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# Hooke’s Law

### Hooke’s Law

In this lesson you will learn what Hooke's Law is, to describe the property of elasticity.

Some objects may stretch, compress or bend when you apply a force to them, then return to their original shape when the force is removed. Try to guess what we call these types of objects.

A spring is a good example of an **elastic object**. If you stretch a spring and it returns to its original shape and length, we say that it was elastically deformed.

If you continue to add force to a spring, eventually the spring will no longer return to its original shape and length. What might we call the type of deformation that the spring undergoes now?

Hooke's Law states that **the extension of an elastic object is directly proportional to the force applied to it**. By the way, it's called "Hooke's Law" because it was the scientist Robert Hooke who first stated this law of elasticity.

If the extension of a spring is $6\space cm$with a force of $10\space N$applied, what is the extension if $5\space N$ of force is applied?

Hooke's Law tells us that **the extension of an elastic object is directly proportional to the force applied to it**, but which factor other than force will influence the extension of a spring?

How easily a spring can be stretched or compressed is measured in Newtons per metre $(N/m)$ . We call this property the **spring constant**.

Answer **TRUE** or **FALSE**: The higher the spring constant, the more loose the spring.

When using the **spring constant** in calculations, the units used are *Newtons per metre*. This means you must always convert your extension measurements into metres. If you measured an extension of $5\space cm$ , what is this in metres?

The force applied to a spring is$2\space N$, the extension of the spring is$0.1\space m$, and the spring constant is$20\space N/m$. **What is the formula** that links force, extension and spring constant?

The formula for Hooke's law is written as$F=kx$. Try to guess which symbol represents the spring constant.

If a spring has a spring constant of $40\space N/m$ , and its extension is $15\space cm$ , how much force has been applied to cause the extension?

If the force applied to a spring is$4\space N$, and its extension is$4\space cm$, what is the spring constant? Remember to convert the extension to metres before using the formula.