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Simple resolution of forces

  1. May 20, 2009 #1
    1. The problem statement, all variables and given/known data
    A bag of sand weighing 100 N is hanging on the end of a long, light rope. The bag is pulled to one side by a horizontal force so that the rope makes an angle of 250 with the vertical. Find the magnitudes of the horizontal force and the tension in the rope.

    3. The attempt at a solution

    I know that the horizontal force makes an angle of 1150 to the rope.
    I know that the magnitude of the horizontal force + the force on the rope equal 100N.
    I'm stuck on which way to go. Some sort of pendulum formula?
  2. jcsd
  3. May 20, 2009 #2


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    The bag still weighs 100N so there is a force of 100N straight down: that is -100 j. There is an unknown force Xi. The sum of those two forces is Xi- 100j and, because the only off setting force is the tension in the rope, at 25 degees with the vertical, if we call the tension "T", that vector is T sin(25)i- T cos(25)j. Set those equal and you have two equations to solve for X and T.
  4. May 20, 2009 #3


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    Why do you say this? Draw a free body diagram of the bag, identifying all forces acting on it, and the direction of those forces. Then apply Newton 1 in the x and y directions.
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