A large rectangular load is lifted with a dynamometer showing 6,000 pounds at lift point A, and then 4,000 pounds at lift point B when the other end is lifted; the lift points are 120 inches apart. Where is the CG along its length from point A?

A large rectangular load is lifted with a dynamometer showing 6,000 pounds at lift point A, and then 4,000 pounds at lift point B when the other end is lifted; the lift points are 120 inches apart. Where is the CG along its length from point A?

• A. 48 inches
• B. 60 inches
• C. 72 inches
• D. 96 inches

Answer: (A)

When a load is lifted from two points, the weight distribution between those points tells you where the center of gravity lies along the length. The total weight is the sum of the two lift readings, and the distance between the lift points sets the lever arm for the moment created by that weight. Here, the total weight is 6,000 + 4,000 = 10,000 pounds, and the lift points are 120 inches apart. Take moments about the first lift point. The only forces producing a moment about that point are the lift at the second point and the load’s weight. The moment from the second lift is 4,000 × 120 = 480,000 in-lb. The weight acts at the center of gravity a distance x from the first lift point, producing a moment of 10,000 × x. For equilibrium, these moments balance: 10,000 × x = 480,000, so x = 48 inches. Therefore, the CG is 48 inches from the first lift point.

When a load is lifted from two points, the weight distribution between those points tells you where the center of gravity lies along the length. The total weight is the sum of the two lift readings, and the distance between the lift points sets the lever arm for the moment created by that weight.

Here, the total weight is 6,000 + 4,000 = 10,000 pounds, and the lift points are 120 inches apart. Take moments about the first lift point. The only forces producing a moment about that point are the lift at the second point and the load’s weight. The moment from the second lift is 4,000 × 120 = 480,000 in-lb. The weight acts at the center of gravity a distance x from the first lift point, producing a moment of 10,000 × x. For equilibrium, these moments balance: 10,000 × x = 480,000, so x = 48 inches. Therefore, the CG is 48 inches from the first lift point.