(Solution) - A support bar will be in equilibrium balanced at the -(2025 Original AI-Free Solution)

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A support bar will be in equilibrium (balanced) at the fulcrum, O, if m1x + m2y = m3z, where m1, m2, and m3 represent masses and x, y, and z represent the distance of the masses to the fulcrum. Draw a diagram for each question and calculate the answer.

a. A 40 in. bar is in equilibrium when a weight of 6 lb is hung from one end and a weight of 9 lb is hung from the other end. Find the position of the fulcrum.
b. While in the park, Michael and his two sons, Justin and Alden, go on a 16 ft seesaw. Michael, who weighs 150 lb, sits at the edge of one end while Justin and Alden move to the other side and try to balance. The seesaw balances with Justin at the other edge and Alden 3 ft from him. After some additional experimentation the see saw balances once again with Alden at the edge and Justin 5.6 ft from the fulcrum. How much does each boy weigh?