W&B 2-3

Figure 2-4. Finding balance point with datum located off the lever. Item Weight (lb) Arm (in) Moment CG 5,000 9,000 30,000 44,000 110 Weight A Weight B Weight C 100 100 200 400 50 90 150 Figure 2-5. Locating balance point. C = 200 A = 100 B = 100 −20 −60 110 +40 CG Original datum New datum Figure 2-6. Proving balance point with three weights is correct. 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 Figure 2-7. Locating balance point with datum at C. C = 200 A = 100 B = 100 −60 −100 Datum Figure 2-8. Determining new balance point. Item Weight (lb) Arm (in) Moment CG −10,000 −6,000 0 −16,000 −40 Weight A Weight B Weight C 100 100 200 400 −100 −60 Figure 2-9. Locating balance point with datum left of original. C = 200 A = 100 B = 100 −40 Datum −20 −60 +40 determine the balance point by making a chart like the one in Figure 2-4. As noted in Figure 2-4, A weighs 100 pounds and is 50 inches from the datum; B weighs 100 pounds and is 90 inches from the datum; C weighs 200 pounds and is 150 inches from the datum. The total of the weights is 400 pounds, and the total moment is 44,000 lb-in. Determine the balance point by dividing the total moment by the total weight. A balance point is equal to the CG and can be mathematically written as: CG = total moment total weight To prove this is the correct balance, move the datum to a location 110 inches to the right of the original datum and determine the arm of each weight from this new datum. [Figure 2-5] Then, make a new chart similar to the one in Figure 2-6. If the balance point is correct, the sum of the moments is zero. The new arm of weight A is 60 inches (the difference between 110 and 50), and since this weight is to the left of the datum, its arm is negative or –60 inches. The new arm of weight B is 20 inches (110 – 90), and it is also to the left of the datum, so it is –20; the new arm of weight C is 40 inches (150 – 110). It is to the right of the datum and is therefore positive. The lever is balanced when the sum of the moments is zero. The location of the datum used for determining the arms of the weights is not important; it may be in various locations, but all of the measurements must be made from the same datum location. The procedure for finding the balance point is the same anywhere the datum is located. In Figure 2-7, the datum is located at C. Weight A has an arm of –100 inches (negative because it is to the left) of the datum and weight B has an arm of –60 inches from the datum. The table in Figure 2-8 is used to determine the new balance point. To verify that this is the correct balance point, move the datum 40 inches to the left of the original datum and determine the arm of each weight from this new datum as in Figure 2-9.