Question

A spring has a length of 0.236 m when a 0.252 kg mass hangs from it, and a length of 0.82 m when a 2.13 kg mass hangs from it. What is the force constant of the spring?

Answer 1

Let the natural length of spring be x and spring constant be k
as mass is hanging on spring then ,mass force(mg) must be balance by spring force (kx)
k(0.236-x) = 0.252g .......(1)
k(0.82-x)=2.13g ......(2)
on dividing (1)by (2)
and after simplyfy we get x=0.157
on putting value of x in 1 we get
k=3.189N/m