Finding resultant of coplanar concurrent forces using components method

[markow202]

Hi everyone,

I have a statics question I am having a bit of trouble on. I don't know how I will put the diagram in here that it comes with but the question is

"Determing the resultant of the coplanar concurrent force system shown. Compute the magnitude, sense, and angle of inclination with thr X-axis. Use the method of components."

Final Answers in back are R= 388lb
O= 38 degrees

The diagram is a X, Y diagram with the magnitudes of directions in lbs and the angles of them.

What I have been doing is Fx, Fy then doing R (squared) to give me R
and O = tan-1 to give me the angle of inclination.

Is this the "method of components" that I am doing? I am kind of lost.

 

[FredGarvin]

I can't say I am familiar with the term that you are referring to. I would venture a guess that that is the correct method to use. It's the method I would sure use.

To be a bit more specific on your method, you would want to sum all of the x components and then sum all of the y components to give you the resultant vector. You can then divide the resultant's components by the magnitude of the resultant to give you the directional cosines and thus the inclination from both axes.

 

[Pyrrhus]

Or to find the inclination with the x-axis directly, you can also do the dot product of the resultant with the unit vector i.

$$\frac{\vec{R} \cdot \vec{i}}{|\vec{R}|} = \cos \theta$$

 

[FredGarvin]

That is saying the exact same thing, just not on both components of the resultant.