Solving Physics Problems with "Conceptual Physics" 10th Ed.

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The discussion revolves around solving a physics problem from "Conceptual Physics" 10th Ed. involving a 500 kg load suspended from a boom at a 45-degree angle. Participants are tasked with finding the tension in the supporting cable and the inward force exerted by the boom on the wall. The problem emphasizes the importance of understanding the forces at play, including tension and static equilibrium. Suggestions include analyzing the problem step-by-step and using sample problems from the textbook as a guide. The conversation highlights the need for a clear plan when approaching physics problems.
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INTRODUCTION:
This is a problem from my Introduction to Physical Science class using "Conceptual Physics" 10th Ed.by Paul G. Hewitt

EXACT PROBLEM:
"A 500 kg load is suspended from the end of the horizontal boom, as depicted in the diagram. The angle between the boom and the cable supporting its end is 45 degrees. Assuming that the boom's mass can be neglected compared to that of the load, find:"

PROBLEMS FACED:
a) the tension in the cable
b) the inward force that the boom exerts on the wall

MY THOUGHTS:
What am I doing here?
 
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So what's your plan of attack? Doing a simple sample problem in your text will point you in the right direction
 
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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