1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Centroid problem

  1. Oct 27, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the centroid of the region in the first quadrant of the xy-plane bounded by the graphs of the equations:
    x=0, x=1, y=x-x^2, and y^2=2x

    2. Relevant equations
    xbar: integral of x dA/ integral of dA
    ybar: integral y dA/ integral of dA

    3. The attempt at a solution

    my attempt at it was not so great, i determined the limit for the x values were from 0 to 1, the y limits were from x-x^2 to square root of 2x. Im not sure if the limits I chose are even valid, but that is what I could grasp. Then integrated dydx respectively with the limits, and ended up with 1/2 as the dA. I tried to find ybar and ended up with 29/15, which is clearly wrong if I have the concept of centroids correct. I attempted xbar but I cant seem to get too far.

    Can I get some help please? this is a test review and need to understand this concept
     
  2. jcsd
  3. Oct 28, 2012 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Hello 3soteric. Welcome to PF !

    First of all, sketch the region of interest.

    The area is not 1/2. Is that what you had?

    What Is it that you integrated for the area, A, for xbar for ybar?
     
  4. Oct 28, 2012 #3
    thanks for the welcome sam!

    do i sketch it and upload the image? the area seems to be limited vertically in y sense by x-x^2 and sqrt2x, horizontally by x=0, and x=1, for area yes i ended up with 1/2 but can you show me why is it wrong or the process? for ybar i got 29/15 and i couldnt calculate xbar by the nature of integration but i ended up with 10.8 as the final value if i remember which seems wrong as well
     
  5. Oct 28, 2012 #4

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    It seems that you do understand the region correctly.

    The area is simply [itex]\displaystyle \text{A}=\int_{0}^{1} (\sqrt{2x}-(x-x^2))\,dx\ .[/itex]

    The integral for [itex]\bar{x}[/itex] should be less complicated than the integral for [itex]\bar{y}\ .[/itex]
     
  6. Oct 28, 2012 #5
    yo sam thanks ! i ended up getting the values for x bar, y bar respectively as .5141, .408 which make much more sense than the values i derived at the beginning of the problem.:cool:
     
  7. Oct 28, 2012 #6

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    What did you get for the area?
     
  8. Oct 28, 2012 #7
    i ended up getting .776!
     
  9. Oct 28, 2012 #8

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    That's correct, (if it's not a factorial LOL).

    I got something a bit different for [itex]\bar{x}\,,[/itex] but I wasn't all that careful in getting it.
     
  10. Oct 28, 2012 #9
    LOL its not a factorial ! phew!

    im sure i have the right idea regardless right?

    by the way you think you can help me with the new problem i posted in this same section about cylindrical coordinates LOL, if you have time of course. ive been trying for the longest and dont seem to understand the concept
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Centroid problem
  1. Centroid problem (Replies: 1)

Loading...