Understanding the Balance: Equal Weight, Unequal Position

[krishna mohan]

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?

 

[Lobezno]

The arms of the balance move up and down, leaving the only position for equilibrium as exactly straight, for equal mass arms.

 

[krishna mohan]

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...

 

[rude man]

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.

 

[pmacias]

It is a common misconception that a balance will remain stable in any position as long as the torque around the center is zero. While this may be true for a perfectly balanced system, in reality, there are other factors at play that can affect the balance's stability. These factors include the distribution of mass, the shape and size of the balance arms, and external forces such as air resistance.

In the case of a common balance, the arms are designed to be equal in weight and length, creating a symmetrical system. This allows for the center of mass to be located at the center of the balance, making it easier for the balance to remain in a horizontal position. However, if there is any slight imbalance in the arms or if external forces are present, it can cause the balance to tilt towards the heavier side.

Additionally, the distribution of mass along the arms can also impact the balance's stability. If the mass is concentrated towards one end of the arm, it will create a larger torque and cause the balance to tilt towards that side. This is why it is important to evenly distribute mass on both arms when using a balance.

In summary, while a balance may appear to be stable in any position due to the zero torque around the center, there are other factors that can affect its stability. Understanding these factors can help to alleviate confusion and ensure accurate measurements on a balance.