How a suspended rod shares its weight between two cords
Shifting one cord changes each cord's load in fixed proportion
Three brief propositions with diagrams of a horizontal rod hung from two cords analyse how the rod's weight is distributed between its supports. When the cords hang from the two ends the weight is shared equally; when one cord is slid toward the middle, weight passes from the fixed cord to the moved one in a proportion equal to the cord's displacement relative to the remaining span. The lower diagram carries fractional labels marking the shifted support points.
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Equal sharing when cords hang at the ends
A rod suspended by two cords attached at the extremities of its length shares its weight equally between those two cords. This is the base case from which the following variations depart.
Sliding one cord toward the middle
If one cord is moved toward the middle of the rod, the weight taken from the fixed cord and added to the moved one is proportional to the distance moved compared with the remaining span held between the two cords. The block is marked 3 3.
Proportion of weight transferred between fixed and moved cord
With one cord fixed and the other moved toward it, weight leaves the fixed cord and joins the moved one. The transferred weight bears the same ratio to the remaining original load as the cord's movement bears to the original distance between the cords.