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

[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:
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.

 

[berkeman]

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...

 

[Hashika]

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

 

[berkeman]

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...?

 

[Hashika]

You set the forces equal to zero, but how are you supposed to get W1 as a function of delta using the constants?

 

[berkeman]

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...

 

[GOPgabe]

I tried that and ended up with a mass jumble of variables. What did you guys get?

 

[Hashika]

I'm still having a lot of trouble managing everything. Our professor told us that point B was movable. It's so confusing.

 

[berkeman]

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)