How are the principles of rotational equilibrium applied in a triple beam balance?
The triple team balance is a tool to measure masses with very high precision. Basically, it works by moving masses along the three beams, away from the pivot point, to balance the weight of the object placed on the scale. By moving these individual masses along the lever (changing the length of the lever arm), the torques are changed. When the beams and the object are finally balanced, rotational equilibrium will be achieved.
Each beam on this type of scale represents a different value of measurement, as pictured below:
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As stated earlier, a triple beam balance does its job by equalizing the torque on both sides of the fulcrum. In a mathematical sense, this means that \( \sum \tau = 0 \rightarrow \sum \tau_{left} = \sum \tau_{right} \). Through this realization, I can answer my driving question: |
A triple beam balance utilizes the principles of rotational equilibrium to balance an unknown object against three known masses. Through the position of these known masses (with reference to the fulcrum), we can calculate the mass of the unknown object with the help of the following formulas:
- \( \tau = F \cdot r \)
- \( \tau \) is torque,
- \( r \) is the distance from the fulcrum to the point where the force is exerted,
- and \( F \) is the magnitude of said applied force.
- \( F = ma \)
- \( F \) is force,
- \( m \) is the mass of an object
- and \( a \) is the acceleration affecting said object.
- \( \sum \tau_{left} = \sum \tau_{right} \)
Since the device is designed in such a way that we know the torque of one side, if we reach rotational equilibrium, we know that the torque of the unknown object is the same. We can then substitute the above formulas into each other to solve for \( m \):
- \( \tau = (ma)(r) \)
- \( m = \frac{ ar }{ \tau } \)