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Resultant of a force problem

  1. Dec 13, 2013 #1
    1. The problem statement, all variables and given/known data
    The resultant of the two forces has a magnitude of 650 lb. Determine the
    direction of the resultant and the magnitude of P.
    [See Attachment for Figure]


    2. Relevant equations
    Well, I only know is R^2=Fx^2+Fy^2
    im still confused by this problem


    3. The attempt at a solution
    I tried using cosine law but it doesn't work well since the answer in the back is
    (a) 71.8 degrees and (b) 235lb
    Can someone help me?
    Very Much appreciated.
     

    Attached Files:

  2. jcsd
  3. Dec 13, 2013 #2

    Simon Bridge

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    You have to show your working ... start by sketching the vectors out head-to-tail.
    The cosine rule will work if you have the correct angle and the correct relationships between the sides.
    i.e. you have to understand what you are doing instead of just putting numbers into equations.
     
  4. Dec 13, 2013 #3
    I see. Okay I've tried this
    Summation of Px = pcos30
    summation of Py = -Psin30
    summation of Ny (which is the 500lb force) = -500
    R = 650lb
    Rx = 650cos@?
    Ry = 650sin@?
    I'm not really sure on what equations should I use.
    Thanks for the reply.
     
  5. Dec 13, 2013 #4

    Curious3141

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    In this case, I would suggest that the magnitude of P is easier to work out first.

    You've already resolved P into horizontal and vertical components. There is an additional 500lb force acting vertically downward.

    What is the total horizontal force? What is the total vertical force? All in terms of P.

    Now what is the magnitude of the resultant force in terms of P. Use Pythagoras' theorem.

    Equate that to 650. Can you solve that equation for P?

    Remember that sin 30 deg and cos 30 deg are "nice" results - apply this.
     
  6. Dec 13, 2013 #5
    What do you mean by "Now what is the magnitude of the resultant force in terms of P. Use Pythagoras' theorem."
    It got me confused.
    I now know the horizontal and vertical force in terms of P but they are all equations.. I've build up 2 equations.
     
  7. Dec 13, 2013 #6

    Curious3141

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    How do you work out the resultant of two forces at right angles to each other?

    Think about a right angled triangle.
     
  8. Dec 14, 2013 #7
    You have two forces, 500 lb down and the force P at an angle of 60 degrees to the vertical. You want to find the vector sum of these two forces. In terms of P and the angle, what is the equation for the vertical component of the sum of the two forces (which is the same as the sum of their vertical components)? In terms of P and the angle, what is the equation for the horizontal component of the sum of the two forces? In terms of P, what is the resultant of these combined horizontal and vertical components?
     
  9. Dec 14, 2013 #8

    Simon Bridge

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    You have determined already: F=-500j, and P=Pcos(30)i - Psin(30)j, and you know the resultant Q=|Q|=640 (all forces in lbs and "down" is negative).

    You also know that Q=F+P
    Do you know how to add vectors?
    Do you know how to find the magnitude of a vector?
     
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