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Math Help - find force fj and angle B

  1. #1
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    find force fj and angle B

    Hello,
    I am having problems solving this system of equations to find actual values for Fj and angle B. Here are the equations below thank you for your help in advance.

    Fm*cos(70) + W*sin(5)-Fj*cos(B)=m(w X (w X r))
    --> 11193 + 3.07 - Fj*cos(B) = 464228
    --> -Fj*cos(B) = 453032 where Fj = -453032/cos(B)

    Fm*sin(70) + W*cos(5) - Fj*sin(B) = m(alpha X r)
    --> 32726 + 35.09 - Fj*sin(B) =36444
    --> -Fj*sin(B) = 3683 where Fj = -3683/sin(B)
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  2. #2
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    Re: find force fj and angle B

    Quote Originally Posted by nivek0078 View Post
    -Fj*cos(B) = 453032

    -Fj*sin(B) = 3683
    There are two ways to approach this. I think the simplest is to divide the bottom and top equations:
    \frac{-F_j sin(B)}{-F_j cos(B)} = \frac{3683}{453032}

    That will give you a value for B. Then plug that into either of the two original equations.

    -Dan
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    Re: find force fj and angle B

    Thank you Dan for your help! My other question is just a check to see if i did the cross products correctly in the two main equations.

    The first equation that is listed is on the Y-axis and the second is on the X-axis.

    I was given the values for w=114.6, r=.5198, alpha=1031 and m=68
    to solve for in the first equation m(w X (w X r)) and in the second equation m(alpha X r)

    The numbers are not in coordinate format i,j,k so I do not use a matrix correct? Since I am dealing with the planes individually do I just multiple the values straight out. Please provide any information. Thank you.
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    Forum Admin topsquark's Avatar
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    Re: find force fj and angle B

    Quote Originally Posted by nivek0078 View Post
    Thank you Dan for your help! My other question is just a check to see if i did the cross products correctly in the two main equations.

    The first equation that is listed is on the Y-axis and the second is on the X-axis.

    I was given the values for w=114.6, r=.5198, alpha=1031 and m=68
    to solve for in the first equation m(w X (w X r)) and in the second equation m(alpha X r)

    The numbers are not in coordinate format i,j,k so I do not use a matrix correct? Since I am dealing with the planes individually do I just multiple the values straight out. Please provide any information. Thank you.
    Supposing r and w are perpendicular (as they usually are) then yes. As to the y equation is alpha the tangential acceleration? If so then yes for the y equation as well. More I cannot say until the other forces are defined.

    -Dan
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  5. #5
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    Re: find force fj and angle B

    These questions were just one piece of a much larger problem that I've been working on for a while now and I was starting to confuse myself. Thank you again for straightening me out!
    -Kevin
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