Static Equilibrium: Finding More than One Balance Point

In summary, when trying to achieve static equilibrium in a system with two pans, the sum of the moments around the center must be zero. This is similar to a fulcrum problem, where the weight on one side must equal the weight on the other side multiplied by their respective moment arms. If the pans are identical, the moment arms must also be identical. There may be multiple positions for the weight on Pan B to achieve balance, but it must be at the same distance from the center as the weight on Pan A.
  • #1
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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  • #2
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.
 
  • #3
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?
 
  • #4
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.
 

1. What is static equilibrium?

Static equilibrium is a state in which all forces acting on a system are balanced, resulting in no net force and no net torque. This means that the system remains in a state of rest or constant motion.

2. How is static equilibrium different from dynamic equilibrium?

In dynamic equilibrium, forces acting on a system are balanced but the system is still in motion. In static equilibrium, forces are balanced and the system is at rest or in constant motion.

3. What is the significance of finding more than one balance point in static equilibrium?

Finding more than one balance point in static equilibrium can provide valuable information about the stability of a system. It can also help in designing structures that can withstand different external forces.

4. How do you determine the position of multiple balance points in a system?

To determine the position of multiple balance points in a system, you will need to use the principles of static equilibrium, including the sum of forces and the sum of torques equaling zero. You can also use mathematical calculations and experimentation to find the exact positions.

5. What are some real-life applications of static equilibrium?

Static equilibrium has many practical applications in various fields, including engineering, physics, and architecture. It is used to design stable structures such as buildings and bridges, to analyze the stability of vehicles, and to understand the motion of objects in space. It is also used in industries such as construction and manufacturing to ensure the safety and stability of structures and machines.

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