Using the opposite distance method for calculating CG, how is End1 calculated?

Using the opposite distance method for calculating CG, how is End1 calculated?

• A. End1 = End2 weight x total length
• B. End1 = End2 weight/total weight x total length
• C. End1 = End2 x End length
• D. End1 = End2 weight/End1 total length

Answer: (B)

The idea behind the opposite distance method is to locate the center of gravity along a span by balancing moments: the distance from End1 to the CG is proportional to the weight on the opposite end relative to the total weight. If End2 carries the other weight, then the distance from End1 to the CG is End2 weight divided by the total weight, multiplied by the total length between the ends. In formula form, End1 distance = (End2 weight / total weight) × total length. This reflects the intuition that a heavier weight on the opposite end pulls the CG closer to that end, increasing End1’s distance. The total length is split between End1 and End2 distances so their sum equals the full length. The other expressions don’t satisfy the moment-balance relationship because they omit the normalization by total weight or mix the quantities incorrectly.

The idea behind the opposite distance method is to locate the center of gravity along a span by balancing moments: the distance from End1 to the CG is proportional to the weight on the opposite end relative to the total weight. If End2 carries the other weight, then the distance from End1 to the CG is End2 weight divided by the total weight, multiplied by the total length between the ends. In formula form, End1 distance = (End2 weight / total weight) × total length. This reflects the intuition that a heavier weight on the opposite end pulls the CG closer to that end, increasing End1’s distance. The total length is split between End1 and End2 distances so their sum equals the full length. The other expressions don’t satisfy the moment-balance relationship because they omit the normalization by total weight or mix the quantities incorrectly.