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Dot products and angle between cables

  • Thread starter musicmar
  • Start date
  • #1
100
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Homework Statement


This is actually for an engineering class, but it's pretty basic vector addition.

Determine the angle θ between the two cables attached to the post.

I've attached the picture.


Homework Equations



The Attempt at a Solution



From the picture:
F1:
α=?
β=?
γ= 35°

F2:
α= 45°
β= 60°
γ= 120°

First, to find F2, I used the angles and the formula cos(α)=(F2x/F2)

F2=<282.84,200,-200>

To find F1, I used the 35° from the vertical to find the z component, then used the 20° in the xy plane to find the x and y components.

F1=<215.59,-78.47,327.66>


F1·F2=F1F2cosθ

θ=cos-1(F1·F2/4002)
=cos-1(-600.84/4002)=90.2°


According to the back of the book, the answer is 97.3°. So, I've made a mistake somewhere. Any help finding it would be greatly appreciated.
 

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Answers and Replies

  • #2
gneill
Mentor
20,744
2,736
There's something funny going on with your angle calculation. Check your value for F1 dot F2. It should be in the neighborhood of -20,000 N2.
 
  • #3
100
0
You're right. It was actually -20249 N^2. Thank you!
 

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