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Homework Help: 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


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    Gold Member

    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


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    Gold Member

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