In Calculate CG, which expression gives End1?

In Calculate CG, which expression gives End1?

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

Answer: (B)

Center of gravity on a two-load span comes from balancing moments. If you measure from the end where one weight sits, only the weight at the other end creates a moment about that reference. The distance to the CG from that end is the moment divided by the total weight. With span length L and weights W1 at End1 and W2 at End2, the moment about End1 is W2 × L, and the CG is located a distance x = (W2 × L) / (W1 + W2) from End1. This matches the expression End1 = (End2 weight / total weight) × total length. So End1 equals the right-end weight divided by the total weight, multiplied by the total length. The other forms don’t represent the moment-to-distance conversion correctly: they either omit dividing by total weight, use End1 in the denominator, or add quantities that don’t reflect a balance of moments.

Center of gravity on a two-load span comes from balancing moments. If you measure from the end where one weight sits, only the weight at the other end creates a moment about that reference. The distance to the CG from that end is the moment divided by the total weight. With span length L and weights W1 at End1 and W2 at End2, the moment about End1 is W2 × L, and the CG is located a distance x = (W2 × L) / (W1 + W2) from End1. This matches the expression End1 = (End2 weight / total weight) × total length.

So End1 equals the right-end weight divided by the total weight, multiplied by the total length. The other forms don’t represent the moment-to-distance conversion correctly: they either omit dividing by total weight, use End1 in the denominator, or add quantities that don’t reflect a balance of moments.