What is the Relationship Between Kinetic Energy and Momentum?

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Kinetic energy (K.E) is mathematically related to momentum (p) through the equation K.E = p^2/m, where m represents mass. This relationship indicates that as momentum increases, kinetic energy increases quadratically, assuming mass remains constant. Understanding this connection is crucial for solving problems in physics related to motion and energy. The discussion emphasizes the importance of grasping these concepts for effective problem-solving. Overall, the relationship between kinetic energy and momentum is foundational in classical mechanics.
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Homework Statement



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Homework Equations


K.E = p^2/m

The Attempt at a Solution


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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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