How Do You Calculate Kinetic Energy in Relativistic Collisions?

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The discussion revolves around calculating the kinetic energy of a particle with mass m colliding with a stationary particle of mass 2m, resulting in a composite mass of √17m. The initial attempts involved using conservation of mass-energy and momentum, but the user struggled to derive the required kinetic energy value of k = 2mc². A request for detailed work on the calculations was made, emphasizing the need for clarity in problem-solving. Ultimately, the user resolved the problem independently and expressed gratitude for the assistance. The thread highlights the importance of detailed problem-solving steps in physics discussions.
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Homework Statement



We have a particle mass ##m## with kinetic energy ##k## colliding with a stationary particle of mass ##2m##. The collision creates a composite mass of ##\sqrt{17}m##. Find the value of ##k##

Homework Equations

The Attempt at a Solution



I have tried using mass-energy conservation and also momentum conservation, but I can't seem to get the required result of ##k=2mc^2##
 
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Please show your work. Simply generically describing what you tried unsuccessfully isn't helpful at all.
 
vela said:
Please show your work. Simply generically describing what you tried unsuccessfully isn't helpful at all.

My apologies. Fairly new round here... I've figured it out now, but many thanks anyways
 
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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