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.
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 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.
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!