# Thread: find force fj and angle B

1. ## 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)

2. ## Re: find force fj and angle B

Originally Posted by nivek0078
-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

3. ## 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.

4. ## Re: find force fj and angle B

Originally Posted by nivek0078
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

5. ## 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