How does a Triple Beam Balance work?

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A Triple Beam Balance requires a horizontal position to ensure accurate measurement because it relies on torque and the equilibrium of forces. When the balance is horizontal, there is no moment acting due to the horizontal displacement of the center of mass, allowing for precise comparisons of mass. If the balance is not horizontal, the forces can create a moment that skews the measurement, even if it appears close to correct. The stability of the balance is dependent on the suspension point being above the center of mass, ensuring that the arms remain horizontal and the 'leg' vertical. Therefore, achieving a horizontal position is essential for determining equal masses accurately.
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so I understand that it balances both sides of the scale but why does it have to be horizontal? in other balancing systems the beams do not have to be horizontal but in this system they do. I know it has to do with torque but can't seem to understand how the balance can be close to the right mass and not be moving but it is not correct unless it is horizontal.
 
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For any balance to be stable, the suspension point has to be slightly above the CM of the suspended mass. Only when the beam is horizontal is there no moment acting due to the horizontal displacement of the CM. Imagine an exaggerated arrangement consisting of an inverted T, with the suspension at the top. A perfect T will hang with the leg vertical but, put unequal masses on the arms and the T will still balance but with the leg not vertical. Only when the leg is vertical can you say that the masses are equal. The triple beam balance, likewise, needs the (very short) hanging 'leg' to be vertical and the arms horizontal. Then the moments on each side can be said to be equal.
 
For simple comparison, I think the same thought process can be followed as a block slides down a hill, - for block down hill, simple starting PE of mgh to final max KE 0.5mv^2 - comparing PE1 to max KE2 would result in finding the work friction did through the process. efficiency is just 100*KE2/PE1. If a mousetrap car travels along a flat surface, a starting PE of 0.5 k th^2 can be measured and maximum velocity of the car can also be measured. If energy efficiency is defined by...

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