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Concurrent Forces Problem

  1. Apr 15, 2014 #1
    1. The problem statement, all variables and given/known data
    Two forces acting at the origin of the x-y axes have a resultant of 2000 N in the positive direction of y. If one force acts at 40° to the x direction and the other has a magnitude of 1800 N, find:
    (a) The magnitude of the 40° force.
    (b) The direction of the 1800 N force.


    2. Relevant equations



    3. The attempt at a solution
    I drew a free-body diagram but still can't find any other values to help solve the problem.
     
  2. jcsd
  3. Apr 15, 2014 #2
    Provide your free-body diagram as a start. That way we can see where you are at and have a common reference. The problem has all the info needed but you will have to use a trial and error solution method.
     
  4. Apr 15, 2014 #3

    donpacino

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    You don't need to use a trial and error solution method...
    the sine of the angle relative to the x axis will tell you the y component of that vector.
    therefore...

    y=A*sin(theta)

    we know the two forces add up to 2 kN, so
    y1+y2=2 kN
    y1=A*sin(40)
    y2=1800*sin(theta)

    there are two unknowns with one equation. therefore there are an infinite number of solutions, unless you further constrain the answer
     
  5. Apr 15, 2014 #4

    SteamKing

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    Not so fast. You've stopped short in your analysis. Remember, you still have horizontal components to consider.

    If you continue your analysis, you may stumble across a basic trigonometric identity which will prove helpful in eliminating most of that infinite number of solutions.
     
  6. Apr 15, 2014 #5

    donpacino

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    Haha. I'm a dummy. I interpreted op as saying there was an unknown x force, not as the force was purely y.

    @OP. using a method similar to the one i previously used, you can determine an equation for net x force. If the force is purely in the y direction that means the x force is......
    using the resulting equation you have 2 equations, 2 unknowns, and you can solve for the answer
     
  7. Apr 15, 2014 #6
    The additional constraint is that the sum of forces in the x direction is zero. That gives two equations with two unknowns which contain trigonometric functions. I used EXCEL to iterate on angle to see where the forces were equal. Before doing that, you could try assuming a small angle and letting sin(theta) = theta and cos(theta) = 1-theta. The equations can then be solved for F and theta. Plug them back into the original equations to see if the answers are consistent.
     
  8. Apr 15, 2014 #7

    SteamKing

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    You don't need to iterate. By analyzing the relationships between the horizontal and vertical components, you'll eventually stumble on the identity sin^2 + cos^2 = 1. By suitable algebraic manipulations, you'll wind up with a quadratic equation in the unknown magnitude of one of the forces, which can then be used to determine the unknown angle of the other force vector.
     
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