Answer:
The bench should be located 1.8 meters from the 82 kg man for the board to balance.
Step-by-step explanation:
We have a board that is 3.0 meters long and weighs 5.0 kg. The fulcrum is a small bench. An 82 kg man sits on one end and a 64 kg woman sits on the other end. For the board to balance, the torques on either side must be equal. Let's define the distance the 82 kg man sits from the fulcrum as x meters. Then the distance the 64 kg woman sits from the fulcrum will be (3.0 - x) meters.
Using the torque equation: Torque = Force * Distance, we can write:
⇒ Torque on man's side = (82 * 9.81 * x) Nm
⇒ Torque on woman's side = (64 * 9.81 * (3.0 - x)) Nm
Since the torques must be equal for balance, we can set the two equations equal and solve for x:
⇒ (82 * 9.81 * x) = (64 * 9.81 * (3.0 - x))
Solving this gives:
x = 1.8 meters
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⊂ (Your answer of 5.4 meters is incorrect, it would cause an imbalance and the board would not balance.)