Work Done by Tension in Cable: More Than Gravity?

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The discussion centers on the work done by tension in a cable compared to the work done by gravity. It questions whether the tension's work should exceed that of gravity due to horizontal displacement. Participants seek clarification on the direction of the force and its relation to displacement. The conversation highlights the need to analyze the vector components of force and displacement to determine the actual work done. Understanding these dynamics is crucial for accurately assessing the work done by tension in a cable system.
rootX
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This questions asks what is the work done by the tension in the cable. And, the book answered that it is equal to the work done by the gravity.
But shouldn't it be more than the work done by the gravity? (because there is also a horizontal displacement)
see the attached image
attachment.php?attachmentid=9780&stc=1&d=1176673900.jpg
 

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I can't see your attachment yet, what is the direction of the force? So what is \vec{F} \cdot \vec{d} ?

AM
 

Thread 'Magnitude of buoyant force in fluids of different densities'

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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