Question

Supose that you need 2 Joules to expand a spring from its natural length of 30 cm to 42 cm: A)How much work its required to expand it from 35 to 40 cm? B)How long will expand from its natural length if a force of 30N is aplied to it?

Answer 1

Given,

`W_"ext" = 2"J"`

`Deltax_1 = 0.12"m"`

Recall,

`W_"ext" = 1/2kDeltax^2`

Let's derive the spring stiffness constant,

`=> k = (2W_"ext")/(Deltax^2) approx (278"N")/"m"`

And by extension find the work required to accomplish `("a")`:

Given,

`k = (278"N")/"m"`

`Deltax = 0.05"m"`

Hence

`W_"ext" = 1/2kDeltax^2 approx 0.69"J"`

of work are required for the first part.

For the second part, we must recall,

`F_"ext" = kDeltax`

Given,

`F_"ext" = 30"N"`

`k = (278"N")/"m"`

Hence, the spring will displace from equilibrium by,

`=> Deltax = F_"ext"/k approx 10.8"cm"`