Force Vectors

Eigendorf

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Oct 3, 2017
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Hello, I'm working on a statics problem and I'm having difficulty understanding one portion of the solution.

I always seem to have good luck coming here for help so here goes!

Here is a picture of the question and diagram set up first for clarity.

Problem 2-135.jpg

The basic solution involves finding the position vector of AB.

R_AB = (Bx-Ax)i + (By-Ay)j + (Bz-Az)k

R_AB = -1.5i + 3j +1k

Unit_Vector of R_AB is just the R_AB / Magnitude_R_AB

Magnitude of R_AB = sqrt(12.25) = 3.5

Unit_R_AB = (-1.5)/3.5 i + 3/3.5 j + 1/3.5 k

Now to solve for F_parallel I need to project the Force Vector onto Unit_R_AB

I'm having difficulty setting up the cartesian coordinates for the Force vector though.

I'm trying to conceptualize how the Force Vector takes the form given in the study material.

The force vector's cartesian form is [-90*cos(60)*cos(45)]i + [90*cos(60)*sin(45)]j + [90*sin(60)]k

I understand the k component because its 60 degrees from the z axis.

I'm trying to understand why the i and j components are multiplied by two trig angles though. I'm probably missing something very basic and I would appreciate help in understanding this better.

I don't want to be that guy who just memorizes formulas just for the test!


The solution after solving the parallel force is simple arithmetic to solve the perpendicular force and I understand that part of the problem.

Thank you again for the help!
 
I figured out what I was doing wrong!

I had to project the force onto that line in the XY-Plane first then split the components apart using trig. Thats why there are two cosines / sines.

Sorry for asking a question and then answering. Please delete this thread if needed.
 
I figured out what I was doing wrong!

I had to project the force onto that line in the XY-Plane first then split the components apart using trig. Thats why there are two cosines / sines.

Sorry for asking a question and then answering. Please delete this thread if needed.
In my opinion, that shows you really learnt it! I bet you will breeze through problems like that when you meet those next time (I teach Statics and I know you will meet those - again - so next time will come).
 
Congrats! Hey, if you are feeling up to it could you write out your solution? It might help someone else down the line.

-Dan
 
Congrats! Hey, if you are feeling up to it could you write out your solution? It might help someone else down the line.

-Dan

Sure thing, glad to help where I can.

I'll write it out and upload a pdf real quick.

Cheers
 
Hmm, 19.5K limit for pdf's

If anybody want's a more detailed solution I can message you the pdf or find some other way to get it to you.

I've run this thing through various compression programs and smallest i can get it is 70kb, I don't have time to do the math language mark up right now.
 
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