Is the 45-Degree Angle Between the Y-Axis and F2?

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SUMMARY

The discussion focuses on the calculation of the resultant force from two vectors, F1 and F2, with specific angles in a three-dimensional coordinate system. F1 is defined as having components of (300cos(30)i, 0j, 300sin(30)k), while F2 is positioned 30 degrees down from the y-axis in the yz plane and makes a 45-degree angle with the x-y plane. The confusion arises around the interpretation of the angles, particularly the 45-degree angle's role and the resultant force calculation, which is stated to be 733, contrasting with an incorrect calculation of approximately 900.

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Hibbler.ch2.p69.jpg


Find the result force of the two forces.
This problem seemed easy at first, but I think I'm confused as to how to find the coordinate angle (gamma) . For the ( i,j,k) components of F1, I got (300cos(30)i, 0j, 300sin(30)k) I don't understand the function of the 45 degree angle, either. What am i doing wrong? Is the 45 degrees the angle between the y-axis and F2? and also would that make 135 degrees the angle between F2 and Z? then that would make 60 degrees the angle between the x-axis and F2. However, the answer for the resultant force is 733... and i got a number close to 900.
 
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Interpretation of the figure seems pretty straight-forward to me. F2 is 30 degrees down from the y-axis on the yz plane and if you create a plane that is perpendicular to the yz plane and contains the F2 vector, F2 is out 45 degrees put on that plane from the line it makes with the yz plane. F1 is obviously 30 degrees down from the x-axis on the xz plane.
 
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New to this site, Sorry.
 
phinds said:
Interpretation of the figure seems pretty straight-forward to me. F2 is 30 degrees down from the y-axis on the yz plane and if you create a plane that is perpendicular to the yz plane and contains the F2 vector, F2 is out 45 degrees put on that plane from the line it makes with the yz plane. F1 is obviously 30 degrees down from the x-axis on the xz plane.
I look at it from a different, but equivalent, perspective. The force F2 makes an angle of 45 degrees with the x-y plane. Its projection onto the x-y plane makes an angle of 30 degrees with the y-axis and 60 degrees with the x axis.

Chet
 
Chestermiller said:
I look at it from a different, but equivalent, perspective. The force F2 makes an angle of 45 degrees with the x-y plane. Its projection onto the x-y plane makes an angle of 30 degrees with the y-axis and 60 degrees with the x axis.

Chet

HA ... you are right of course. An optical illusion, sort of. Seems totally open to interpretation.
 

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