## 2- Stretching

### HOOKE’S LAW

One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That linear dependence of displacement upon stretching force is called Hooke’s law.

When a force pulls a spring, the spring stretches. The extension of the spring is directly proportional to the pulling force. This is Hooke’s Law. It states that

`The extension of a spring is directly proportional to the force pulling it, provided that the limit of proportionality is not exceeded.`

In equation form,  where  is spring constant and  is the extension of spring after pulling.

### EXPERIMENT TO MEASURE HOOKE’S LAW

1. Set up the apparatus as shown in the figure.
2. Place the hangar on the end of the spring and take the reading off the rule.
5. After all the loads are added, reverse the process by taking off one load at a time. Measure the extension concurrently.
6. Tabulate the readings into the table below

The result will show that the extension of the load is directly proportional to the load added. Plotting a graph of extension against mass, a straight line graph that pass through the origin is obtained.

### LIMIT OF PROPORTIONALITY

Hooke’s law is not a universal law. By this I mean that it is only applicable under certain condition and the condition is the limit of proportionality is not exceeded. Limit of proportionality is the point which if exceeded, the spring extension will no longer be proportional to the load. Usually, when we pull a spring, it will restore back to the original length once the pulling force is removed. If pulled hard enough, the spring will not spring back to the original length. The maximum extension to which it can restore to original length is called the elastic limit. This elastic limit usually coincide with the limit of proportionality.

### HOW MATERIALS ARE AFFECTED BY STRETCHING

Some strings such as guitar strings break easily after the limit of proportionality is exceeded. However, rubber can stretch a lot for a small force. The polymers in the rubber is straightened during stretching. This allows rubber to stretch a long extension before breaking. Metal such as copper wire can also stretch easily, but the wire gets thinner as it stretches more. This happens until the wire finally breaks.

# Elasticity

Elasticity is the property of an object or material which causes it to be restored to its original shape after distortion. It is said to be more elastic if it restores itself more precisely to its original configuration. A rubber band is easy to stretch, and snaps back to near its original length when released, but it is not as elastic as a piece of piano wire. The piano wire is harder to stretch, but would be said to be more elastic than the rubber band because of the precision of its return to its original length. A real piano string can be struck hundreds of times without stretching enough to go noticeably out of tune. A spring is an example of an elastic object – when stretched, it exerts a restoring force which tends to bring it back to its original length. This restoring force is generally proportional to the amount of stretch, as described by Hooke’s Law. For wires or columns, the elasticity is generally described in terms of the amount of deformation (strain) resulting from a given stress (Young’s modulus). Bulk elastic properties of materials describe the response of the materials to changes in pressure.

# Elastic limit

In reality, materials obey Hooke’s law only up to a certain limit, as Figure 10.34 shows. As long as stress remains proportional to strain, a plot of stress versus strain is a straight line. The point on the graph where the material begins to deviate from straight-line behavior is called the “proportionality limit.” Beyond the proportionality limit stress and strain are no longer directly proportional. However, if the stress does not exceed the “elastic limit” of the material, the object will return to its original size and shape once the stress is removed. The “elastic limit” is the point beyond which the object no longer returns to its original size and shape when the stress is removed; the object remains permanently deformed.

 Figure 10.34  Hooke’s law (stress is directly proportional to strain) is valid only up to the proportionality limit of a material. Beyond this limit, Hooke’s law no longer applies. Beyond the elastic limit, the material remains deformed even when the stress is removed.

Materials are classified into

Elastic and Plastic