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Answer :
To balance a beam, the moments around the fulcrum must be equal. The distance at which a 27.597N weight needs to be placed to balance a beam with a 30.641N weight set at 10.395cm from the fulcrum is found by solving the equation: (30.641 N imes 10.395 cm) / 27.597 N.
The question involves the concept of static equilibrium in a balance beam, which falls under the domain of Physics. To balance a beam, the moments (or torques) around the fulcrum must be equal. The formula for the moment is force multiplied by distance from the fulcrum (Moment = Force x Distance). Using this concept, the distance for the second weight to balance the beam can be calculated using the equation:
30.641 N imes 10.395 cm = 27.597 N imes x
Where x represents the unknown distance for the 27.597 N weight. Solving for x, we get:
x = (30.641 N imes 10.395 cm) / 27.597 N
Once you calculate x, you'll know the distance from the fulcrum to place the 27.597 N weight in order to achieve static equilibrium.
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