A block of 2 kg slides on a parallel surface at a speed of 4 m/s. It falls on an unpressed spring and presses it until the block is completely motionless. The amount of kinetic friction is 15 N and the spring constant is 10,000 N/m. Spring presses with _____.

The correct answer is 5.5 cm.

• The total kinetic energy possessed by the block goes into the potential energy of the spring and the work done against friction.
• K.E. supplied = Work done against friction + P.E. of spring  
  • \({1\over2} mv^2= Fx+{1\over2} kx^2\)
• Suppose x be the compression of the spring.
• Here:
  • mass=2 kg,υ = 4 m/s
  • Force of kinetic friction, F = 15 N
  • spring constant, K = 10000 N/m
• \({1\over 2}×2×4^2=15x+{10000\over 2}x^2\)
• \( 5000x^2+15x−16=0\)
• \(x=0.055m=5.5cm\)

Additional Information

• Kinetic energy, the form of energy that an object or a particle has by reason of its motion.
  • If work, which transfers energy, is done on an object by applying a net force, the object speeds up and thereby gains kinetic energy.
•  Kinetic friction is defined as a force that acts between moving surfaces.
  • A body moving on the surface experiences a force in the opposite direction of its movement.
  • The magnitude of the force will depend on the coefficient of kinetic friction between the two materials.