Question

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?

Answer 1

`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 * 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 `8kg` weight.

`W = mg`

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

`m` is mass

and `g` is gravitational field strength.

on Earth, `g ~~ 9.81` newtons per kilogram, N/kg.

the force applied is `8`kg `* 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 `20/100`m, which is `0.2`m.

`F = k * e`

`78.48`N `= k * 0.2`m

`k = (78.48/0.2)` N/m

`78.48/0.2 = 78.48 * 5 = 392.4`

`k = 392.4` N/m