Yeah, I see I made at least a couple mistakes there.
1. First of all, FR should be pointing down for this free body diagram, like this:
2. I am working with vertical forces in the second step but with FL I accidentally used the angle of the moment line (which I used in the torque equation) from the vertical line. Too many lines on my paper.
So, the torque equation is correct in my first post for the updated diagram of this post.
After the torque equilibrium equation I have:
FL = 1.91FR
Then I use equilibrium of forces, working with vertical forces. FM up the other two down.
0 = FM - FLV - FRV
FM = FLV + FRV
FM = FL(cos25) + FR(cos55)
FM = 1.91(FR)(cos25) + (FR)(cos55)
FM = 1.73(FR) + (.57)(FR)
FM = 2.30(FR)
FR = 1000/2.30 = 434.78
I can't subtract FR from FM to get FL like I did at first because FM is a vertical force and the other 2 aren't. But I know the relationship of FL to FR.
FL = 1.91FR
FL = 1.91(434.78) = 830.43
I know you mentioned using the sums of verticals and sums of horizontals. Is that really necessary in this case when I already know the angle of both FL and FR relative to the vertical and torque equilibrium gave me the relationship between the two? Seems the sums would only be useful when I don't know the angle so I could find the vector using sqroot of FLH2 + FLV2. (those 2s are squares)
If I need to use the vertical and horizontal, please help me understand why this way doesn't work. Thanks. :-)