Ablock of mass m=5.20\; \mathrm{kg}m=5.20kg is being suspended at rest by an extended spring of spring constant k=36.0\; \mathrm{n/m}k=36.0n/m and an external force f=20.0\; \mathrm{n}f=20.0n downward. the spring is attached to the ceiling and has an extended length of s=2.45\; \mathrm{m}s=2.45m. what is the relaxed length s_0s 0 of the spring?

x₀ = 1,894 m

Explanation:

For this exercise let's use Hooke's law

     F = - k Δx = - k ( –x₀)

Let's write this equation for the given conditions, the extended length of the spring is the final length (xf = 2.45 m), the sense of force always opposes displacement

With the force applied

         F = -k ( - x₀)

        ( - x₀) = - F / k

        x₀ =   + F / k

        x₀ = 2.45 + (-20.0) / 36.0

        x₀ = 2.45 - 0.556

        x₀ = 1,894 m

This is the so-called natural spring length