# If the length of a 26 cm spring increases to 46 cm when a 8 kg weight is hanging from it, what is the spring's constant?

Mar 3, 2018

$392.4$N/m

#### Explanation:

the spring constant is the direct proportion between:

the force applied on the string

and the extension of the string when the force is applied on it.

they have the relationship

$F = k \cdot e$

where

$F$ is the force in newtons, N

$k$ is the 'spring constant' in newtons per metre, N/m

and $e$ is the extension in metres, m.

here, the force is that applied on the $8 k g$ weight.

$W = m g$

where $W$ is weight (force due to gravity)

$m$ is mass

and $g$ is gravitational field strength.

on Earth, $g \approx 9.81$ newtons per kilogram, N/kg.

the force applied is $8$kg $\cdot 9.81$N/kg

which is $78.48$ N.

the extension is from $26$cm to $46$cm.

$46$cm $- 26$cm $= 20$cm

$20$cm is $\frac{20}{100}$m, which is $0.2$m.

$F = k \cdot e$

$78.48$N $= k \cdot 0.2$m

$k = \left(\frac{78.48}{0.2}\right)$ N/m

$\frac{78.48}{0.2} = 78.48 \cdot 5 = 392.4$

$k = 392.4$ N/m