Static Equilibrium: Finding More than One Balance Point

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Homework Help Overview

The discussion revolves around a static equilibrium problem involving a system with two weights on pans, exploring the conditions under which the system can balance. Participants are examining the principles of moments and fulcrum mechanics in this context.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the requirement for the sum of moments to equal zero and the implications of weight placement on balance. There is questioning about the possibility of multiple balance points and whether the assumptions about symmetry and distance from the pivot are sufficient.

Discussion Status

The discussion is active, with participants sharing their interpretations and questioning the assumptions made about the balance points. Some have offered insights into the mechanics of the problem, while others express uncertainty about the existence of multiple positions for weight placement.

Contextual Notes

Participants are considering the constraints of the problem, including the symmetry of the pans and the requirement for equal moment arms when weights are identical. There is an acknowledgment of the need for further exploration of the conditions that allow for balance beyond the intuitive placements.

unctarheels1
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Static Equilibrium?

Summing the moments up from around the center, it is easy to find the intuitive location for the weight at B which would be the same as the A side. But how are there more locations to make this system balance??
 

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Assuming the pans are symmetrically located and of the same size, then one simply needs the sum of the moments to be zero.

This is essentially a fulcrum problem in which the product of the weight of mass A (mAg) and its moment arm about the central axis (pivot point) must equal the product of weight B (mBg) and its moment. If the weights are identical, then the moment arms must also be identical.
 
Right, so summing up the moments from the center would say you would have to put the weight on Pan B the same distance from the center as the weight on Pan A.

The questions makes it seem like their are more than one position that the weight can be placed on Pan B to balance the system. Am I missing something?
 
unctarheels1 said:
Right, so summing up the moments from the center would say you would have to put the weight on Pan B the same distance from the center as the weight on Pan A.
Yes
unctarheels1 said:
The questions makes it seem like their are more than one position that the weight can be placed on Pan B to balance the system. Am I missing something?
I was wondering about that myself. Other than moving the mass B perpendicularly (in or out of the plane of the paper), I don't readily see an alternative. The centers of mass of A and B have to be at the same moment arm, unless I am missing something.
 

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