Calculating Reaction Forces on an Angled Column

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The discussion revolves around calculating the reaction forces on an angled column due to a weight of 600 kg and a tension of 3000 N in a wire. The vertical reaction force at point C was calculated to be 8282 N, but the textbook states it should be 8480 N. Participants noted that while vertical forces were considered, the horizontal forces also need to be accounted for in the calculations. The importance of including all force components to arrive at the correct reaction force is emphasized. Accurate calculations require a comprehensive approach to both vertical and horizontal forces.
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Homework Statement


The mass of the weight is 600[kG], the tension in the wire 3000[N]. what is the force of reaction at C

Homework Equations


Disassembling of forces using pitagoras formula

The Attempt at a Solution


The vertical reaction at C:
$$3000\cdot \sin 53^0+5886=8282$$
In the book 8480
 

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Karol said:

Homework Statement


The mass of the weight is 600[kG], the tension in the wire 3000[N]. what is the force of reaction at C

Homework Equations


Disassembling of forces using pitagoras formula

The Attempt at a Solution


The vertical reaction at C:
$$3000\cdot \sin 53^0+5886=8282$$
In the book 8480
You've accounted for the forces in the vertical direction. What about the horizontal forces?
 
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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