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Math Help - Triple vector problem

  1. #1
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    Triple vector problem

    Three forces in a plane act on an object. The forces are 7 N, 11 N, and 15 N. The angle between the 7 N and 11 N forces is 105degrees, between the 11 N and 15 N forces is 147degrees, and between the 15 N and 7 N forces is 108degrees.

    a) Are the vectors in equilibrium?

    b) If not, find the magnitude and the direction of the resultant force.

    I can do problems with two vectors just fine, but I'm not sure how to solve with three vectors.
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  2. #2
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    Re: Triple vector problem

    What happens if you ignore the thrid for a moment and calculate the resultant of the other two?
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  3. #3
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    Re: Triple vector problem

    project each vector on coordinate system (x,y for instance or x,y,z for 3 dimensional)
    and calculate. if the sum equals zero then vectors in equilibrium.
    else you'll have new vector coordinates.
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  4. #4
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    Re: Triple vector problem

    I can't really make any ordered pairs out of these vectors because none of them are in standard position.

    If I calculated the resultant of just two vectors, let's say the 7 N and 11 N vectors, I would get:

    sqrt{(11)^2 + (15)^2 - 2(11)(15)cos33degrees} = 8.32 N
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  5. #5
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    Re: Triple vector problem

    Quote Originally Posted by explodingtoenails View Post
    I can't really make any ordered pairs out of these vectors because none of them are in standard position.
    then make a sketch and place them in standard position ...
    Attached Thumbnails Attached Thumbnails Triple vector problem-vectors1.jpg  
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  6. #6
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    Re: Triple vector problem

    I only know their y-values though, so I still couldn't turn them into points.
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  7. #7
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    Re: Triple vector problem

    Quote Originally Posted by explodingtoenails View Post
    I only know their y-values though, so I still couldn't turn them into points.
    x-components for the three ...

    7

    11\cos(105)

    15\cos(-108)

    resultant of the x-components ...

    R_x = 7 + 11\cos(105) + 15\cos(-108)


    y-components for the three ...

    0

    11\sin(105)

    15\sin(-108)

    resultant of the y-components ...

    R_y = 0 + 11\sin(105) + 15\sin(-108)
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  8. #8
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    Re: Triple vector problem

    Why did you use 105 and not 147 to measure the x value of the 11 N vector?
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    Re: Triple vector problem

    Quote Originally Posted by explodingtoenails View Post
    Why did you use 105 and not 147 to measure the x value of the 11 N vector?
    because my calculator uses the positive x-axis as the reference direction
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  10. #10
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    Re: Triple vector problem

    So to get the x-value of a line segment you multiply its length by the cosine of the reference angle?
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  11. #11
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    Re: Triple vector problem

    Quote Originally Posted by explodingtoenails View Post
    So to get the x-value of a line segment you multiply its length by the cosine of the reference angle?
    correction ...

    to get the x-component of a vector in standard position
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  12. #12
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    Re: Triple vector problem

    So the coordinate pairs for the three vectors would be:

    for the 7 N = (7,0)

    for the 11 N = (-2.847009496,11)

    for the 15 N = (4.635254916,-15)
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  13. #13
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    Re: Triple vector problem

    Quote Originally Posted by explodingtoenails View Post
    So the coordinate pairs for the three vectors would be:

    for the 7 N = (7,0)

    for the 11 N = (-2.847009496,11)

    for the 15 N = (4.635254916,-15)
    these are incorrect ... see post #7 again
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  14. #14
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    Re: Triple vector problem

    Quote Originally Posted by skeeter View Post
    these are incorrect ... see post #7 again
    I took a break from this problem and I still can't solve it. Can you please explain what I'm doing wrong?
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  15. #15
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    Re: Triple vector problem

    Quote Originally Posted by explodingtoenails View Post
    I took a break from this problem and I still can't solve it. Can you please explain what I'm doing wrong?
    I have no idea ... you haven't shown any work.
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