 10 feet, which equals £432.

Thao Trinh · Answer

So for this question, um, it is, um, various directly and inversely variation, so we can tell that it is Ah, join variation problem. So we, um, the maximum safe, low aim. All right, I&#x27;m here equals two It, um very hysterically with the with top of you and this wear off the heights. So H swear and inversely there inversely varies with the length. So times want over out and over a k, which is the constant off variation. And, uh, this is the variation equation to answer for part eight, part B. Ah, they give us the with IHS 18. Ah, the height ISS to the link is eight. And and as to 70 based on these equipped on these values, we can find our constant of aeration. So k e coast to em over w times each swear times one over l and just going to substitute the numbers on the left through 70/18 times to swear times 1/8. The answer here is 30 and I will just rewrite the variation equation by substitute K into the equation. So we have this variation equation right here, and, um, the second bar off part B is that they give us this the safe low off the same dimension, which is the same with and the same height. I&#x27;ll just right of the game. And but this time, the length it&#x27;s different. The length is 12 feet instead, off eight as a both. And we got a sum that we&#x27;re gonna, um, calculate does say float off based on these values. So M equals to 30 times with this 18 now, each swear so twos. Where and length is tough want over 12 and the answer is 1 £80.

Petros Markopoulos · Answer

this is a continuation of the previous exercise will calculate the deflection of the same beam if you flip it to its side. So it was two inch wide and eight inch deep, which now turns into a being that is eight inches wide and two inches deep. Variation models said that d equals K over W cubed with me being the deflection w being the with an L being that that&#x27;s and we had calculated K to be 281.6. So this is our formula now. We will plug in these new values and calculate the new value of the reflection, which is 281.6 over eight times to cubed, which is 281 point 6/8 times eight, which is then equal to 181 point 6/64 which gives us a final unser of 4.4 inches. You will note this is significantly bigger than the previous deflection we had calculated because death is cubed and switching these two numbers made the depth significantly smaller and because it is tubed, this affects their answer in a significant way

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Freshwater is flowing into a brine solution, with…

Problem 34 Easy Difficulty

The rate of change of the vertical deflection $y$ with respect to the horizontal distance $x$ from one end of a beam is a function of $x$ For a particular beam, the function is $k\left(x^{5}+1350 x^{3}-7000 x^{2}\right)$ where $k$ is a constant. Find $y$ as a function of $x$ if $y=0$ when $x=0$

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