A spring is originally 0.4m. When a 23N force is applied it stretches to a total of 0.7m. How far is the spring been extended? What is the spring constant of the spring?

Recall the force applied to a spring and its extension/compression:

F = kΔx

Δx is the change in the spring's length (measured from its original length).

x = 0.7 m

x₀ = 0.4 m

Δx = x-x₀ = 0.7 m - 0.4 m = 0.3 m

F = 23 N

Substitute and solve for k:

23 = k*0.3

k = 7.67 N/m