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    evejack's Avatar
    evejack Posts: 1, Reputation: 1
    New Member
     
    #1

    May 12, 2011, 07:13 AM
    forces
    two forces F1 and F2 of magnitudes PN an QN acting in the directions I-2j and 4i+3j respectively. Given that the resultant of F1 and F2 is F, show that P=16 and find Q where F=(48i+14j)N.
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
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    #2

    May 12, 2011, 10:32 AM

    Make a sketch, this will greatly help you.

    From the sketch, you know that:



    Also that:



    It's simultaneous equations :)
    jcaron2's Avatar
    jcaron2 Posts: 986, Reputation: 204
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    #3

    May 12, 2011, 01:24 PM

    It doesn't work out to 16. It works out to .

    To start with, you have



    or



    From that, you can just separate into two equations (since i and j are orthogonal to each other, they're linearly independent):

    The i terms:

    The j terms:

    We can solve by elimination by doubling the first equation and adding the two together to get:





    Plugging that back into the first equation, we get







    Evejack, is there a typo in your question? If F1 points in the (i-2j) direction, there's no way both P and F can simultaneously have rational components.
    Newton1Law's Avatar
    Newton1Law Posts: 60, Reputation: 5
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    #4

    May 13, 2011, 02:28 PM
    As I read this question they have given you that P = 16 Newtons of force acting in the direction given by I-2j. Since this sets the direction of the force, P, you get that P is acting at an angle of -63.43 degrees. The angle is found by converting the unit direction vector of I-2j to its polar equalivent, [email protected] degrees. I am assuming no affect for the unit vector here except to give direction, so the P vector would be given as, [email protected] degrees. Then adding the Q vector to this we get a resultant force vector F of 48i+14j = [email protected] degrees. Now if you subtract the two vectors from each other you get:
    F - P = Q; (48i+14j) - (7.16i-14.31j) = 40.84i+28.31j = [email protected] degrees = QN

    jcaron2's Avatar
    jcaron2 Posts: 986, Reputation: 204
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    #5

    May 13, 2011, 02:50 PM
    Newton1Law, I agree with your math, but my interpretation of the question is different. To me the question pretty clearly says to show that P=16, not to find Q if P=16. Besides, it's crystal clear that Q is supposed to be in the 4i+3j direction (36.9 degrees if you want to convert to polar coordinates). Your answer for Q is not in that direction. My only conclusion is that the question must be invalid as written.
    jackeve's Avatar
    jackeve Posts: 13, Reputation: 2
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    #6

    May 26, 2011, 02:00 PM
    Comment on jcaron2's post
    Yes it had a typo. Thanks the answers are correct. Thanks jcaron2's
    jackeve's Avatar
    jackeve Posts: 13, Reputation: 2
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    #7

    May 26, 2011, 02:02 PM
    Comment on Unknown008's post
    yes it is a simultaneous equation. Thanks man.
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
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    #8

    May 27, 2011, 12:41 PM

    You're welcome :)

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