Real vs Ideal Springs: How Do Forces and Stretches Compare?

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In the discussion, the impact of mass on a real spring's force and stretch is analyzed compared to an ideal spring. It is established that a real spring, having mass, will exert a greater force on an attached mass due to its own weight, resulting in a smaller stretch than an ideal spring. The differences in behavior between real and ideal springs are illustrated through free body diagrams. Participants emphasize the importance of considering the mass of the spring in calculations. Understanding these distinctions is crucial for accurate physics problem-solving.
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Since a real spring has mass, if another mass was attached to it, would the spring exert a greater force on the mass and have a smaller stretch, versus if this spring was an ideal spring?
 
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Show a free body diagram for both cases.
 
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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