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A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It a trikes an uncompressed spring and compresses it till the block is motionless. The kinetic frictional force is 15 N and spring constant is 10,000 N/m. The spring is compressed by : 8.5 cm 5.5 cm 2.5 cm 11.0 cm Plz give me detailed answer

A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It a trikes an uncompressed spring and compresses it till the block is motionless. The kinetic frictional force is 15 N and spring constant is 10,000 N/m. The spring is compressed by :
  1. 8.5 cm
  2. 5.5 cm
  3. 2.5 cm
  4. 11.0 cm
Plz give me detailed answer 

Grade:11

1 Answers

Arun
25750 Points
5 years ago
Dear Ananya
 
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.. applyling the work energy theorm... Work done(external force) + work done (non conservative force ) = change in kinkinetic 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 qquadric equation ie 5000x² - 15x -16=0 solving this equation x = 0.056m or 5.6 cm (approximately)

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