# Mechanical properties of matter

- stress, strain, Young modulus
- force-extension graphs, energy stored

For many students, this topic will be the first time in physics they have been asked to explicitly link microscale structure (molecular bonds) with observed behaviour (stiffness and other characteristics). Their familiarity with the language used will vary depending on previous study, which will include design and technology, engineering and science. It's often worth spending a little time making sure that everyone is happy using the scientific terms precisely, as many of them have everyday uses which are not quite correct. You may like to remind them that they already know the terms mass, weight and gravity are used in a very particular way by physicists; the terms stiffness, stress and strength are the same. A possible structure might include:

- to recap Hooke's Law and other previous work done describing the behaviour of materials that stretch
- having students calculate stiffness of lab springs/materials using obtained data and apply experimental language to their work
- being precise when introducing and defining the terms stress and strain
*.*You can show how they are related by the Young modulus for a given material, and how this is independent of the shape of the sample - checking understanding of mathematical relationships, units and symbols is a good opportunity to discuss techniques for revision, as well as having a clear physics benefit
- students taking practical measurements to calculate Young modulus and compare this to accepted values
- discussing the relevance of material characteristics to their uses, being sure to include a range of applications from prosthetics, sports equipment design and consumer products as well as civil engineering
- students are often keen to use simulations and computer models in design and analysis; discussions of the benefits and limitations of this can be illuminating
- students being confident with the derivation and calculation of energy stored by a spring and knowing they must be able to find an approximate answer by using the area under a force-extension graph

Whilst this list provides a source of information and ideas for experimental work, it is important to note that recommendations can date very quickly. Do NOT follow suggestions which conflict with current advice from CLEAPSS or recent safety guides. eLibrary users are responsible for ensuring that any activity, including practical work, which they carry out is consistent with current regulations related to Health and Safety and that they carry an appropriate risk assessment. Further information is provided in our Health and Safety guidance.

## Links and Resources

### Episode 227: Hooke’s Law

Most students will have encountered Hooke's law before, as it is covered in most KS3 courses. Some will have revisited it during GCSE when it will have been linked to the idea of calculating elastic potential energy. The practical guidance here from the IoP focuses on reminding students of the measurements to be made and the calculations that can then be performed.

Some of the practical work described may be familiar to students as stretching carrier bags has featured in GCSE assessed practical work several times. The terms are carefully distinguished and the idea of springs in series and parallel is introduced as - excuse the pun - extension.

### Mechanics of Elastic Solids

This is one of a series of engineering lesson plans intended for teachers in the USA to use when planning to their Common Core Standards. Predictably the entire content is not a perfect match for our syllabus but individual resources can be very useful. This sequence - grades 10-12 translates well to lower sixth - places stress, strain and Young modulus measurements firmly in the context of engineering applications, from the World Trade Centre to hip replacements (a linked resource applies it to medical diagnosis as a cancerous tumour has a different elasticity to healthy tissue).

As well as the lesson presentations, the worksheets and homework included will be particularly useful for colleagues; answers are included, which students may find online with relative ease. The vocabulary section is also very clear.

With this as any web-based resource, it's worth checking that symbols used are those students will encounter in textbooks and exam materials.

### Stretching copper wire

This is one of a selection of practical suggestions from the Getting Practical project. Full instructions and useful tips are included, as well as alternatives appropriate for different ages. This particular example shows how a small change can still be measured accurately, giving rise to interesting discussions about the challenges faced by experimental physicists.

### Episode 228: The Young Modulus

Another IoP resource (the complete mechanics set is on the eLibrary) this moves on from Hooke's law to the relationship between stress and strain. Different practical approaches are compared and student materials include guidance on creating and interpreting stress/strain graphs. Sample data is supplied for various materials.

Of particular interest to most colleagues will be the suggestions for different ways to measure extension during the practicals. This would be an excellent stimulus for discussion about experimental methods in general and the application of scientific language to a particular practical.

### Modulus of Elasticity

This page is one from the School Physics website created by an experienced teacher and author, Keith Gibbs. It is intended for students to access independently and is a useful explanation of the three main ways in which 'modulus of elasticity' may be used in textbooks. In most cases the Young modulus is intended but for those with an interest in engineering the understanding of other approaches will be useful. Be clear with students about what concepts they will need for their exam.

### Masses and Springs

All students should take measurements of a stretched spring and use the data collected to calculate characteristics for the material such as stiffness. Not only is this of historical interest - the mathematical description in the 17th century was one of the first such relationships described - but it produces reliable results in the school lab (for most of the new specifications it is a required practical, as it offers students many opportunities to develop skills).

That said, a simulation is often a useful addition. The PhET version linked here allows students to change the stiffness of the spring as well as the strength of gravity. Results can be collected, plotted and compared to those from 'hands-on' practicals. In itself, this may prompt a useful discussion of the value of scientific modelling. You may choose to set tasks using this as preparation for the practical lesson, or as a follow-up to consolidate their knowledge. The reference to damping will be useful when you cover oscillations, and the discussion of energy will help link the topics together.

### Elastic Energy

Students have probably already encountered the calculations for the energy stored in a stretched spring (or a compressed solid, although this is less commonly explained). The explanation at Hyper Physics is clear and shows the graphs used. Similar definitions can be found at School Physics and in the stress/strain lesson from the IoP's Teaching advanced physics sequence. The latter includes clear definitions of key terms and some useful diagrams. It is worth giving several examples and ensuring students can explain where the expression derives from as well as being able to calculate the energy stored by finding (exactly or approximately) the area under force-extension graphs.

### The Study of Matter

Unlike the previous links, which are two materials which can be used directly with students, this publication is really for us as teachers. A collection of short discussion pieces about the role of materials science in teaching, it may provide useful contexts and anecdotes for what we teach our students. It is interesting to see how quickly some parts have become almost standard, for example the discussion on page 38 about 'virtual' materials testing.

Subject(s) | Science |
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Tags | n.a |

Age | 16-19 |

Last updated | 12 July 2016 |

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URL | https://www.stem.org.uk/lxpb7 |