I have a question for Problem 46 of The \"Fundamentals of Physics 10th Edition\"

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I have a question for Problem 46 of The "Fundamentals of Physics 10th Edition" Halliday and Resnick. I'm having a really hard time figuring out how to connect K.E to this whole problem. They give us a lot of values which seem to deal with Tensional strain, but how at all does that deal with K.E? They introduce work, which i saw as the Integral of the force of collision, but still leaves us with unknown K.E and U (potential energy) values? Is there a way to solve for force and relate it to Kinetic Energy? Thank you for your time!

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Iam solving

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