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Quick statics question.

  1. Oct 14, 2012 #1
    1. The problem statement, all variables and given/known data
    A uniform ladder is 10m long and weighs 400 N. It rests with its upper end against a frictionless
    vertical wall. Its lower end rests on the ground and is prevented from slipping by a peg driven
    into the ground. The ladder makes a 30◦ angle with the horizontal. The magnitude of the
    force exerted on the peg by the ladder is:

    A. zero
    B. 200N
    C. 400N
    D. 470N
    E. 670N


    2. Relevant equations
    torque = r x F




    3. The attempt at a solution
    First I identified the forces. So normal force, frictional force, weight, and force from the wall and force from the peg which acts horizantally.
    Basically, I just took moments about the base of the ladder. I got -400(5cos30) + 5Fw = 0.
    Then I solved for Fw getting 346.
    Then I set all x forces equal to each other. Getting 346 = Fpeg + Ffrictional.
    And I got stuck lol.

    I don't know if there's no frictional force at all and that the peg is acting in place of it or if it's the sum of them together that provides the x component.
     
  2. jcsd
  3. Oct 14, 2012 #2
    any ideas
     
  4. Oct 14, 2012 #3

    PhanthomJay

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    There is no friction at the peg. So calculate the horizontal force that the peg exerts on the ladder. Don't forget the vertical force also.
     
  5. Oct 14, 2012 #4
    oh thanks.
    But I keep getting 529 as the magnitude which isn't any of the answer choices. And the answer is supposed to be 470N
     
  6. Oct 14, 2012 #5

    PhanthomJay

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    Yeah, that's what I get. looks like a book error to me.
     
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