Understanding Hooke's Law

This problem involves Hooke's Law, which states that the force needed to stretch or compress a spring is proportional to the amount of deformation (stretch or compression). Mathematically:

* F = kx

* F = force applied

* k = spring constant (a measure of the spring's stiffness)

* x = displacement (stretch or compression)

Solving the Problem

1. Find the spring constant (k):

* We know F = 5 N and x = 6 cm (0.06 m)

* Substitute these values into Hooke's Law: 5 N = k * 0.06 m

* Solve for k: k = 5 N / 0.06 m = 83.33 N/m

2. Calculate the displacement for 15 N:

* We have k = 83.33 N/m and F = 15 N

* Substitute into Hooke's Law: 15 N = (83.33 N/m) * x

* Solve for x: x = 15 N / 83.33 N/m = 0.18 m (or 18 cm)

Answer: A 15 N force will cause the spring to stretch 18 cm.