re: Solving for two Resultants
I am working on a problem and a bit rusty at how I might solve the problem with resolving components in the X & Y directions for a Foce Polygon Diagram.
Using the Tip to Tail Method I have a triangle as such (starting at 0,0 and returning to 0,0)
Segment cb = -2800 on the y axis (direction down)
Segment ca (unknown force) = Fca @ 50 deg (direction to quadrant -,+)
Segment ab (unknown force) = Fca @ 25 deg (direction to quadrant +,+)
Here are the equations I set up (summing forces in X & Y directions:
E Fy: Fca (sin50) + Fab(sin 25) = -2800 lb
E Fx: - Fca(cos50) +Fab (cos 25) = 0
E Fx: - Fca(.643) = (1 / Fab (.906)
E Fx: - Fca = (1 / Fab (.906) / (.643)
E Fx: Fca = - (1 / Fab (.906) / (.643)
I remember that I can plug Fca back into the first equation, but I don't recall how to work it out from here. I tried working it out, but I get Fab to be 1612.04. I know this is incorrect because I checked the numbers using a graphical analysis.
E Fy: - (1 / Fab (.906) / (.643) * (sin50) + Fab(sin 25) = -2800 lb
I need to solve the resultants Fab and Fca. It seems easy, but I can't remember the rules for multiplication and addition of variables and moving them around to solve for Fab. It has been too many years.
Thanks,
Rob
I am working on a problem and a bit rusty at how I might solve the problem with resolving components in the X & Y directions for a Foce Polygon Diagram.
Using the Tip to Tail Method I have a triangle as such (starting at 0,0 and returning to 0,0)
Segment cb = -2800 on the y axis (direction down)
Segment ca (unknown force) = Fca @ 50 deg (direction to quadrant -,+)
Segment ab (unknown force) = Fca @ 25 deg (direction to quadrant +,+)
Here are the equations I set up (summing forces in X & Y directions:
E Fy: Fca (sin50) + Fab(sin 25) = -2800 lb
E Fx: - Fca(cos50) +Fab (cos 25) = 0
E Fx: - Fca(.643) = (1 / Fab (.906)
E Fx: - Fca = (1 / Fab (.906) / (.643)
E Fx: Fca = - (1 / Fab (.906) / (.643)
I remember that I can plug Fca back into the first equation, but I don't recall how to work it out from here. I tried working it out, but I get Fab to be 1612.04. I know this is incorrect because I checked the numbers using a graphical analysis.
E Fy: - (1 / Fab (.906) / (.643) * (sin50) + Fab(sin 25) = -2800 lb
I need to solve the resultants Fab and Fca. It seems easy, but I can't remember the rules for multiplication and addition of variables and moving them around to solve for Fab. It has been too many years.
Thanks,
Rob