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Load on ladder leaning against a wall

  1. Oct 10, 2005 #1
    Hello, I got this problem from a book

    "A light ladder leans against a perfetly smooth vertical wall at an angle of 30 degrees to the horizontal. A load of 800N is placed 3-quarters of the way up the ladder. If the ladder rests on a rough horizontal surface which prevents slipping, find the magnitude and direction of the reaction between the ladder and the ground"

    Since the system is in equilibrium, I resolved vertically and got

    R sin(theta) = 800

    where R is the reaction force, and theta is the angle of the reaction force with the horizontal.

    The problem is I can't get another equation so that I can find R and theta.

    Any help is appreciated, thanks!
     
  2. jcsd
  3. Oct 10, 2005 #2

    mezarashi

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    Okay, first of all, my definition of "reaction" is the normal force produced by any surface, which I think does not coincide with your definition. In anycase, This problem involves three equations which are easily solved.

    1. Fnet = 0 (in the x direction)
    2. Fnet = 0 (in the y direction)
    3. Mnet = 0 (torque, no rotation)

    The frictionless wall will only produce a force in x. The floor will only produce a force in y. The friction at ladder's base will produce a force in -x. The 800 N load will produce a force in the -y.

    Now for moments. Take the moments about the ladder's base (you can choose any point, but this point is particularly easy. Then the two forces that will create a torque around this point will be the 800N load (counter clockwise) and the reaction force of the wall (clockwise). They must sum up to zero.

    Go get em =)
     
  4. Oct 10, 2005 #3
    No mention of the ladder length is made, so I cannot use moments
     
  5. Oct 10, 2005 #4

    mezarashi

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    Are you sure? Try denoting the length of the ladder as L. Leave it as L (you don't need to substitute a number), and see what happens.
     
  6. Oct 11, 2005 #5
    Solved

    Did that, and solved it

    Thanks
     
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