1. If F1 = F2 = 30lb, determine the angles and so that the resultant force is directed along the positive x axis and has a magnitude of FR = 20 lb.
2. Express the Force F2 in Cartesian vector form.
3. The antenna tower is supported by three cables. The forces in these cables are as follows: FB = 520 N, FC = 680 N, and FD = 560 N. Write the resultant of these three forces as a vector.
4. The cable AO exerts a force on the top of the pole of F = {—120i — 90j — 80k} lb. If the cable has a length of 34 ft, determine the height z of the pole and the location (x,y) of its base.
5. The ball joint is subjected to the three forces shown. Find the magnitude of the resultant force.
6. Express the force F1 in Cartesian vector form.
7. Determine the projection of the position vector r along the aa axis.
8. What is the projection of the force F2 along the positive axis?
9. Determine the magnitude and direction of the position vector r which points from point A to point B.
10. Determine the magnitude of the x and y components of the 700-lb force.
11. Determine the magnitude and direction of the resultant force.
12. The gusset plate G of a bridge joint is subjected to the two member forces at A and B. If the force at B is horizontal and the force at A is directed at = 30°, determine the magnitude and direction of the resultant force.
13. If = 20° and = 35°, determine the magnitudes of F1 and F2 so that the resultant force has a magnitude of 20 lb and is directed along the positive x axis.
14. Determine the angle between the pole AC and the wire AB.
15. Two forces act on a block. Determine the angle between them.
16. Determine the magnitude of the x and y components of the 2—kN force.
17. Cable BC exerts a force of F = 28 N on the top of the flagpole. Determine the projection of this force along the positive z axis of the pole.
18. Determine the magnitudes of the resultant force and its direction measured from the positive x axis.
19. Determine the design angle ( <90°) bretween the two struts so that the 500-lb horizontal force has a component of 600lb directed from A toward C. That is the component of force acting along member AB?
20. Determine the magnitude and direction of F so that this force has components of 40 lb acting from A toward B and 60lb acting from A toward C on the frame.
21. Express each force in Cartesian vector form.
22. Determine the magnitude and direction angles of F2, so that the resultant of the two forces acts upward along the z axis of the pole and has a magnitude of 275 N.
23. Determine the design angle for connecting member A to the plate if the resultant force is to be directed vercially upward. Also, what is the magnitude of the resultant?
24. The cord is attached between two walls. If it is 8 m long, determine the distance x to the point of attachment at B.
25. Determine the magnitude of the resultant force by adding the rectangular components of the three forces.