Question

If the length of a `26 cm` spring increases to `43 cm` when a `4 kg` weight is hanging from it, what is the spring's constant?

Answer 1

`k = 230.82kg/m`

Explanation:

Hooke's Law states that the spring constant `(k)` and displacement of the spring are related to the Force applied on the spring by the equation `F =-kx`

The Force is determined by the mass times gravity.

`m = 4kg`
`g = 9.81 m/s^2`

`F = (4kg)(9.81m/s^2)`

`F = 39.24 N`

`k =?`
`x = -43cm+26cm = 17cm = -0.17m`

`39.24 N = -k(-0.17 m)`

`(39.24N)/(-0.17m) = -k`

`-230.82 = -k`

`k = 230.82kg/m`