Understanding Hooke's Law

Hooke's Law states that the force required to stretch or compress a spring is proportional to the displacement from its equilibrium position. Mathematically, this is represented as:

* F = kx

where:

* F is the force applied

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

* x is the displacement from the equilibrium position

1. Find the Spring Constant (k)

* We know that a force of 90 N stretches the spring 1 meter. Let's plug these values into Hooke's Law to find k:

* 90 N = k * 1 m

* k = 90 N/m

2. Calculate the Work Done

The work done to stretch a spring is given by:

* W = (1/2) * k * x²

where:

* W is the work done

* k is the spring constant

* x is the total displacement (5 meters in this case)

3. Substitute and Solve

* W = (1/2) * (90 N/m) * (5 m)²

* W = 45 N/m * 25 m²

* W = 1125 Joules

Therefore, it takes 1125 Joules of work to stretch the spring 5 meters beyond its natural length.