Statics: Lesson 42 - Intro to Centroid by Calculus Method, Flip the Strip Method

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DR. Hanson, thank you for a fantastic introduction to Centroid by the Method of Calculus. Calculus is important for all upper level courses.

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I saw so many videos about centroids, also went back to my calculus and statics notes and could not understand them! But you've explained it so well, sir. Thank you so much!

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[@ImranKhan-tu7ix]

For arc lenth We take dy/dx of y equation then put value in and get DL a tiny lenth DL square = dx sq + dy sq Then we integrate using x bar y bar formula But in area y equation is itself area Don't take derivative then put x bar y bar Put direct value of y as area And dont forget y is always half when you finding y bar how know I put equation in my calculate and seen graph it shows hole area

[@fulufhelomatidza2868]

Good lesson! So why didn't you say H-y for the height of the strip while getting the x-value of the centriod

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[@Abcdefg123.97]

Hello guys, why do we integrate only h/b, leaving off dX? Can anyone clear it pleaseeee

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[@rabecamohammed9518]

When you integrated dA in terms of x, you didn't subtract the height (left it as h/b * x). But you subtracted the height when you integrated dA in terms of y (b - b/h * y). Why is this the case?

[@RasmusFMS]

Because the triangle sits on the x-axis. In terms of x, the strip gets longer with an increasing x: h/b*x In terms of y, the strip gets shorter with an increasing x: b - h/b*x

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[@cht5086]

Sir, you explain very fast, for example, we know the equation of y=mx+b, but you don't explain especially how to get y=(h/b)x step by step, you just skipped and only indicated h over b and that's it, students need more details of concepts to get the points.

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[@ImranKhan-tu7ix]

One more thing If you integrat y equation you will get area in numbers like 42ft square

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[@ImranKhan-tu7ix]

I was at problem 54 was doing ok but not satisfied I came back to problem 1 which is arc lenth (1, 1) I want share it with ur students coz what ever I learned it becoz of you if am wrong plz someone correct me ok then arc length (1,1) with y^2=x^3 ^ is power Equation for centroid is x bar = intigraation of tiny x × tiny L Who we can find tiny L at point where curve is straight We can find it by ( chang in y ÷change in x We have equation y^2= x^3 If we put 1 value of x then value of y is 1/2 dividing both we will get .5 which is change mean tiny L or delta L Put this value in to x bar equation on top I wrote We will get .5 x bar which is close to book answer .54 but correct why ? Second We have equation y^2 = x^3 If we take derivative of y we will get tiny L or delta L =1.5 under root x If we put this value of dL in x bar equation then answer is .6 which also close to .54 but not correct Why? Third and correct ans dL squar = dx square +dy square Square root both side Divide and multiply inside root by dx to eliminate dx Root of 1 + (dy/dx )^2 left Take derivative of dy put in Get dL and put x bar equation answer is right We can Get dL value from all three methods but why only square roots one is come with correct ans which .54

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