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

• Hashika
In summary, you would set the forces equal to zero on the weight in order to find the weight W1 being measured.
Hashika

## 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:
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.

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:
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.

#### Attachments

• IMAG0110.jpg
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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)

## What is the difference between statics and dynamics?

Statics deals with systems that are in equilibrium, meaning there is no movement or acceleration. Dynamics, on the other hand, deals with systems that are not in equilibrium and involve movement and acceleration.

## What are some common applications of statics and dynamics?

Statics is commonly used in the analysis and design of structures such as buildings, bridges, and machines. Dynamics is used in fields such as physics, engineering, and biomechanics to study the motion of objects and systems.

## What are the main principles of statics and dynamics?

The main principles of statics include Newton's laws of motion, which state that an object will remain at rest or in motion at a constant velocity unless acted upon by an external force. Dynamics principles include the concepts of force, mass, acceleration, and energy.

## How are statics and dynamics related to each other?

Statics and dynamics are closely related as they both involve the study of forces and motion. In order to understand dynamics, one must have a good understanding of statics principles. Additionally, the principles of statics are often used as a basis for solving more complex dynamic problems.

## What are some common problem-solving techniques used in statics and dynamics?

Some common problem-solving techniques in statics include the method of joints, method of sections, and the use of free body diagrams. In dynamics, techniques such as the use of equations of motion, conservation of energy, and momentum are commonly used to solve problems.

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