Determing unknown weight of an hanging object in a systen

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In summary: Also, you should be able to find θ1 and θ2 in terms of the known variables and the unknown weight, w2. Then you can write an equation involving only w2. And if you have more than one object, you could do the same thing using the angles for each object and the known weights of each one to get a system of equations in w2, w3, etc.In summary, the conversation discusses a problem involving testing a new device for measuring the weight of tissue samples. The device consists of two light wires attached to a support, with one wire holding a known weight and the other holding the sample to be measured. The wires are stretched apart by electromagnets and the angles they make with
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GoGoGadget
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Homework Statement



1. You have been asked to test a new device for measuring the weight of tissue samples. The device
consists of two light wires attached at one end to a support. A small container is attached to the other
end of each wire. Initially each container hangs straight down. The wires are far enough apart so the
containers hanging on them don’t touch. One of the containers has a very accurately known weight
while the other contains the sample whose weight you wish to determine. A power supply is slowly
turned on so that electromagnets in each container cause them to slowly move away from each other.
When the power supply is kept at its operating value, the containers stay at the same horizontal level.
At that point, each of the wires supporting them makes a different angle with the vertical and that angle
is measured. To test the device, you calculate the weight of one container and its contents from the
measured angles and the known weight of the other container. You will then check your calculation in
the laboratory using a variety of different objects as samples.

Homework Equations



F = ma

w = mg

The Attempt at a Solution



Below are my attached picture and diagram of the system. In the first picture, I drew what the system looked like in equilibrium. In the second picture, I show the changes in the system when the angles are present when the wires are stretched out vertically. What I have so far:

Variables:

Fs = Force of stopper

Fw = Force of wire

FE1 = Force of Earth on container 1

FE2 = Force of Earth on container 2

Equations:

Fx = Fw - Fs Cos θ = 0


Fy = Fw - F E1 Sin θ

F y = Fw - FE2 Sin θ

From my understanding of this problem, I believe I need to find the weight of container 1, where the F = E1. And I know we do know the weight of container 2, E2. But from here, I have no idea how to go about setting the equations to be equal to one another or how to connect the two containers together into one equation. Any help is greatly appreciated.
 

Attachments

  • Two hanging objects in equilibrium.jpg
    Two hanging objects in equilibrium.jpg
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  • Weight of hanging objects in changed system.jpg
    Weight of hanging objects in changed system.jpg
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  • #2
I'm not sure about your diagrams. What's the block in the middle? As I read the question, each wire is on its own support. Since, with the power on, the wires hang at different angles yet the containers are at the same horizontal level, I would assume either the supports are at different heights or the wires are of different lengths (or both). I've a suspicion they haven't told you quite enough.
In your equations, you have one for each weight, yet you have the same symbols Fy, Fw and theta in each. That's confusing, since each each of them can be different.
And what exactly do your Fx and Fy stand for? If they're net horizontal and vertical forces then your equations are quite wrong.
 
  • #3
haruspex said:
I'm not sure about your diagrams. What's the block in the middle? As I read the question, each wire is on its own support. Since, with the power on, the wires hang at different angles yet the containers are at the same horizontal level, I would assume either the supports are at different heights or the wires are of different lengths (or both). I've a suspicion they haven't told you quite enough.
In your equations, you have one for each weight, yet you have the same symbols Fy, Fw and theta in each. That's confusing, since each each of them can be different.
And what exactly do your Fx and Fy stand for? If they're net horizontal and vertical forces then your equations are quite wrong.


In my original equation, I think I had misunderstood the problem and drew the diagram to show the wires hanging from the same stopper, which the block was supposed to represent. I've redrawn the problem in the attachments below. The only I wasn't sure of was how to show the angles that are represented. I drew the system, show it in equilibrium and then with the wires hanging so they can potentially form an angle. However, I didn't show my angles in my second diagram as I was not sure how I can show them without drawing in extra variables that aren't there. However, I know that vectors could be shown too for the sides of the potential triangles that each wire makes. FW1 could shown FW1x and FW1y on the wire hanging on the left and then FW2 could be shown with FW2x and FW2y on the right. And Fx and Fy were supposed to show the sum of forces in either direction. So potentially now, I'm thinking:

Fx: FW2 sin θ2 + FW1 sin θ 1 = 0

Fy: FW2 cos θ2 - E1 +FW1 sin θ1 - E2 = 0

I'm not sure if I'm thinking about this correctly or not. Any further input is great. Thanks a lot!
 

Attachments

  • Physics 1201W Sample exam Question One-Equilibrium.jpg
    Physics 1201W Sample exam Question One-Equilibrium.jpg
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  • Physics 1201W sample exam Question One-Angles.jpg
    Physics 1201W sample exam Question One-Angles.jpg
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  • #4
GoGoGadget said:
Fx: FW2 sin θ2 + FW1 sin θ 1 = 0
If you're measuring both angles in the same direction (so one will be negative) then yes.
Fy: FW2 cos θ2 - E1 +FW1 sin θ1 - E2 = 0
There is no relationship between the vertical forces on one and the vertical forces on the other. That should be two separate equations.
 
  • #5


As a scientist, it is important to approach problems like this with a systematic and analytical mindset. The first step would be to clearly define all the variables and their relationships in the system. From there, we can use the given equations (F=ma and w=mg) to set up a system of equations to solve for the unknown weight.

Let's start by defining the variables:

m1 = mass of container 1
m2 = mass of sample in container 2
g = acceleration due to gravity
θ1 = angle made by wire 1 with the vertical
θ2 = angle made by wire 2 with the vertical
Fw1 = force of wire 1
Fw2 = force of wire 2

Based on the given information, we can set up the following equations:

Fw1 = m1g (since the container is in equilibrium)
Fw2 = (m1+m2)g (since the sample and container are attached to the same wire)
Fw1 = Fs1cosθ1 (from the free body diagram of container 1)
Fw2 = Fs2cosθ2 (from the free body diagram of container 2)

Now, we can set these equations equal to each other and solve for m1:

m1g = Fs1cosθ1
(m1+m2)g = Fs2cosθ2

Solving for m1 in the first equation, we get:

m1 = Fs1cosθ1/g

Substituting this into the second equation, we get:

(Fs1cosθ1/g + m2)g = Fs2cosθ2

Simplifying, we get:

Fs1cosθ1 + m2g = Fs2cosθ2

Finally, we can solve for m2:

m2 = (Fs2cosθ2 - Fs1cosθ1)/g

This gives us the mass of the sample in container 2, and from there we can use the given equation w=mg to calculate the weight of the sample. It is important to note that this method assumes that the wires and containers have negligible mass. If this is not the case, we would need to take the mass of the wires and containers into account in our calculations.

In conclusion, by setting up a system of equations and solving for the unknown weight using known values and equations, we can determine the weight of the hanging object in the given system.
 

1. How do you determine the weight of an unknown hanging object in a system?

To determine the weight of an unknown hanging object in a system, you can use the principles of equilibrium and the equations of motion to calculate the weight of the object based on the forces acting on it.

2. What are the necessary tools or equipment needed to determine the weight of an unknown hanging object?

The necessary tools or equipment needed to determine the weight of an unknown hanging object may include a spring scale, a ruler or tape measure, and a calculator. You may also need a support stand, string or wire, and weights to create an equilibrium in the system.

3. What are the steps involved in determining the weight of an unknown hanging object in a system?

The steps involved in determining the weight of an unknown hanging object in a system include setting up the system with the object and weights to create equilibrium, measuring the length of the string or wire, and using the equations of motion to calculate the weight of the object based on the forces in the system.

4. Are there any factors or variables that may affect the accuracy of determining the weight of an unknown hanging object in a system?

Yes, there are several factors that may affect the accuracy of determining the weight of an unknown hanging object in a system. These include friction in the string or wire, air resistance, and the precision of the measuring tools used. It is important to minimize these factors to ensure accurate results.

5. What are some real-world applications of determining the weight of an unknown hanging object in a system?

Determining the weight of an unknown hanging object in a system is a common task in many fields, such as engineering, physics, and construction. It is used to measure the weight of objects that are difficult or dangerous to weigh directly, such as heavy machinery or suspended structures. It is also used in scientific research to determine the weight of objects in space or other environments where traditional weighing methods may not be feasible.

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