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

Click For Summary
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 solve for the angle between two forces, one can use the dot product formula, \vec a·\vec b = |a||b|cos(φ), and apply symmetry when the magnitudes of the forces are equal, leading to the conclusion that the angle is θ/2.

PREREQUISITES
  • Understanding of vector operations in physics
  • Familiarity with trigonometric identities
  • Knowledge of the dot product in vector mathematics
  • Basic principles of Engineering Statics
NEXT STEPS
  • Study vector addition and subtraction in physics
  • Learn about the application of trigonometric identities in force calculations
  • Explore the concept of symmetry in force systems
  • Investigate the use of coordinate systems in vector analysis
USEFUL FOR

Students in engineering, particularly those studying statics, physics enthusiasts, and professionals involved in force analysis and vector calculations.

narutoish
Messages
25
Reaction score
0

Homework Statement


hv2tjl.jpg


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.
 
Physics news on Phys.org
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
 

Similar threads

  • · Replies 20 ·
Replies
20
Views
3K
  • · Replies 6 ·
Replies
6
Views
4K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
Replies
2
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 1 ·
Replies
1
Views
4K
Replies
9
Views
3K
  • · Replies 14 ·
Replies
14
Views
3K