Stretching springs

Springs are designed to stretch longer distance when force is applied on them. We can measure the stretched length , called “Extension” or “Displacement” of spring from mean position.

EXPLANATION:

Consider a spring hung from a rigid support such that its top end is fixed. The spring can stretch due to the weight or load attached to the lower end of spring. As the load is increased the stretched length of spring will also increase., as shown in figure:

KEY OBSERVATIONS:

• When the load is increased in regular steps the length of the spring also increases simultaneously.

• When the load is removed, the spring returns to its original length. This is called elastic change.

• If the load is increased greatly beyond the elastic limit of spring, the spring will change its shape permanently.

FORMULA:

The extension in the length of spring can be shown by following expression:

$\text{Length of stretched spring = Original length + Extension}$

OR

$L' =L + \text {x}$

$\boxed{\text{x} = L' -L}$

Here,

$\text x$ = Extension in spring or Springs displacement from its un-stretched mean position.

$L$ = Original un-stretched length of spring.

$L'$= Final Stretched length of spring after adding load or application of force on it.

GRAPHICAL REPRESENTATION:

The graph show the relation of extension in spring with the load. It has two parts:

1. Initially the graph slopes up steadily. This shows that the extension increases in equal steps as the load increases.

2. Then the graph bends. This happens when the load is greater enough to damage the spring permanently. As a result the spring will not return to its original length.