# 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?

Jun 23, 2016

$k = 230.82 k \frac{g}{m}$

#### Explanation:

Hooke's Law states that the spring constant $\left(k\right)$ and displacement of the spring are related to the Force applied on the spring by the equation $F = - k x$

The Force is determined by the mass times gravity.

$m = 4 k g$
$g = 9.81 \frac{m}{s} ^ 2$

$F = \left(4 k g\right) \left(9.81 \frac{m}{s} ^ 2\right)$

$F = 39.24 N$

k =?
$x = - 43 c m + 26 c m = 17 c m = - 0.17 m$

$39.24 N = - k \left(- 0.17 m\right)$

$\frac{39.24 N}{- 0.17 m} = - k$

$- 230.82 = - k$

$k = 230.82 k \frac{g}{m}$