4 1 8 PROBLEMS 



PROBLEM 3. TEST OF EQUILIBRIUM OF FORCES. 

 (a) Problem. Test the following forces for equilibrium by means 

 of force and equilibrium polygons : 



7.8 10.8 12.2 



P/-~ (4.75", 0.0") ; P 2 (475", 77") ; P* (-"> 7-o") ; 

 90 45 



P 4 (475", 6.4"): P,~- (275", 6.4"); Pc^Jr(275", 77")- 



The forces are given in tons. Check by using a second pole and 

 equilibrium polygon ; also draw a line through the intersection of the 

 corresponding rays, and check as in Problem 2. Give amount and 

 direction of the equilibrant. Scale of forces, i" = 5 tons. 



(b) Methods. Start force polygon at (0.8", 1.5"). Take first 

 pole at (3.2", 2.7"). Start equilibrium polygon at (4.75", 9.1")- 

 Take second pole at (4.0", 3.2"). Start second equilibrium polygon at 

 (475", 8.2"). 



(c) Results. If the system of forces was in equilibrium the equi- 

 librium polygons would close, and the first and last strings / and /, 

 and /' and /' would coincide, respectively. The equilibrant will be 

 equal to a couple with a moment represented by the rays / or /' multi- 

 plied by the distance h or h f . In general in any system of non-current 

 forces if the force polygon closes the equilibrant of the system is a 

 couple. If the system is in equilibrium the arm of the couple is zero. 

 It is evident that in order that any system of non-concurrent forces 

 be in equilibrium it is necessary that both the force polygon and an 

 equilibrium polygon must close. The check line must be parallel to the 

 line O-O' joining the poles, and also pass through the intersections of 

 corresponding rays as in Problem 2. 



PROBLEM 3a. TEST OF EQUILIBRIUM OF FORCES. 

 (a) Problem. Test the following forces for equilibrium by means 

 of force and equilibrium polygons : 



P 1 (475", 0.0") ; P 2 (4.75", 77") ! P, (.o", 7-o") ; 



(475", 6.4") ; P 5 l (275", 6.4") ; P.s (275", 77") 





