4 20 PROBLEMS 



PROBLEM 4. RESOLUTION OF FORCES. 



(a) Problem. Given the following forces : 



13.2 5.0 3.2 



fY- -(1.0",-); P 2 - -(2.8",-); P,- (6.8",-). 

 270 270 270 



Forces are given in tons, (i) Find the resultant, R, by means of 

 force and equilibrium polygons. (2) Resolve R into two parallel forces 



? ? 



P' - -(3.2",) and P" - - (5.4",). (3) Find the moment, M, of 

 270 90 



R about a point Z at (4.0", ). Check by the algebraic method giv- 

 ing all equations. Scale of forces, i" = 5 tons. 



(b) Methods. Start force polygon at (5.7", 0.5"), and take 

 pole at (1.7", 3.0"). In the algebraic method take moments about the 

 left border in finding the point of application of R, and take moments 

 in the line of action of P" in resolving R into P' and P". 



(c) Results. (i) The position of R is at the intersection of 

 strings a and d. (2) Prolong string a until it intersects P 1 ' , take the 

 intersection of string d with P" ; then string e is the closing line of the 

 polygon. (3) The moment of R is found graphically by multiplying 

 the intercept, y, by the pole distance, H. (4) To find position of R 

 algebraically take moment of P 19 P 2 , and P 8 , about the left border, and 

 divide by R, which is the sum of P lt P 2 , P 3 . (5) The moment of R 

 about Z is equal to R X (4.0 2.28) ", = 36.8 in.-tons. 



PROBLEM 4a. RESOLUTION OF FORCES. 

 (a) Problem. Given the following forces: 



T 3- 2 / " \ . 5- 



~ 



>8 ~ 



Forces are given in tons, (i) Find the resultant, R, by means of 

 force and equilibrium polygons. (2) Resolve R into two parallel forces 



~ (3-2", -) and P" . (54 ", _) . (3) Find the moment, M, of 



R about a point Z at (4.5", ) . Check by the algebraic method giv- 

 ing all equations. Scale of forces, i" = 5 tons. 



