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A 2kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring and compresses till he block is motionless. The Kinetic friction force is 15 N and spring constant is 10000 N/m. The spring compresses by ?

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Continuation of Question :The Kinetic Friction force is 15 N and spring constant is 10000 N/m. The spring compresses by how much ?

As the block is moving with some initial velocity it must be having must KE. Finally, it comes to rest so kinetic energy final will be zero.. it ll have some potential energy. As frictional force is also given it will some work done by friction.. applying the work-energy theorem... Work done(external force) + work done (non conservative force ) = change in kinetic energy+ change in potential energy. 0 + 15x = kf - ki + pf - pi. 0 + 15x = 0 + 1/2mv2 + k/2x² - 0. On putting the values you get a quadratic equation ie 5000x² - 15x -16=0 solving this equation x = 0.056m or 5.6 cm



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