Let's imagine that we are pulling down a spring. We can imagine that the spring will extend more if we pull it with a stronger force. But exactly what relationship do the force applied on the spring and the extension of the spring have? 😕

**Hooke's Law**

Hooke's law explains the **relationship between the force applied on a spring and the extension of the spring**. According to Hooke's law, the force applied on a spring and the extension of the spring are **directly proportional**.

If the force applied on the spring is doubled, the extension of the spring will also double.

**F = k x e**

F = force applied on spring (N)

k = spring constant (N/m)

e = extension of spring (m)

Each spring has its own spring constant, and the spring constant is a measure of how stiff the spring is.

**If you want to investigate whether the spring obeys Hooke's law using the above apparatus, what should you do?**

- You also need a ruler to measure the length of extension of the spring.

- First, measure the original length of the spring without any weight added to the spring.

- Then, add a known weight to the spring.

- Next, measure how much the spring has extended due to the weight.

- Repeat the experiment for a range of values of the weight added to the spring.

- You can also repeat the same experiment a few times for each weight and calculate the average value of spring extension.

- When you have obtained experimental data for the weight added and corresponding extension length of spring, you can plot the force-extension graph.

**If the spring obeys Hooke's law....**

- The graph should be a linear graph passing through the origin.

- The force applied on the spring (weight) is proportional to the extension of the spring.

- The slope of the graph is the spring constant of the spring used.

**Using Hooke's law numerically**

If the spring extended 4 cm when 8 N weight was added to the spring, how much will the spring extend if 10 N of weight is added to the spring?

**Solution** 👉

Step I. Calculate the spring constant.

8N = k x 4cm = k x 0.04m

k = 8N / 0.04m = 200 N/m

Step II. Find the extension of spring when 10 N of weight is added.

10N = 200N/m x e

e = 10N / (200N/m) = 0.05 m = 5 cm