Statics: Lesson 43 - Centroids by Calculus Example Problem
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- Опубліковано 21 чер 2020
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You really scared me there when you just stared at you work in silence
😊😊
Professor Hanson, thank you for another classic Statics lecture on Centroids using old fashion Calculus. A solid background in advanced mathematics would be helpful to any student in Statics.
If anybody has a problem finding y bar. This is explained by Prof. Jeff in the Statics: Lesson 44 at the timestamp 20:35. In that problem, you don't flip the strip but instead use your (height of the shape x (height of the irregular shape - half of the height of the irregular shape)). That will find you ydA. The value you should get is 72.9. While dA stays the same at 20.25. So y bar is 3.6
By height of the irregular shape do you meant of the rectangle with base dx? Or the actual shape?
Can you explain further? I tried and I wasn't getting the answer
@@adi2.054 I meant by the equation of y=-1/6x²+2x which is the curved equation of the line
@@dakpotor1 In order to find integral of ydA, you can simply keep the equation of dA as it is, don't change it. But the tricky part is how do you find the "y". To find out y, you would have to locate the centre of the height of the strip. The height of the strip you already found it in the dA equation, ignoring the dx. You need to half that value of the height of the strip. Next, you need is the line of the strip which corresponds on it. This is obtained from the equation of the of the curved line.
Next, to obtain the ydA, it is given by:
(height of the strip) *(line equation of the curve - (1/2 height of the strip)). The limits are 0 to 9
What a legend!@@firstlegend5105
Great example Mr. Hanson!!
Guys, if you took Calculus 3, you can assume your mass density function to be 1 (constant), and do the double integrals for mass and moment about the region. I got x=4.5 and y=3.6 that way. Hope it works.
Yes. Absolutely do this
could you link a video or something explaining this further? thanks
@@alinaveed1793 ua-cam.com/video/WNZ8vMgaPgg/v-deo.html
Yes, there's a formula
thank you for helping me get an A in statics
I can't express my gratitude to you sir.
PHILIPPIANS 4:13 THANK YOU FOR YOUR WORD OF GOD YOU SHARE US AND TOUGHT US MECHANICS MY GOD BLESS YOU YOU AND YOUR ALL FAMILY.FROM ETHIOPIA COUNTRY
Excellently explained, keep it up sir
Time 8:35 “so that becomes” was that moment for me when I was like “thank god because 9^3 does not equal 81…” lol thank you as always got entertainment and education!!!
This is absolute calculus!
Please can you do the y bar as well, with those given equation?
3.6
عمي انت وردة شرحك يخبل
It seems that to find Y bar you have to find the length of dA, which would be x2 minus x1, but I cannot find a way to express the x1 of the parabola as a function of y to do that.
What am I missing?
Good thinking
you are the best
why dun show for y-bar... it is hard
When solving for y-bar, what would be your limits? from 0 to what? As far as i can tell, instead of 0 - 9, you would need the height, which isn't given?
Your upper bound would be the maximum height of the upper function. To find the maximum for the upper function, find the derivative of it, set y-prime = 0 , and solve x. Then take that x-value, and plug it back into the original y equation. This will give you the maximum value (Hint: the height is 6). You'll integrate from 0 to 6 with respect to y. Get both of those 2 functions in terms of y, (so, x=) and then do (right function - left function) under the integrand. Solve.
@@jasonmalouin9580 Thank you!
Note also you'll have to do the integration in two pieces. First piece is from y=0 to y=4.5, where the "top" of the dA strip is the parabola and the "bottom" of the strip is the straight line. Second piece is from 4.5 to 6, where both ends of the dA strip are the parabola. That last part is fairly tricky.
how to find upper function equation of x in terms of y? (x=..)
@@jasonmalouin9580 how to find the upper equation of x?
Hi Professor, I am confused because dx is not really over the X axis, instead should the dA rectangle be perpendicular to the line y=0.5x ?
I think there was a mistake at point 7:15 in the video where it should be 9^3 = 729 and not 9^2 = 81
UPDATE: nevermind, I see this is corrected at point 9:10 in the video after its erased. Thank you for all your videos btw!
I was trying to solve the problem and I made a mistake, I look the question and I said this integral can not be negative, i looked again and solved the problem. Then i watched the video to see how did you do, and you made the same mistake that I did
please how do i get the equation of dA for Y bar?
did you figure it out?
xcellent
does the ybar here is 4.725?
no
The mistake me made was that he took x^3 of 9 as 81.
I thought I was the only one that noticed
The moment he knew he messed up.
mmmmmmmm static