Determine the arm of weight B by dividing its moment,  –5,000 lb-in, by its weight of 200 pounds. The arm is –25  inches. To balance the lever at its center, weight B must be  placed so its CG is 25 inches to the left of the center of the  lever.  [Figure 2-13] The new arm for weight A would be –100 + 40 = –60; for  weight B, –60 + 40 = –20; and point C, is +40. The lever is  balanced and the balance point is correct when the sum of  the moments is zero.  [Figure 2-10] One common weight and balance problem involves moving  or shifting weight from one point to another in order to move  the balance point or CG to a desired location. This can be  demonstrated by using a lever with three weights to work  out the problem. As the lever is loaded in  Figure 2-11,  it balances at a point 72 inches from the CG of weight A. Figure 2-14 indicates that the shift in weight depicted in  Figure 2-13  allows the lever to balance as the sum of the  moments is zero. The following formulas can be used to determine the distance  weight must be shifted to obtain a desired change in the CG  location. The equation can also be rearranged to fi d the  amount of weight required to be shifted to move the CG  to a desired location, to find the distance the CG is moved  when a specified amount of weight is shifted, or to find the  total weight that would allow shifting a specified amount of  weight to move the CG a given distance. To shift weight B so the lever balances about its center, 50  inches from the CG of weight A, first determine the arm of  weight B that produces a moment that causes the total moment  of all three weights around this desired balance point to be  zero. The combined moment of weights A and C around this  new balance point is 5,000 lb-in, so the moment of weight B  must be –5,000 lb-in for the lever to balance.  [Figure 2-12] Weight to be shifted  = Δ CG Total weight  Distance weight is shifted Total weight =  Weight shifted × Distance weight is shifted Δ CG Weight shifted =  Total weight shifted × Δ CG Distance weight is shifted Δ CG  =  Weight shifted × Distance weight is shifted Total weight Distance weight is shifted =  Total weight × Δ CG Weight shifted 2-4 Figure 2-12.  Proving the new balance point is correct. Figure 2-11.  Locating balance point with three weights. Figure 2-14.  Weight shift provides correct CG. Figure 2-13.  Weight distribution to balance lever. Figure 2-10.  Proving the new balance point is correct. Basic Weight and Balance Equation Solution by Chart Shifting the Balance Point or CG Item Weight (lb) Arm (in) Moment (lb-in) −5,000 −5,000 +10,000 0 Weight A Weight B Weight C 100 200 200 −50 −25 +50 Item Weight (lb) Arm (in) Moment (lb-in) −5,000 +10,000 +5,000 Weight A Weight B Weight C 100 200 −50 +50 B = 200 A = 100 C = 100 −50 50 −25 CG Datum After Weight Shift C = 200 B = 200 = 100 80 72 100 CG Datum Before Weight Shift Item Weight (lb) Arm (in) Moment (lb-in) −6,000 −2,000 +8,000 0 Weight A Weight B Weight C 100 100 200 −60 −20 40