What is the equation for calculating resultant force in Engineering Statics?

AI Thread Summary
The equation for calculating the resultant force in Engineering Statics is given by F^2 (resultant) = F1^2 + F2^2 - 2F1F2cos(theta). The magnitude of the resultant force can be simplified to F (resultant) = F sqrt(2 - 2cos(theta)). To find the angle between two forces, one can use the dot product formula, where the angle is represented as φ. In cases of symmetry, the angle can be determined as theta/2 when the magnitudes of the forces are equal. This approach effectively aids in solving for angles in static force problems.
narutoish
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Homework Statement


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Homework Equations



F^2 (resultant ) = F1^2 + F2^2 -2F1F2cos(theta)

The Attempt at a Solution



i calculated the magnitude using the equation above and it ended up being :

F (resultant) = F sqrt(2-2cos(theta))

i don't know how to solve for the angle.
 
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Well in this particular case you can use symmetry (the magnitude of the forces are the same) to find it out.

In general, you could find the angle between two angles by solving for ##\phi## in this equation: \vec a\cdot \vec b=|a||b|cos\phi
(Of course, you would want to use some coordinate system to find ##\vec a\cdot \vec b##)
 
So in this case we say it's theta/2?
 
narutoish said:
So in this case we say it's theta/2?
Yep
 
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