Question

If the length of a `12 cm` spring increases to `20 cm` when a `10 kg` weight is hanging from it, what is the spring's constant?

Answer 1

`1225 N/m`

Explanation:

A spring constant for a 'simple spring' is usually written as the `k` in:
`F= -kx`

For force of a `10 kg` weight is calculated using gravity:
`F = mg`

`F = 10*9.8 = 98 N`

The `x` in the equation above is relative to the relaxed length of the spring. If the length of the spring is `12 cm` without any mass attached, we call this position zero and we can see that the additional length with the mass attached is `8 cm` longer.

We now know `F` and `x` and we can solve for `k`. Notice that the direction of the force is opposite to the direction of gravity, so the sign has changed.

`F = -kx`

`-98 N = -k * 0.08 m`

`98/0.08 N/m = k = 1225 N/m`