Question

How do you derive the effective spring constant?

Answer 1

You can measure it, the spring constant (k) is

`k = F/x`

where F is the force applied to stretch (or compress) a spring,
x is the elongation (or compression) measured after the force is applied.

Explanation:

A) Concept:

The spring constant of a spring is how much a spring will stretch or compress if a force is applied to it.

For example, if 1-N force stretches a spring by 2cm, then its

spring constant`= (1N)/(2cm) = 0.5 N/(cm)= 50 N/m`

50 N/m is the spring constant `-` read: it requires 50 N to stretch the spring by 1.0 m.

It is a constant because If you apply 10-N force, you expect the spring to stretch by 20 cm.

Spring constant = 10N/20 cm = 0.5 N/(cm)= 50 N/m #

If you stretch the same spring by 5 cm, how much force must you use? Since each cm requires 0.5 N, then 5 cm requires 5 x .5N= 2.5 N.

We can formulate this relationship of Force to elongation
`F/x = k` where k is the spring constant

`F = k x`

where F is the force applied in Newton, and x is the elongation (or compression) in meter. If k = 50 N/m,

then `F = 50 x`

The spring force found inside the spring, however, is opposite to the force you applied to it, there the spring force is

`F_("spring") = - kx`

B) Measurement...