Professor Hanson, there was once a time I had doubted my need for your videos. I am sorry for forsaking your name and I would like to say thank you for this easily digestable video on centroids.
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
@@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
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.
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.
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!!!
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.
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.
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?
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
You really scared me there when you just stared at you work in silence
😊😊
Professor Hanson, there was once a time I had doubted my need for your videos. I am sorry for forsaking your name and I would like to say thank you for this easily digestable video on centroids.
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
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.
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 th-cam.com/video/WNZ8vMgaPgg/w-d-xo.html
Yes, there's a formula
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
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!!!
i dont have words on how much i aprrciate you sir hope you are good sir thanks so much
thank you for helping me get an A in statics
I can't express my gratitude to you sir.
This man is mastermind of students challenge
I love your approach
Please can you do the y bar as well, with those given equation?
3.6
Great example Mr. Hanson!!
This is absolute calculus!
Excellently explained, keep it up sir
عمي انت وردة شرحك يخبل
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?
Thank you very much.
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
please how do i get the equation of dA for Y bar?
did you figure it out?
you are the best
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 ?
why dun show for y-bar... it is hard
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
The moment he knew he messed up.
The mistake me made was that he took x^3 of 9 as 81.
I thought I was the only one that noticed
does the ybar here is 4.725?
no
Ehere is y bar
xcellent
mmmmmmmm static