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!

Homework Help: Proving what the reaction force equals with moments in mechanics.

  1. Feb 10, 2010 #1
    1. The problem statement, all variables and given/known data
    A horizontal piece of wood that has a weight 40N is held in equilibrium by two brackets, A and B. The wood is 1.6m long (CD). A is 0.4m from C and B is 0.2m from D. Meaning that there is 1.0m between A and B. At rest the reaction force at A is 24 N and at B 16N. When an object is put on the wood at xm from C, show that the vertical reaction force on the shelf at A is (24-W(x-1.4))N

    2. Relevant equations
    Moment=Force x Distance

    3. The attempt at a solution
    I understand that the W(x-1.4) is the moment of the object but I cant seem to get the 24.
    If taking moments about B:
    (x-1.4)W + (24 x 1) = 40 x 0.6
    which isn't right

    Any help at all would be greatly appreciated. many thanks.
  2. jcsd
  3. Feb 10, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    The 24 N force at A is the reaction force before the object W is placed on the plank. It is given to you (or it could be calculated). By the superposition principle, the additional reaction at A as caused by W acting alone , is added to the existing 24N reaction at A.

    If you wish to start from scratch, it's
    (1.4 -x)W -A(1) + 40(.6) =0
    Solve for A. You have to watch your plus and minus signs (counterclockwise vs. clockwise moments) when summing moments about a point.
    Last edited: Feb 10, 2010
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook