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What is the rule that one must use to determine if two masses on either side of a fulcrum will balance?

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Answer:

The rule for something to be balanced is called the principle of moments and is written as follows: The principle of moments. When an object is balanced (in equilibrium) the sum of the clockwise moments is equal to the sum of the anticlockwise moments. Force 1 x distance 1 from pivot = Force 2 x distance 2 from pivot.

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