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Moments and Stuff

  1. Jun 3, 2005 #1
    I found the following question in a textbook:



    Two men are carrying a uniform ladder of length 12m and weight 250N. One man holds the ladder 2.0m from the front end and the other man is 1.0m from the back of the ladder.

    Calculate the upward contact forces that each man exerts on the ladder.



    The answer section in the textbook says the forces are 110N and 140N. But how do you go about calculating that? I really need an explanation as I just don't understand. I can see the forces add up to 250N, but I'm not sure how to calculate each force. Maybe I'm just dumb.

    Any help would be greatly appreciated.
     
  2. jcsd
  3. Jun 3, 2005 #2

    arildno

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    The moments of forces must cancel about any one point as well.
    Let us call the man near the front "A", who exerts a force [tex]F_{A}[/tex] on the ladder a distance 4m from the centre of the ladder.
    Let us call the man near the front "B", who exerts a force [tex]F_{B}[/tex] on the ladder a distance 5m from the centre of the ladder.
    Thus, we must have:
    [tex]4F_{A}-5F_{B}=0\to{F}_{A}=\frac{5}{4}F_{B}[/tex]

    We also have that the sum of forces acting on the ladder must be zero:
    [tex]F_{A}+F_{B}-250=0[/tex]
    Thus, [tex]\frac{9}{4}F_{B}=250\to{F}_{B}=\frac{1000}{9}=111.111...\approx110[/tex]

    Got it?
     
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