# If the length of a 23 cm spring increases to 82 cm when a 5 kg weight is hanging from it, what is the spring's constant?

Jan 17, 2017

I got $k = 83 \frac{N}{m}$

#### Explanation:

In this type of problems you need to use Hooke's !aw and Newton's second law:

We can write:
$- k x - m g = 0$
But the elongation (in meters), according to our coordinate system, is negative so we get:
$- k \left(- 0.59\right) - \left(5 \cdot 9.81\right) = 0$
$k = \frac{5 \cdot 9.81}{0.59} = 83 \frac{N}{m}$