Question

A block of mass 2 kg is dropped from a height of 40 cm on a spring of force constant is 1960 newton per metre the maximum distance through which the spring is compressed by

Answer 1

Mass of the body is ( m ) = 2 Kg

spring's constant ( K ) = 1960 N/m 

height of the body = 0.4 m

Let the maximum distance spring will compressed = x m

    see the attachment , it is clear that 

initial potential energy of body = mg(h + x) 

final potential energy = spring potential energy = 1/2 Kx² 

                        according to law of conservation of energy,

initial potential energy = final potential energy

  mg(h + x) = 1/2 Kx²

   2mgh + 2mgx = Kx²

  Kx²  - 2mgx - 2mgh = 0

 ⇒ 1960x² - 2*2*9.8*x - 2*2*9.8*0.4 = 0 

⇒ 1960x² - 39.2x - 15.68   = 0

 after solving this quadratic equations , we get x = 0.1m

     hence, answer is x = 0.1m