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.
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:
Fs = Force of stopper
Fw = Force of wire
FE1 = Force of Earth on container 1
FE2 = Force of Earth on container 2
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.
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