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!

Coordinates of centre of mass of lamina

  1. May 15, 2013 #1
    An industrial tool is made from alaminar material occupyingthe region between thestraight lines y =2, y=1 2x and y =3−x. The density of thematerial varies and is given by thefunction σ(1 + x), where x is the horizontal distancefrom the y-axis and σ is aconstant. The mass of the tool andthe position of its centre of mass are sought.

    (a) Sketch the region, and find the coordinates of the vertices.

    (b) Calculate the mass of the tool in terms of σ.

    (c)Find the coordinates of the centre of mass of the tool.


    a)

    graph_zpsce5f92de.jpg

    The vertices are the points (1,2), (2,1) and (4,2)

    b)
    The mass M is the sum of these double integrals

    Integrlas_zps60d1efb1.jpg

    When you do all the calculations M=4δ

    c)
    Now I'm confused on how I find the coordinates of the centre of mass.
    Since the coordinates are
    coordinates_zps6e7cafbd.jpg

    But I have two double integrals, then do I need to sum both of the X double integrals to find the X-coordinate?
     
  2. jcsd
  3. May 15, 2013 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Yes, and there will be two integrals involved in finding the y-coordinate of the C.O.M.as well.
     
  4. May 16, 2013 #3
    ok, so this is what I did

    coordinate_zpsf96e2734.jpg

    But the result is 303/16≈18.94 and this clearly is not the X-coordinate of the centre of mass.

    Can anyone help??
     
  5. May 16, 2013 #4

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    You are not showing the details of your calculations. If you post these, you might get some suggestions.
     
  6. May 16, 2013 #5
    Ok, I think I did a mistake when I did the calculations. I've done it again and the X-coordinate is 89/16≈5.56

    xcoordinate_zps06f5c67f.jpg
     
  7. May 16, 2013 #6

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    C.O.M. coordinates generally lie within the boundaries of the body. Your calculation shows the C.O.M well outside.
     
  8. May 16, 2013 #7

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    You don't show your working for M. I get 5, not 4.
    In the calculation starting at (2), the coefficient of x3 is wrong in the second line.
     
  9. May 17, 2013 #8
    Yes, you are right.
    I've done the calculations again and the M=5
    Also I've done the calculations again for the coordinates and everything looks correct since the coordinates lie within the shape.

    Thank you for your help.
     
  10. May 18, 2013 #9
    hi
    i also stuck on this problem can you show me how do you get 5 sigma coz i try it many time but i got 4
    thanks
     
  11. May 18, 2013 #10

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Pls post your working
     
  12. May 19, 2013 #11
    Hi I'm stuck on the integral if sigma(1+x) it self as I every time I got different value can you please show me how to integrate this
    Thank you
     
  13. May 19, 2013 #12

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    That is why you should post your working, so that we can point out to you where your mistake is. We are not mind readers.
     
  14. May 19, 2013 #13
     
  15. May 19, 2013 #14

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    The range y= 3-x to y=2 gives ∫(1+x) (2 - (3-x))dx. If you don't understand POST ALL YOUR WORKING!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Coordinates of centre of mass of lamina
  1. Centre of Mass (Replies: 3)

  2. Centre Of Mass (Replies: 9)

  3. Centre of mass (Replies: 6)

Loading...