**What is the Hooke’s Law?**

**Hooke’s law** states that the extension of a spring is directly proportional to the applied force provided the elastic limit is not exceeded.

- Figure shows a graph of extension, x of a spring against applied force, F.

(a) The portion of graph from zero to P is where Hooke’s law applies.

(b) Beyond point P, Hooke’s law does not apply anymore.

(c) Point P is known as the**elastic limit**of the spring. Any force beyond point P will cause the spring to be permanently deformed.

- Figure shows a graph of extension, x of a spring against applied force, F.

- Sometimes, it is more convenient to plot the graph of F against x to formulate the formula for a spring that obeys Hookes law.

(a) Figure shows a graph of F against x for a spring. From the graph, F is directly proportional to x.

**F ∝ x**

Where, F = force on the spring,

x = extension of the spring. Therefore,

**F = kx**

where k is the gradient of the F-x graph.

(b) The value of k is known as the force constant of the spring. It is also known as the spring constant. Therefore,

The SI unit for k is N m^{-1}.

(The unit N cm^{-1}is more commonly used)

**Example 1. **The graph in Figure shows the extension, x of a spring due to an applied force, F.

What is the force constant of the spring?

**Solution:**

The force constant of the spring is the gradient, k of the F-x graph. Therefore,

k = 5/4

= 1.25 cm N cm^{-1}

**Example 2.** A spring with a force constant of 3.5 N cm^{-1} is extended 2.4 cm. Calculate the force applied for this extension.

**Solution:**

k = 3.5 N cm^{-1}; x = 2.4 cm

F = kx

= 3.5 x 2.4

= 8.4 N