Understanding the Balance: Equal Weight, Unequal Position

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SUMMARY

The discussion centers on the mechanics of a common balance scale, specifically addressing why it stabilizes in a horizontal position despite equal weights on both arms. The key conclusion is that while the torque around the center is zero in any position, the restoring torque arises from the weight of the pointer and its distance from the pivot point when the scale is unbalanced. The relationship between potential energy and torque is clarified, emphasizing that the balance achieves equilibrium through a closed-loop mechanism rather than relying solely on open-loop principles.

PREREQUISITES
  • Understanding of basic physics concepts such as torque and equilibrium
  • Familiarity with potential energy and its relationship to mechanical systems
  • Knowledge of balance scales and their operational principles
  • Basic grasp of closed-loop versus open-loop control systems
NEXT STEPS
  • Research the principles of torque in mechanical systems
  • Explore the design and functionality of balance scales
  • Study closed-loop control systems in engineering applications
  • Investigate potential energy calculations in various mechanical contexts
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in the principles of balance and equilibrium in mechanical systems will benefit from this discussion.

krishna mohan
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Confused about a simple thing...

For a common balance, since both arms have equal weight, what causes the pole to choose a horizontal position?
Shouldnt it be stable in any other position as the torque around the centre is zero for any other position too?
 
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The arms of the balance move up and down, leaving the only position for equilibrium as exactly straight, for equal mass arms.
 
I am a little confused here...

Even if you move the balance to some other position, the potential energy is not going to change..as the increase in PE due to one mass moving up is compensated by the decrease due to the other moving down..

In a slightly tilted position, where does the restoring torque come from? The two masses seem to contribute equal and opposite torque leading to zero torque...
 
If the pointer points below the pivot point then if the scale is unbalanced the pointer provides a restoring torque = W*l*sina where W = weight of pointer, l = distance from pivot to pointer's c.g. and a = offset angle. Since scales are always balanced with known weights, the "open-loop" quantity da/dm is of no first-order importance. Scales are always used in a closed-loop manner.

I don't know much about scales but I would think that's how they're designed.
 

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