Question

If the length of a `21 cm` spring increases to `57 cm` when a `5 kg` weight is hanging from it, what is the spring's constant?

Answer 1

We should expect `k` to be somewhere in the hundreds for typical springs.

This is simply looking at the equation

`\mathbf(F = -kDeltay)`

...for when an object is hanging off a spring.

So, the only force acting on the spring is the force `\mathbf(F_g)` due to gravity `\mathbf(g)`. The generic force `F`, then, is `F_g`. Thus, with `g < 0` (where down is negative):

`F_g = -kDeltay`

`mg = -k(y_f - y_i)`

`(mg)/(y_i - y_f) = k`

`color(blue)(k) = (("5 kg")(-"9.80665" cancel"m""/s"^2))/("0.21" cancel"m" - "0.57" cancel"m")`

`= color(blue)("136.20 kg/s"^2)` or `color(blue)("N/m")`