1. Limited time only! Sign up for a free 30min personal 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!

Center of Mass of open top cylinder

  1. Jul 25, 2015 #1
    1. The problem statement, all variables and given/known data

    The attached diagram shows a uniform density hollow cylindrical shell with a solid bottom and an open top. It has radius R and height h.

    Find the height for the center of mass of this cylinder, taking the origin of the coordinate system at the center of the bottom. Use "pi" for π.

    2. Relevant equations
    x_cm=m_1x_1+m_2x_2+m_3x_3/m_1+m_2+m_3

    3. The attempt at a solution
    I'm not even really sure how to start but I tried this

    If the top wasn't missing then the cylinder would have a center of mass at h/2 and the missing top has a center of mass at h so

    CM = (h/2*(2*pi*R*h+2*pi*R^2)-h*pi*R^2)/2*pi*R*h+2*pi*R^2-pi*R^2

    = pi*R*h^2/2*pi*R*h-pi*R^2
     

    Attached Files:

  2. jcsd
  3. Jul 25, 2015 #2

    Borg

    User Avatar
    Science Advisor
    Gold Member

    If you had just the top piece located at height h, could you determine the center of its mass?
     
  4. Jul 25, 2015 #3
    Wouldn't it just be h?
     
  5. Jul 25, 2015 #4

    Borg

    User Avatar
    Science Advisor
    Gold Member

    And can you determine the mass of it?
     
  6. Jul 25, 2015 #5
    Wouldn't the masses cancel though? h = h*m/m?
     
  7. Jul 25, 2015 #6

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    You really ought to parenthesise expressions correctly. You mean
    (h/2*(2*pi*R*h+2*pi*R^2)-h*pi*R^2)/(2*pi*R*h+2*pi*R^2-pi*R^2)
    or in LaTex
    ##\frac{\frac h2(2\pi Rh+2\pi R^2)-h\pi R^2}{2\pi Rh+2\pi R^2-\pi R^2}##
    But you made a mistake in simplifying to
    ##\frac{\pi Rh^2}{2\pi R h-\pi R^2}##
    (Note that that would make it > h/2.)
     
  8. Jul 25, 2015 #7
    I'm having trouble finding where the mistake is. Is the first expression correct?
     
  9. Jul 25, 2015 #8

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Yes, it's just the last line that's wrong. Check the signs.
     
  10. Jul 25, 2015 #9
    Ahhh yes! Thank you
     
  11. Jul 25, 2015 #10

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Rather than that:

    If both the top and bottom were missing, then the CM would be at h/2.

    To this add in the bottom, which has CM at 0 .

    It makes the algebra a bit easier.
     
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: Center of Mass of open top cylinder
Loading...