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!

Center of gravity of a plank

  1. Nov 26, 2007 #1
    1. The problem statement, all variables and given/known data

    A uniform plank of length 4.6 m and weight 210 N rests horizontally on two supports, with 1.1 m of the plank hanging over the right support. To what distance x can a person who weighs 448 N walk on the overhanging part of the plank before it just begins to tip?

    2. Relevant equations
    W1(x1)=W2(x2) = Xcm
    W1+W2



    3. The attempt at a solution

    210(3.5) + 658(1.1)

    210 + 448

    Xcm=1.87m

    Not even sure if this is right, and I'm stuck after this. The way I understand it, once the center of gravity passes the second support, the plank will start to tip. But I don't know how to figure out how to calculate how far the person can walk before the center of gravity gets to that point.
     
    Last edited: Nov 26, 2007
  2. jcsd
  3. Nov 26, 2007 #2

    PhanthomJay

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    your moment calculations are way off. Hint: The plank will start to tip when the reaction at the left support goes to zero...does that help?
     
  4. Nov 26, 2007 #3
    I don't understand...

    W1(x1)=W2(x2) = Xcg
    W1+W2

    Is this the wrong equation?
     
    Last edited: Nov 26, 2007
  5. Nov 26, 2007 #4

    PhanthomJay

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I don't know what you're trying to do with this equation which has some arbitrary numbers in it. When the left support reaction goes to zero, then the moment about the right support, from the cg of the planks weight, must balance the moment about the right support from the person's weight. Equate the moments and solve for the distance from the person to the right support. As he walks beyond that point, the plank tips because the left support cannot withstand an upward load (assuming its not bolted down, in which case she'd never tip).
     
  6. Nov 26, 2007 #5
    ok i'm still completely lost...could you maybe baby step me through this?
     
  7. Nov 26, 2007 #6

    PhanthomJay

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    The first step is to recognize that the planks weight of 210N acts at its cg of 2.3m from the left support..at its midpoint. So it acts at 1.2m to the left of the right support. So now equate moments about the right support, with the knowledge that the left support provides no support at the tipping point:
    210(1.2) = 448(x). Solve for x, the distance to the right of the right support that the person must be for the beam to just start to tip. I get x= .56m. Aternatively, if you like your equation better and you understand where it's coming from, then with the cg of the system at the right support, you can sum moments about the left support and come up with
    (210 +448)(3.50) = 210(2.3) + 448(3.5 + x), which yields the same result in a rather cumbersome manner. So why sum about the left support when it is much easier to sum about the right support
    (210 + 448)(0) = 210(1.2) - 448(x) = 0; x = .56m.
    Does this help or only serve to confuse?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?