22 Force Extension Graphs 297t0x2

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Force Extension GraphsForce Extension Graphs

Force extension graphs show the extension of a sample of a substance as the load on the sample is varied.

Force / N

Extension / m

GCSE

During your work at GCSE, you will have plotted the independent variable, the force or load, on the abscissa (x-axis). However, it is common to see the extension plotted on the abscissa (x-axis) and the force or load plotted on the ordinate (y-axis).

GCSE

During your work at GCSE, you will have plotted the independent variable, the force or load, on the abscissa (x-axis). However, it is common to see the extension plotted on the abscissa (x-axis) and the force or load plotted on the ordinate (y-axis).

© TPS 2008

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Force / N

Extension / m

AS level

We shall continue with the extension plotted on the abscissa, as you should be able to interpret the graph whichever way it is plotted.

AS level

We shall continue with the extension plotted on the abscissa, as you should be able to interpret the graph whichever way it is plotted.

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Load

This is usually a weight that is hung on the end of the sample being investigated.

This is labelled “force” on the graph.

Load

This is usually a weight that is hung on the end of the sample being investigated.

This is labelled “force” on the graph.

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Extension / m

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Extension

This is the length of the sample with the load attached, less the length with no load attached.

Sometimes this is referred to as the length less the original length.

Extension

This is the length of the sample with the load attached, less the length with no load attached.

Sometimes this is referred to as the length less the original length.

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Care

It is common practice to load the sample up gently, taking measurements as you go and then unload the sample, again taking measurements as you go.

This can reveal much about the behaviour of the sample.

Care

It is common practice to load the sample up gently, taking measurements as you go and then unload the sample, again taking measurements as you go.

This can reveal much about the behaviour of the sample.

Force / N

Extension / m

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Care in adding weights to the sample

Never drop the weights onto the end of the sample.

The weights already on the sample should be supported, new weights added and then the support gently removed.

Failure to do this will overstress the sample.


Never drop the weights onto the end of the sample.

The weights already on the sample should be supported, new weights added and then the support gently removed.

Failure to do this will overstress the sample.Force / N

Extension / m

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Because different substances, and even different sized samples of the same substance, behave differently, different techniques are required to measure the extension of the different samples.

We shall look at some later.


Because different substances, and even different sized samples of the same substance, behave differently, different techniques are required to measure the extension of the different samples.

We shall look at some later.Force / N

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Care with your eyes, face and arms

A sample under stress can snap suddenly.

When it does so, it can cut you. You should wear eye protection, keep others away from the experiment and, if at all possible, use a safety screen of some kind around the experiment.

Care with your eyes, face and arms

A sample under stress can snap suddenly.

When it does so, it can cut you. You should wear eye protection, keep others away from the experiment and, if at all possible, use a safety screen of some kind around the experiment.

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Extension / m

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This apparatus is quite adequate to investigate the extension of a rubber band, as the loads required are quite modest and the extensions sufficient for the accuracy of a meter rule.

Remember to support the lower bulldog clip so there is no load when measuring the initial length and to include the weight of the lower bulldog clip in your values for the load.

Table

Heavy weight

Clamp stand

Load

Rubber band

Clamped metre

rule

Bulldog clip

Bulldog clip

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Force Extension GraphsForce Extension GraphsThe results for a rubber band are

interesting!

This is what happens as we load the rubber band.

With small loads, the rubber band seems reluctant to stretch much at first.

Small loads produce small extensions. As the load increases, the rate of extension increases too.

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interesting!

However, after a while, the rate of extension decreases again.

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interesting!

This is what happens as we unload the rubber band.

The pattern is similar but the extensions are always greater for a given load, than when loading the rubber band, except when it is completely unloaded.

It returns to its original length.

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Extension / m

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This happens because work is being done on the rubber band.

The area bound by the two curves represents that work being done.

If you repeatedly and quickly stretch and slacken a rubber band, it gets hot.

This is where the energy goes that has been used in doing work on the rubber band.

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This type of “loop” which is directional, shows a phenomenon called hysteresis.Force / N

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This apparatus can be used if you have nylon thread that is thin enough and weights that are heavy enough to produce a reasonable expansion.

A knot in the thread at the top and the bottom gives the bulldog clips something to grip on and stops it from slipping.

Table

Heavy weight

Clamp stand

Load

Nylon thread

Clamped metre

rule

Bulldog clip

Bulldog clip

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Table

Weights providing the load

Clamped metre rule

G clamp

Nylon

If the previous setup is not providing enough extension, the setup used above can be used.

The extension is measured by the orange marker which is taped onto the nylon.

Again knots are used to help to attach the nylon to the G clamp and the weights.

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Force Extension GraphsForce Extension GraphsThe results for nylon

are especially interesting!

This is what happens as we load the nylon.

The curve is not unlike the curve for a rubber band, except that the lines between the curves are straighter.

At the first bend, a neck forms – the thread is narrower at the neck.Extension / m

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Force Extension GraphsForce Extension GraphsThe results for nylon

are especially interesting!

This is what happens as we unload the nylon.

This is a straight line and indicates that there is a permanent extension in the nylon.

Extension / m

Force / N

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Table

Weights providing the load

Clamped metre rule

G clamp

Copper wire

The same apparatus is used as before.

Permanent deformations can be made in the copper wire.

It is also quite practical to test the wire to destruction.

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Force Extension GraphsForce Extension GraphsWe shall look at what happens to copper in

stages.

Initially, the line rises linearly.

This means that along this section, the extension is proportional to the load.

If unloaded at any part on this stretch of the curve, the unloading line will be the same as the loading line and the wire will return to its original length.

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stages.

Any further extension beyond this point and the extension will not be proportional to the load.

For this reason, this point is called the:

limit of proportionality.

At any stage along this line, the copper will return to its original length when unloaded.

Limit of proportionality

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stages.

After the limit of proportionality has been reached, any additional load added will produce more extension per unit load.

This means the line on the graph becomes a curve, with a smaller gradient (slope) than it did have.


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stages.

At some point, any additional load will result in a permanent extension of the copper.

This point is called the:

elastic limit.

(The elastic limit may actually coincide with the limit of proportionality.)


Elastic limit

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stages.

Additional loading continues to stretch the copper permanently.

If the copper was to be unloaded now, it would not return to its original length.

However, we shall consider what would happen if we had continued to load the copper.


Elastic limit

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stages.

Eventually, the

yield point

is reached.

At this point, the internal structure of the copper changes.

Planes of copper atoms are sliding over each other at this point and beyond.


Elastic limit

Yield point

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stages.

Further increases in load cause very large extensions as the copper begins to flow.

This is called the plastic region.

The plastic region is characterised by the copper flowing and large extensions.


Elastic limit

Yield point

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Plastic region

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stages.

Since the copper is flowing in the plastic region, the copper will be getting thinner.

No increase in load is required for the copper to flow in the plastic region.


Elastic limit

Yield point

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Plastic region

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stages.

Eventually, an increased load is required to produce more extension.

This is because the plastic will have caused dislocations of atoms in the structure of the copper. The dislocations add strength to the copper.

This process is called work hardening.


Elastic limit

Yield point

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Plastic region

Work hardening

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stages.

The deformation of the copper will finally result in the creation of a neck in the copper. This is a region where the cross-sectional area becomes smaller than in the rest of the copper.


Elastic limit

Yield point

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Plastic region

Work hardening

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stages.

A ductile fracture will occur at the neck.

The breaking stress (σ) is given by:

σ = Force / Area

Where the force is the breaking force and the area is the cross-sectional area where the sample breaks.

(σ is the Greek letter sigma – lower case.)


Elastic limit

Yield point

Extension / m

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Plastic region

Work hardening

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Useful phrases

A ductile fracture will occur at the neck.

The breaking stress (σ) is given by:

σ = Force / Area

Where the force is the breaking force and the area is the cross-sectional area where the sample breaks.

(σ is the Greek letter sigma – lower case.)

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22 Force Extension Graphs 297t0x2