# Troubleshooting a FBD of a Pulley

• STEMucator
In summary, the conversation is about a problem involving tension and a pulley. The person understands some parts of the problem but is confused about a specific part of the force equation. They mention a triangle and how the coordinates of points C, D, and B can be determined. It is suggested to project the plane CDE onto the y-z coordinate plane to determine the position of point E.
STEMucator
Homework Helper

## Homework Statement

I'm having a bit of trouble understanding something from this:

http://gyazo.com/88a466b57d8516d2df1b12008947be43

## The Attempt at a Solution

I understand how to get the components of reaction at ##A## as well as the tension in segment ##BE##.

What I'm having trouble with is the FBD of the pulley used to determine the tension in ##DEC##. I'm not quite sure how they have come up with a part of the force equation, namely:

##\sum F_z = 0 \Rightarrow 2(\frac{4}{\sqrt{96}})T - \frac{1}{\sqrt{5}}(1677.05) = 0##

The term ##2(\frac{4}{\sqrt{96}})T## is what is confusing. I understand you need twice the tension since it's symmetric, but how on Earth are they getting ##\frac{4}{\sqrt{96}}##?

I figure they are applying ##\frac{T_z}{T} = \frac{4}{\sqrt{96}}## to a triangle, but I'm not seeing the triangle.

If you look at the diagram, write the coordinates of points C, D, and B.

When the pulleys are under tension, one can see that CDE make a triangle and a plane. You can also assume that the line BE will also lie in that same plane. You can determine the position of the point E by drawing a projection of the plane CDE in the y-z coordinate plane, and extending it to the line AB on the y-axis. Once the coordinates of point E are known, you can calculate the length of line DE, which is Sqrt (96) feet.

## 1. What is a FBD and why is it important for troubleshooting a pulley?

A FBD, or free body diagram, is a visual representation of all the forces acting on a single object. It is important for troubleshooting a pulley because it allows us to analyze the forces involved and determine any potential issues or malfunctions.

## 2. What are the common problems that can occur with a pulley and how can they be identified on a FBD?

Common problems with a pulley include misalignment, wear and tear, and insufficient tension. These can be identified on a FBD by looking for imbalanced or non-parallel forces, as well as any forces that are not in line with the intended direction of movement.

## 3. How can tension be adjusted on a pulley using a FBD?

By analyzing the forces on a FBD, the tension on a pulley can be adjusted by either increasing or decreasing the magnitude of the forces acting on the pulley. This can be achieved by adding or removing weights, adjusting the position of the pulley, or using a tensioning device.

## 4. Can a FBD help in identifying potential safety hazards with a pulley?

Yes, a FBD can help identify potential safety hazards with a pulley by highlighting any imbalanced or excessive forces that could cause the pulley to fail or malfunction. It can also help identify any potential pinch points or entanglement hazards.

## 5. How can a FBD be used to troubleshoot and solve pulley problems?

A FBD can be used to troubleshoot and solve pulley problems by allowing us to analyze the forces involved and identify any potential issues. By adjusting the forces on the pulley and ensuring they are balanced and aligned, many common pulley problems can be solved. Additionally, a FBD can help in determining the appropriate repairs or adjustments needed to fix the pulley.

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