# How Much Weight Can a Walkway Hold Before Balance Is Lost?

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• Emmanems08
In summary, the problem is to determine the maximum weight that can be placed in the middle of a system before the weights on the outside exceed the capacity of the pulleys. The equation for this is ∑F=Fc+Fa-Fb=0, where Fb is the downward force, Fa is the upward force to the left, and Fc is the upward force to the right. To solve for d (the distance of the sag), the equations ∑Fx=Fc cosθ+Fa cosθ=0 and ∑Fy=Fc sinθ+Fa sinθ-Fb=0 are used, with the known quantities of m (mass of each counterweight), L (length), and M (mass of the
Emmanems08
This problem is trying to find out how much weight can be placed in the middle of a system before the weights on the outside go over the pulleys.

A diagram of the problem can be found here http://www.physics.umn.edu/classes/...ds/208321-1201Lab3_P4_Equilibrium_Walkway.pdf

We are trying to find d (the distance of the sag) in terms of known quantities. We will know m (the mass of each counterweight), L (the length), and M the mass of the center weight.

So far I have...

∑F=Fc+Fa-Fb=0
ƩFx=Fc cosθ+Fa cosθ=0
∑Fy=Fc sinθ+Fa sinθ-Fb=0

All from the middle point P, where Fb is the force down, Fa is the force up to the left, and Fc is the force up to the right.

sinθ=d/L1 =d/√(d2+(L/2)2)

That check mark is supposed to be a squareroot if that wasn't clear.

I am not sure where to go from here to solve for d.

The linked page is not public, so the diagram is unknown. Taking the algebra on trust to the final equation, and assuming theta is known, it is just a matter of squaring both sides, multiplying out to remove the fraction, and collecting up like terms, to find a simple expression for d2.

## 1. What is equilibrium in a walkway?

Equilibrium in a walkway refers to the state where the forces acting on an individual walking on a walkway are balanced, resulting in a stable and comfortable walking experience.

## 2. How is equilibrium achieved in a walkway?

Equilibrium in a walkway is achieved when the downward force of the individual's weight is evenly distributed across the surface of the walkway, and the frictional forces between the individual's feet and the walkway are strong enough to prevent slipping or sliding.

## 3. What factors can affect equilibrium in a walkway?

The factors that can affect equilibrium in a walkway include the design and construction of the walkway, the surface material and texture, the weight and movement of the individual, and external factors such as wind or uneven terrain.

## 4. How can we maintain equilibrium in a walkway?

To maintain equilibrium in a walkway, it is important to regularly inspect and maintain the walkway to ensure it is in good condition. Additionally, individuals should walk with proper posture and take caution when walking on wet or uneven surfaces.

## 5. What are the consequences of an unbalanced walkway?

An unbalanced walkway can lead to accidents and injuries such as slips, trips, and falls. It can also cause discomfort and fatigue for individuals walking on the walkway, as they have to constantly adjust their balance and exert more effort to maintain stability.

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