Question

three forces act on the bracket. determine the magnitude and direction θ of f so that the resultant force is directed along the positive x-axis and has a magnitude of 8 kn.

Answer 1

The question involves determining the appropriate magnitude and angle for a third force so that the total resultant force acts along the positive x-axis with a magnitude of 8 kN. This requires the use of vector addition, the Pythagorean theorem, and trigonometry to solve.

Step-by-step explanation:

To determine the magnitude and direction θ of force (F) so that the resultant force is directed along the positive x-axis and has a magnitude of 8 kN, we need to use vector addition for the forces acting on the bracket. The given forces acting are F1 and F2, and we need to find F such that the resultant vector R has a magnitude of 8 kN and is directed along the positive x-axis.

1. Begin with the vector addition of the forces F1 and F2.
2. Apply the Pythagorean theorem to find the magnitude of the resultant vector R formed by F1 and F2.
3. Use trigonometry to find the angle θ of F so that when it is added to R, the final resultant vector is along the positive x-axis.
4. Determine the magnitude of F by ensuring that the x-component of the combination of R and F is 8 kN.