Question

A spring is compressed by 15 cm, which requires 150 N of force. What is the spring constant of the spring? How much potential energy is stored in the spring? A 20 kg box is attached to the spring. This arrangement is placed such that the spring is horizontal and the box will slide along a frictionless, horizontal track. What is the maximum speed of the box after the spring is released?

Answer 1

Given,

Compression, x = 15 cm = 0.15 m

Force required, F = 150 N

So,

Spring constant, k = F/x = 150/0.15

                              = 1000 N/m

Now,

Potential energy stored, E = 1/2*k*x² = 0.5*1000*0.15*0.15

                                           = 11.25 J

Now,

mass of the block, m = 20 kg

let maximum velocity attained be v

So, applying conservation of energy

=> Energy stored in spring = kinetic energy of block

=> 11.25 = 1/2*m*v²

=> 11.25 = 0.5*20*v²

=> v² = 1.125

=> v =

         = 1.1 m/s