Find tension using sum of torque (two strings, one beam, one box)

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The discussion revolves around a physics problem involving torque, tension, and a beam with two strings and a box. The user is struggling with their final submission, having received incorrect messages despite following hints and using significant figures. They initially submitted a value of 49363.63, which was marked incorrect, and then tried 49400 with the same result. A key issue identified is a sign error in the calculations between equations, specifically from equation 2 to equation 3. The user expresses gratitude upon realizing the mistake.
dcmf
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Homework Statement
The figure (Figure 1) shows a model of a crane that may be mounted on a truck. A rigid uniform horizontal bar of mass m1 = 90.0 kg and length L = 5.10 m is supported by two vertical massless strings. String A is attached at a distance d = 1.90 m from the left end of the bar and is connected to the top plate. String B is attached to the left end of the bar and is connected to the floor. An object of mass m2 = 2000 kg is supported by the crane at a distance x = 4.90 m from the left end of the bar. Throughout this problem, positive torque is counterclockwise and use 9.80 m/s2 for the magnitude of the acceleration due to gravity.

Find TA, the tension in string A.
Relevant Equations
Tnet=ΣFlsinθ, F=mg
Here's the picture of the situation described, provided by the question.
1710544579144.png


Here's a screenshot of the work I have done.
1710544594573.png


Here's a screenshot of the submission screen.
1710544453555.png


The issue is that I have one attempt left and am not sure what I am doing wrong. Based on the hints, I feel like I'm calculating it right and using the right significant figures but it's just not accepting my answer (which is strange because usually it doesn't care about significant figures). I submitted 49363.63 and was shown the incorrect message above telling me to round to 3 significant figure so I submitted 49400 and got the same message. I feel like there's got to be something really obvious I'm missing or a concept that I am not applying. I'd really appreciate the help! Thanks in advance
 
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You have a sign error going from eqn 2 to eqn 3 (##F_{TA}=##).
 
haruspex said:
You have a sign error going from eqn 2 to eqn 3 (##F_{TA}=##).
Haha I see it! Thank you so much 🤡
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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