How Can You Design a Simple Scale Using Cable Tension and Displacement?

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Homework Help Overview

The discussion revolves around designing a simple scale using cable tension and displacement, specifically for weighing bulk materials in a developing country context. The problem involves a loading platform supported by a cable, with various weights and measurements influencing the system's behavior.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the static equilibrium of the system and the need to analyze forces at point B. There are questions about how to relate the weight being measured to the horizontal displacement (delta) and the constants involved. Some participants mention the importance of free body diagrams (FBD) and the challenges of managing multiple variables.

Discussion Status

The discussion is ongoing, with participants expressing confusion over the setup and variables. Some guidance has been offered regarding the use of free body diagrams and setting forces to zero, but there is no consensus on how to proceed with the calculations or the relationships between the variables.

Contextual Notes

Participants note the fixed nature of point A and the movable nature of point B, which adds complexity to the problem. There is also mention of needing to upload a figure for better clarity, indicating that visual aids may be necessary for understanding the setup.

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Homework Statement



You are working for the Peace Corps in a developing country. Your job is to design a simple, but accurate scale for weighing bulk materials such as food and construction materials. A possible idea consists of a loading platform, D, that is supported by cable AB, where end A is attached to a large tree limb. After loading
platform D, weight W3 is applied, which causes point B to move horizontally by a small distance delta that can be measured using a yardstick.
Assume:
W2 = weight of the loading platform = 50kg
W1 = weight of materials being weighed ≤ 250 kg
Pulley C is frictionless

You are to specify:
L = length of cable AB, where L is less than 5m.
W3 = weight of the counterweight, where W3 ≤ 20kg.

For the specific values of L and W3 you choose, produce a graph with W1 and delta as the vertical and horizontal axes, respectively. Therefore, by measuring the deflection, delta, your graph will tell the user what the weight W1being measured is.

Homework Equations


Newton's Second Law

The Attempt at a Solution


Not a clue how to start, is the system in static equilibrium? If so, then I'd assume to set all the forces at point B = 0. But then I'd have to assign an angle theta that is another variable. I'm so confused.
 
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Hashika said:

Homework Statement



You are working for the Peace Corps in a developing country. Your job is to design a simple, but accurate scale for weighing bulk materials such as food and construction materials. A possible idea consists of a loading platform, D, that is supported by cable AB, where end A is attached to a large tree limb. After loading
platform D, weight W3 is applied, which causes point B to move horizontally by a small distance delta that can be measured using a yardstick.
Assume:
W2 = weight of the loading platform = 50kg
W1 = weight of materials being weighed ≤ 250 kg
Pulley C is frictionless

You are to specify:
L = length of cable AB, where L is less than 5m.
W3 = weight of the counterweight, where W3 ≤ 20kg.

For the specific values of L and W3 you choose, produce a graph with W1 and delta as the vertical and horizontal axes, respectively. Therefore, by measuring the deflection, delta, your graph will tell the user what the weight W1being measured is.

Homework Equations


Newton's Second Law

The Attempt at a Solution


Not a clue how to start, is the system in static equilibrium? If so, then I'd assume to set all the forces at point B = 0. But then I'd have to assign an angle theta that is another variable. I'm so confused.

Welcome to the PF.

I think we will need you to upload a scanned copy of the figure, or link to it if it is online.

From the sound of the bending tree limb, it would seem that you would use some spring force & deflection equation as well...
 
I really appreciate the help, but I believe point A is fixed. I've attached the image.
 

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Hashika said:
I really appreciate the help, but I believe point A is fixed. I've attached the image.

Ah, that's different. In problems like this, you generally start with a free body diagram (FBD) -- in this case of the weight. Show all of the forces on the weight, and then you do what since the weight is not moving...?
 
You set the forces equal to zero, but how are you supposed to get W1 as a function of delta using the constants?
 
Hashika said:
You set the forces equal to zero, but how are you supposed to get W1 as a function of delta using the constants?

More accurately, you set the sum of the forces to zero in each of the x and y directions.

If you draw the FBD and write the two equations, you should be able to start solving for the unknowns...
 
I tried that and ended up with a mass jumble of variables. What did you guys get?
 
I'm still having a lot of trouble managing everything. Our professor told us that point B was movable. It's so confusing.
 
I don't see anybody showing us their work so far... (that's in the PF Rules link at the top of the page, BTW)
 

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