What is Solving a Statics Problem: Finding the Resultant Force?

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Homework Help Overview

The discussion revolves around a statics problem involving the calculation of resultant forces and moments. The original poster is struggling with the application of force components and the moment equation in the context of the problem presented.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to separate the force into components and apply the moment equation but expresses uncertainty about the next steps. Some participants suggest using the vector cross product as an alternative approach to calculate moments.

Discussion Status

Participants are exploring different methods to approach the problem, including the use of trigonometric relationships between force components and the vector cross product. There is a lack of explicit consensus, but guidance has been offered regarding the definitions and relationships involved in calculating moments.

Contextual Notes

The original poster indicates a lack of familiarity with the vector cross product, which is a key concept in the discussion. There are references to specific distances and forces, but the overall context of the problem remains focused on understanding the underlying principles rather than arriving at a definitive solution.

findley
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Homework Statement



Here is a link to the problem that I am having issues with.

http://tinypic.com/r/8zfb5h/7


Homework Equations



F x perpendicular distance



The Attempt at a Solution



http://tinypic.com/r/1tamma/7


I have no idea where to go from there, or if I am even on the right path.

I separated the force into components but I have no idea what to do next.

I tried to for the equation 500 Nm = -Py (1.3164m) - Px (1.2276m) but got stuck.

Any help would be greatly appreciated!

Thanks
 
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findley said:
I separated the force into components but I have no idea what to do next.

I tried to for the equation 500 Nm = -Py (1.3164m) - Px (1.2276m) but got stuck.
You can do it that way, just note that Px, Py, and P are trigonometrically related, so you can solve for P using that relationship.. Usually, using the definition of M = F times perpendicular distance works well, but in this case, try the equivalent definition of a moment using the vector cross product M = r X F
 
Unfortunately I have not done the vector cross product. Is it something I could teach myself in a few days?

Thanks!
 
You can teach yourself the cross product in less than 5mins, it kinda like a cofactor expansion to find a determinant
 
findley said:
Unfortunately I have not done the vector cross product. Is it something I could teach myself in a few days?

Thanks!
The vector cross product r X F is (r)(F)(sintheta), where r is the magnitude of the position vector from the point about which you are summing moments to the point of application of the Force , F is the magnitude of the Force itself, and theta is the smallest of the angle between r and F. If M acts clockwise about the point you are summing moments about, then the moment is negative, and if it is ccw, the moment is positive (or vice versa, depending on sign convention you use). The moment has a direction, cw or ccw, or, mathematically speaking, a direction perpendicular to the plane in which the moment acts. Depending on the problem, one method is easier than the other, but they both lead to the same result.
 
Thank you both very much. I have found the answer to the problem.
 

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