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PROBLEMS 



PROBLEM 5. CENTER OF GRAVITY OF AN AREA. 



(a) Problem. Find the center of gravity of the given figure 

 about the X- and F-axes by graphics. Give the co-ordinates of the 

 C. G. referred to O as the origin. Show all force and equilibrium poly- 

 gons. Check by the algebraic method stating all equations. Scale of 

 figure, i": = i". Scale of forces, i"= I sq. in. 



(b) Methods. Start force polygon (b) at point (2.9", 8.8") and 

 take pole at (5.6", 5.4"). Start force polygon (c) at (6.9", 0.6"), 

 and take pole at (3.25", 2.8"). In the algebraic check take moments 

 about the left-hand edge and the lower edge of the figure. 



(c) Results. The center of gravity of the figure will come at 

 the intersection of the resultants R and R f , which is at the center of 

 area. The areas P lt P 2 , and P 3 , may be taken as acting at any 

 angle, but maximum accuracy is attainecf when the forces are assumed 

 as acting at right angles. If the figure has an axis of symmetry (an 

 axis such that every point on one side of the axis has a corresponding 

 point on the other side at the same distance from the axis) but one force 

 and equilibrium polygon is required. 



PROBLEM 5a. CENTER OF GRAVITY OF AN AREA. 



(a) Problem. Find the center of gravity of a 6" X 4" X i" 

 angle with the long leg vertical and short leg to the right about the 

 X- and F-axes by graphics. Give the co-ordinates of the C. G. re- 

 ferred to O as the origin. Show all force 'and equilibrium polygons. 

 Check by the algebraic method stating all equations. Scale of figure, 

 i" = 2". Scale of forces, i"=2 sq. in. 



