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Forces 4: 4.1 Introduction to subjecting materials to a physical stress force causing deformation - bending, stretching, compressing, effects of tension release, elastic and inelastic materials

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Sub-index of physics notes on FORCES section 4 Elastic potential energy

4.1a Introduction to subjecting materials to a physical force causing deformation

What is an elastic material?  How is energy stored in an elastic material? Does a compressed, bent or stretched elastic material always return to its original shape on releasing the tension?

When a material is subjected to two equal and opposite forces they may change the relative positions of the particles i.e. may change its shape.

This is what happens if you stretch a spring or rubber band, squash moulding clay or bend a strip of plastic or metal.

When springs or elastic material are stretched, elastic potential energy is stored in the system.

When the forces causing the stretching is removed, the spring or elastic returns to its original length (shape)

The more an elastic material is stretched, the greater the elastic potential energy store.


If the forces of compression/stretching are removed, different materials behave in different ways.

A spring or rubber band are likely to return to their original shape and length, displaying their elastic properties.

The potter's clay will stay in its new shape.

The plastic strip like a ruler may return to its original shape.

A strip of the soft metal like lead will be permanently deformed but a strip of strong steel, if not bent too far, is likely to return to its original shape - this happens with a clock spring in a clockwork clock.

Materials which have a tendency to return to their original shape are called elastic.

Those that do not are referred to as inelastic (non-elastic). The more elastic a material, the greater its ability to regain its original shape.

Engineers designing structures like bridges need to understand the different ways forces operate. When the applied forces stretch materials the material is under tension. If the applied forces squeeze or compress the material, it is described as being under compression. In a bridge, the supports on either side are under compression but the main body of the bridge carrying traffic is under tension - this could be the roadway and/or the cables in a suspension bridge.

4.1b Deformation of a material by bending, stretching or compressing

If you want to bend, stretch or compress an elastic object you must apply a force.

As explained above an elastic material is one that can be deformed in shape by applying a force and returns to its original shape if the forces are removed - springs and rubber bands clearly exhibit elasticity.

If an object doesn't return to its original length and shape it is inelastic.

The extension of a simple spring by stretching it with an applied force can be used to illustrate these points.

Initially the extension of a stretched spring is proportional to stretching force applied (e.g. adding increasing weight). This simple law is obeyed until you reach the limit of proportionality (L on the graph) - in other words the graph is linear up to point L.

After that, between point L and point D, the stretching is greater than expected - non-linear graph, but the spring will still return to its original length - the spring is still behaving elastically, but only for a relatively small further increase in the applied force.

However, if you overstretch an elastic material it may only partially contract return to its original shape on removing the applied force, so the spring is permanently deformed. The point at which this first happens is beyond what is called the elastic limit (point D on the graph).

Beyond the elastic limit D, the greater the stretching force applied the greater the permanent deformation (from point D onwards) - the less the object returns to its original shape - this is seen on the graph as it curves over in the extension direction!

When the object doesn't return to its original shape after removing the forces it is called plastic deformation.

With some materials, the elastic limit L, is so low that you see little elastic behaviour and permanent deformation sets in quickly with a relatively small applied force. In these cases, the force - extension graph is a curve (non-linear) with virtually no linear portion at the start.

Sub-index of physics notes: FORCES 4. Elastic potential energy

Keywords, phrases and learning objectives for elastic potential energy

Be able to describe and explain what we mean by elastic and inelastic materials.

Be able to describe the effect of subjecting materials to a physical stress forces that cause deformation e.g. bending, stretching or compressing and also the effects of releasing the tension in stressed materials.


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Sub-index of physics notes: FORCES 4. Elastic potential energy