Class practical

Students make their own springs and use them for investigations involving simple graph construction.

Apparatus and Materials

• For each student group
• Bare copper wire, 26 SWG (0.45 mm), 80-90 cm for each student in group
• Clamp stand and boss
• G-clamp or other method of fixing stand to bench
• Flat-headed nail, large
• Mass hanger with slotted masses (10 g)
• Sticky-backed tape, e.g. ticker-tape
• Eye protection for each student

Health & Safety and Technical Notes

Students should clamp their stand to the bench to prevent it from toppling.

Students must wear eye protection. Eyes may be at the same level as clamp and the nail.

Read our standard health & safety guidance

Use new copper wire. Old wire is often uneven in its hardness as working of copper wire hardens it. Also, twisted wire will produce uneven springs. You can use the wire afterwards for chemical and electrical work.

Procedure

1. Make a spiral spring by winding the copper wire round and round a pencil. Do this by turning the pencil (to avoid twists), for 25-30 turns. Make a twisted loop at each end.

2. Fix the nail horizontally, with its point in the boss on the stand. Hang the spring from the nail.
3. Cut a piece of tape, the same length as the hanging spring. Write number 0 on the tape. That is the number of masses that you have hanging from the spring.
4. Attach the mass hanger to the lower loop of the spring. Cut a new piece of tape, the same length as the stretched spring. Write number 1 on the tape, because there is one 10-gram mass hanging from the spring (the mass of the hanger).
5. Add a mass to the hanger. Cut another piece of tape, the same length as the stretched spring. There are now two 10-gram masses, so write number 2 on the tape.
6. Add more masses, one at a time. Each time, cut a new piece of tape and write the number on it.
7. Draw a horizontal line close to the bottom of a sheet of paper. Paste your pieces of tape side by side. Start with the shortest piece, which has number 0. The bottom ends of each piece of tape should touch the horizontal line. You have made a ‘graph’ of the length of the spring and the number of masses.
8. Write a conclusion for this investigation. You should explain how the number of masses affects the stretch of the spring. Your paper-tape graph should help you to do this.

Teaching Notes

• This activity is intended for students who are developing familiarity and confidence with creation and interpretation of simple graphs. A ruler could also be used to measure the length of the spring if students are able to translate measurements into a graph.
• It is important that each student should make a spring and does not have to passively observe others doing so. The measurements can be done with just one spring for each student. Alternatively, springs could be made from different materials and different wire gauges. In fact anything that stretches will give a set of graphs to discuss.
• Allow students to ‘ruin’ their springs by over-stretching them.
• Encourage students to find answers to questions such as:
• "Does the spring stretch regularly?"
• "What happens if too large a load is attached?"
• "Does a spring always ‘spring’ back to its original shape?"
• "Can you put a stretched spring back into its original shape?"
• For able students, you could point out that the number of masses is the input variable, or independent variable, of this investigation, and that the length of the spring is the output variable or dependent variable. Also, tell students that the usual convention is to plot the input (independent) variable on the x axis of a graph and the output (dependent) variable on the y axis. You could explain that they, as investigators, have complete control of the input (independent) variable but can only observe and measure the output (dependent) variable.
• By cutting off the initial spring’s length from each tape, the graph becomes one of extension against number of masses. Ask students to draw a horizontal line across the graphs at the original length, and then cut along this line.
How Science Works Extension: The results of this extension can be summarized as Hooke’s law. This experiment thus gives an opportunity to discuss what is meant by a ‘law’ in physics, and the etiquette of scientific publishing.
• Robert Hooke (1635-1703) was a few years older than Newton. He studied springs for a specific practical reason: he wanted to devise an improved spring-driven watch. Hence it was important to understand the behaviour of springs. He studied both linear and spiral springs.
• It was important to Hooke to be able to claim priority in the discovery of his law, but at the same time he did not want his competitors to benefit from his findings. He therefore published a summary of his findings in the form of an anagram:
“ceiiinosssttuv”
• Later, he revealed that it was an anagram of a sentence in Latin. Decoded, it said:
“Ut tensio, sic vis.”
• In English, this is:
“As the extension increases, so does the force.”
• In other words, the extension is proportional to the force producing it. Today, it would be regarded as unacceptable for a scientist to keep results secret in this way. Results should be published in a form that allows others to repeat them, and to take the work further if they so desire.

This experiment was safety-checked in September 2004.

Class practical

The behaviour of springs provides a topic through which students can learn about simple relationships between pairs of variables, in a practical context. Seventeenth-century scientists, like Robert Hooke and Robert Boyle, helped to lay the foundations for physics and for other sciences by working in this way.

Apparatus and Materials

• Extendable steel springs, 2 or 3
• Stand, clamp and additional boss
• Flat-headed nail, large
• Metre rule
• Mass hanger and slotted masses (100g)
• Eye protection for each student
• G-clamp
• Rubber bands OPTIONAL
• Set square OPTIONAL

Health & Safety and Technical Notes

Students should clamp their stand to the bench to prevent it from toppling.

Students must wear eye protection. Eyes may be at the same level as clamp and the nail. Also, steel springs store more energy elastically than copper springs and can fly off their supports.

Read our standard health & safety guidance

Provide spare springs. Students will stretch springs beyond their elastic limit and replacements will be necessary. This is not willful destruction but, rather, good science.

If the springs are supplied close-coiled it is better to have the coils separated before issuing them to the students. Hanging about 500-600 g gently on the tightly coiled springs will do this.

Procedure

1. Fix the nail horizontally, with its point in the boss on the stand. Hang a spring from it and secure it so that it does not fly off.
2. Hold the metre rule vertically in the clamp, alongside the spring.
3. Record the metre rule reading level with the bottom of the spring. The number of masses hanging from the spring is 0 and the extension of the spring is 0 cm.
4. Hang a mass hanger from the bottom of the spring. Record the new metre rule reading, the number of masses (1) and the extension of the spring.
5. Add a mass. Record the new metre rule reading, the number of masses (2), and the total extension of the spring from its unstretched length.
6. Repeat this until after the spring has become permanently stretched.
7. Describe the pattern in the results. To do this fully, you will need to plot a graph. Plot the number of masses on the horizontal axis, since it is the input (or independent) variable. The extension of the spring is the output (or dependent) variable and you should plot it on the vertical axis.

Teaching Notes

• This is a more formal variation of this experiment:

  Home-made springs

  There is benefit in doing both, since it will invite discussion and thought on the nature and use of graphs.
• You could discuss whether doubling the load on a spring sometimes or always doubles the extension. This relates to the shape of the graph, whether it is sometimes or always a simple straight line passing through the origin. It thus leads to the concept of proportionality. Proportionality, or linearity, describes a simple form of relationship between variables. This relationship is common in nature.
• Much of physics is devoted to seeking such simplicity. Hooke's law states that, up to a limit, extension is proportional to load. (When the load is doubled then the stretch is doubled.) Robert Hooke noticed this very simple pattern in 1676. Since he was worried that others, maybe even Newton, would steal the credit for this he wrote in code at first, and created an anagram: ceiiinosssttuv. This is taken to mean ut tensio sic vis, which is Latin for: as the stretch, so the force. The fact, though, that Hooke's law is only obeyed by materials up to a limit highlights the fact that nature does not always offer simplicity.
• Invite students to think about applications of springs, in systems from door catches to vehicle suspensions. Point out that engineers must understand the behaviour of springs.
• Extension activity can include investigation of other springs, elastic bands and any other elastic materials (e.g. polythene strips). Comparison of graphs provides opportunity for discussion.
• How Science Works extension: Include among the equipment available for this experiment a second boss and clamp as well as a set square for each student group. Either prompt a discussion initially or leave the students to work out how these extra items might be useful.
• Students can improve the accuracy of their measurements by clamping the metre ruler in place and then using the set square to make the length/extension measurement. They can also use the set square to make sure that the clamped ruler is vertical in relation to the bench. Students might set the clamped ruler at 0 cm when no masses are added and so read the extension directly. This procedure helps them avoid simple mistakes that arise when measuring lengths and then calculating extensions. These refinements provide good illustrations of improving an experimental method.

Further ideas:
• Give students access to extra springs so that they can try series and parallel arrangements. You could also ask them to predict what they expect to happen qualitatively and perhaps even quantitatively.
• Investigating whether the same results are obtained when a materials is loaded and unloaded, particularly if rubber bands are used. Stretched rubber exhibits elastic hysteresis.

This experiment was safety-checked in January 2007

Demonstration

The behaviour of a metal when it is subject to a stretching force reveals clues about the forces between its particles.

Apparatus and Materials

• For each student group
• Bare copper wire, 32 SWG (0.28 mm), at least 1.5 m for each student
• Valve rubber tubing, 2 pieces, each about 2 cm long
• Pencils or wood dowels, 2
• G-clamps, 2, 10 cm and 5 cm
• Hand lens
• Eye protection for each student

Health & Safety and Technical Notes

Students must wear eye protection. Though copper wire does not fly as wildly as steel wire when it breaks, the loose ends nevertheless present an eye hazard.

Warn students not to lean over as they pull on wires, to avoid the possibility of falling when the wire breaks.

Read our standard health & safety guidance

A fresh piece of wire with no bending or kinking in it is needed for each extension.

Procedure

1. Take your length of copper wire and thread each end through the rubber tubing. Hold the rubber tubing about 10 centimetres from the ends. With each short length of wire sticking from the rubber tubing, make two loops around a wooden rod. Wind the remaining ends of the wire around the outside of the rubber tubing.
2. Clamp one of the rods firmly to the bench, and pull the other. Feel how the wire has only a small amount of springiness and then begins to ‘give’.
3. Gradually increase the force until the wire breaks. Take care not to fall! Look at the end of the wire where it breaks. Can you see anything extra with the hand lens?

Teaching Notes

• Copper wire reaches its limit of proportionality, and ceases to obey Hooke’s law, when relatively low forces are applied.
• Each student should feel the elastic stretching of the wire and then the cheesy yielding.
• Allow pupils to look at the broken ends with a magnifying glass. They will see evidence of the narrowing that took place. They could consider why, since all parts of the wire were subject to the same forces, breaking took place at one point and not at others. (The answer lies in the existence of weak points in the metal’s crystal structure.)
• With more advanced students, this is an opportunity to talk about particle ideas. Particles of any material cannot be pushed closer and closer together into a tiny high density dot, because at close distances they repel each other. But we know that these particles must attract each other at intermediate distances, or they would not stay together in the first place. At larger distances, the attraction fades, so that there is no measurable force between two shavings of copper, for example.
• Atoms in a copper wire are normally an ‘equilibrium’ distance apart. Attempts to compress a piece of copper are also attempts to push its atoms closer together, and they have little effect because of the strong repulsion. The act of stretching a copper wire, on the other hand, increases the separation of atoms above the equilibrium distance, so that you can feel the atom-to-atom attraction as the material resists the pull.
• Yielding of the material takes place when layers of atoms in the metal crystals begin to slide over each other. The atoms cannot be pushed back again, and the material becomes permanently stretched.

This experiment was safety-tested in September 2004

Demonstration

With a little ingenuity, even a small change in length of a wire becomes measurable.

Apparatus and Materials

• Bare copper wire, 26 SWG (0.45), new
• Single pulleys on clamps, 2
• Mass hangers with slotted masses (100 g), 2
• Mass hanger with slotted masses (10 g)
• G-clamp
• Polythene for clamping wire, heavy, 2 small sheets
• Needle (e.g. darning needle or knitting needle
• Drinking straw
• Adhesive
• Thread
• Hoffman clip (optional)
• Eye protection

Health & Safety and Technical Notes

Take care when masses fall to the floor. Use a box or tray lined with bubble wrap (or similar) under heavy objects being lifted. This will prevent toes or fingers from being in the danger zone.

A copper wire does not break as violently as a steel wire. However, it is wise for those close to the demonstration (including the demonstrator) to wear eye protection.

Read our standard health & safety guidance

The apparatus should be assembled before the lesson, to save lesson time. In particular, the thread should be glued to the wire, long enough in advance to ensure that the glue has set.

A fresh piece of wire is needed for each extension with no bending or kinking in it.

Procedure

1. Use a G-clamp, with two small polythene pads, to fix the end of about 2 metres of copper wire rigidly to the end of a bench.

2. At the other end of the bench, clamp the two pulleys as close together as possible. Pass the end of the copper wire over one of the pulleys to the larger mass hanger. This should be about 0.5 m above the floor.

3. About 60 cm from this pulley, stick the end of a length of thread to the wire. (Alternatively, use a Hoffman clip with two small polythene jaws to hold the thread and wire together). Pass the thread over the second pulley and hang the smaller hanger from it, so that the base of this hanger is about 30 cm above the floor. Put four 10 g, weights on this mass hanger to make a total of about 50 g. This load, which is not changed, serves to keep the thread taut.
4. Pass a needle through the two holes in the pulley supports, as illustrated. Loop a single turn of the thread round the needle, and push the needle point through a drinking straw to form a pointer. You may want to add a scale, made of card, to allow measurements.
5. When all is taut, note the position of the tip of the drinking straw.
6. Add 100 g masses to the load on the wire. As the wire stretches, the thread will move, rotating the needle and turning the pointer. An additional 500 g added to the wire will shift the position of the tip of the pointer about 3 cm per metre-length of the wire.
7. Reduce the load in 100 g steps to show that the pointer returns to its original position, revealing the elastic nature of the stretching.
8. Reload the wire in 100 g steps to a total of about 1,500 g (using a second mass hanger as well as the first). The wire will yield visibly.
9. Continue loading until the wire breaks. At an extension of about 30 cm, the weight on the thread will reach the ground and disengage. The assembly is protected from damage, since the wire yields gently through a considerable distance. Excitement builds up as students anticipate the snapping of the wire.

Teaching Notes

• You could either use a scale to make measurements, or use the activity simply to illustrate a method of measuring the extension of a wire.
• A simpler method would be to attach a flag to the copper wire some 50 cm away from the pulley, instead of the thread and pointer. A small piece of cotton wool or card makes a suitable flag.
• A discussion of the elastic (Hooke's law) stretching and plastic yielding of the wire could follow the demonstration. Most of the visible stretching of copper wire takes place beyond the elastic limit. (Copper wire stretches in the Hooke's law region only about 1 mm per metre of wire.)
• Students should observe, with a magnifying lens, the broken sharp point of the wire. The wire necks before snapping at its narrowest point. Students might also comment on the silky look of the stretched wire rather than the shiny look of the unstretched wire.
• How Science Works Extension: This experiment shows how a simple but ingenious technique can allow a small quantity to be measured. The extension of the copper wire (in the Hooke’s law region, at least) is small, perhaps a millimetre or two. However, the needle and drinking straw technique magnifies the extension greatly. Discuss why this method is better than the simple ‘flag on the wire’ technique.
• Fix a (circular) scale next to the straw. You might be satisfied with an arbitrary numerical scale; however, you could ask the class how they would set about calibrating the scale. Here are two methods:
• Determine the circumference of the needle, perhaps by measuring its diameter. This distance corresponds to one complete turn of the straw against its scale.
• Alternatively, pull thread so that the straw completes, say, 20 revolutions. Measure the length of thread and divide by 20 to find the extension corresponding to one complete turn.
• Students may be surprised to see the copper wire undergoing plastic deformation. It extends gradually even though the load is unchanging. This would be a good topic for an open-ended investigation.

This experiment was safety-checked in September 2004

Class practical

Though we might claim to know, intuitively, the difference between a large force and small force, we resort to the extension of springs for actual measurement.

Apparatus and Materials

• For each student group
• Forcemeter
• Mass hanger with slotted masses (10 g)
• Unknown masses of between 0.5 and 1.0 kg
• Sticky tape, 'write on' variety
• Forcemeters, selection of different ones

Health & Safety and Technical Notes

Read our standard health & safety guidance

The forcemeter scales need to be blank. You can achieve this by covering the scale of calibrated spring balances with ‘write on’ sticky strips.

Procedure

1. Hold the forcemeter vertically. There is no force pulling its spring (apart from the weight of the hook}, so the reading must be zero. Make a mark on the blank strip that will be the 0 of your forcemeter scale.
2. Pull on the spring with a force of 1 newton. On Earth, the weight of a 100-gramme mass is approximately 1 newton. So if you hang a 100-gramme mass from the forcemeter the Earth will pull it down with a force of about 1 newton. That is the force that stretches the spring. Make a mark on the blank strip that will be the 1 of the scale.
3. Hang another mass from the forcemeter. The force pulling the spring of the forcemeter is now approximately 2 newtons. Make a 2 newton mark on your forcemeter scale.
4. Repeat this up to 10 newtons. You have now ‘calibrated’ your forcemeter so that it has a scale for taking measurements.
5. Take the masses off the forcemeter and hang the unknown mass from it. Record the force of gravity (weight) that acts on this mass. You can now use your forcemeter to measure any force, up to 10 newtons.

Teaching Notes

• This important activity deals with fundamentals of the measurement of force. We have to use indirect means to measure many quantities. We can measure temperature, for example, by looking at the length of a thread of liquid in a glass tube. Here, students see that we measure force using the extension of a spring. To do so we must first calibrate the spring, as students have done.
• To gain familiarity with this new instrument, students should choose an already calibrated meter to measure a range of forces such as open doors and lifting loads. Remember that the weight of an apple (choose the right one) is about 1 N.
• Students could even make their own forcemeter from winding a spring using copper wire (26 SWG). It will not have a linear scale but it must not be extended so far so that it no longer returns to its original length. Give a warning about damaging forcemeters.
• How Science Works Extension: This experiment provides an opportunity to consider various aspects of scientific instrumentation.
• Calibration: Any instrument with a scale must have been calibrated, either by the manufacturer or by the user. Commercial instrument makers are expected to be able to trace their calibration back to a national (and hence international) standard. This would be an opportunity to discuss the work of national bodies such as the National Physical Laboratory (UK) or the Bureau international des poids et mesures (France/international). By considering the process of calibration which they have just carried out, students can assess the uncertainty in any measurement they make with their forcemeter.
• Range and sensitivity: What are the largest and smallest values of force that can be measured using the forcemeter which the students have calibrated? How could they change the range of their forcemeter? If the meter has a greater range, what effect does this have on its sensitivity? (A stiffer spring will give a greater range, but the scale divisions will also be greater, so the meter will be less sensitive.)
• See also the apparatus entry Forces and energy demonstration box.

This experiment was safety-checked in September 2004.

Class practical

To look at a material that does not obey Hooke’s law.

Apparatus and Materials

• Retort stand, boss and clamp
• Mass hanger plus masses (100 g)
• Metre rule
• Selection of rubber bands, elastic cord
• Marker pen

Health & Safety and Technical Notes

Students must wear eye protection.

Read our standard health & safety guidance

Fishing elastic (used by anglers to give a bit of stretch to their lines) comes in a range of thicknesses. Students could investigate the stiffness and breaking strength as a function of thickness.

Procedure

1. Take a rubber band and mark it across its width at two points, one close to each end.
2. Hang the rubber band from the clamp.
3. Hang the mass holder on the lower end of the band.
4. Measure the distance between the two marks on the band.
5. Gradually increase the load on the band, recording the distance between the marks each time.
6. Gradually reduce the load, recording the distance between the marks each time.

Teaching Notes

• Rubber bands provide an interesting contrast to springs. On stretching, they do not obey Hooke’s law very precisely. On unloading, they show hysteresis.
• The experiment must be done with care. Hang a rubber band or length of elastic vertically and attach weights to the lower end. The load must be increased in even steps; as the load is increased, care must be taken to ensure that the rubber is not allowed to slacken. Then the load must be gradually reduced, again ensuring that the rubber does not slacken too much and that it is not stretched more as the load is removed. Unless these precautions are taken, the non-Hookean behaviour may not show up.
• How Science Works Extension: Students can investigate the effects of a range of factors, including width and thickness of the rubber band. Using a hairdryer, they could raise the temperature of the band and observe the effect.
• The worksheet could be used as the basis of an investigation. It includes some questions intended to test students’ understanding of the design of the experiment.
• Table 1 shows some typical data. If students plot a graph of extension against load, the points will appear to fall close to a straight line. However, ask them to pick up the paper and squint along the line; they should be able to see a clear S-shaped curve. The rubber stretches slowly at first, then roughly linearly, then more and more slowly as it becomes stiffer. Emphasise the need to carry out the experiment with care and to plot the data accurately if the detail is not to be lost.

Table 1 Stretching a rubber band (original dimensions: 95 mm x 6.0 mm x 0.85 mm)

Load /N	Length /mm	Extension /mm
0	95	0
1.0	112	17
2.0	137	42
3.0	168	73
4.0	207	112
5.0	242	147
6.0	275	182
7.0	306	211
8.0	328	233

Demonstration

By stretching confectionery laces, students learn that extension is not always proportional to load. They also gain experience in adopting consistent procedures to make and record measurements.

Apparatus and Materials

For each student group

• Strawberry, apple or cola laces (preferably not sugar-coated)
• Retort stand
• Clamp
• Felt-tip pen (dark colour)
• Metre rule
• Clotted massess, 100 g set
• Slottee masses, 10 g set

Health & Safety and Technical Notes

Make sure that students do not eat the laces since eating anything in a laboratory is hazardous.

Read our standard health & safety guidance

If the laces are sugar-coated, take care to avoid getting sugar into other equipment (open the packet over a sink). Wash off the sugar under a cold tap and allow the laces to dry before use.

Procedure

1. Tie one end of a lace around the clamp and the other to a mass-holder. Make two marks on the lace a measured distance apart (approx 0.5 m).
2. Add masses singly or a few at a time. Observe how the lace behaves over a short period after the load is increased.
3. Observe how the lace behaves if the load is removed. For each load, record the distance between the two marks.
4. Continue until the lace breaks.
5. Plot a graph to show how extension varies with load.

Teaching Notes

• This activity can be used for a variety of purposes, depending on the ability, age and experience of the students.
• For some students, it will be a useful exercise in making measurements and displaying them graphically.
• For others, it will provide an example of a material whose load-extension graph is not a straight line (it does not obey Hooke's law) and which exhibits creep (gradual deformation under a steady load). They can be asked to discuss when they should record the extension for a given load (immediately? or after the sample has stopped stretching?). There is no right answer, but students should be consistent and state clearly what strategy they have adopted.
• You might want to discuss the role of tests such as these in the food industry. Measurements can be directly related to how a confectionery product feels when eaten, and samples are tested before a batch of products leave the factory to ensure they are of suitable quality.
• How Science Works extension: If students have obtained a graph from one lace, they may assume that this will describe the behaviour of all laces. A nice extension is to ask them to investigate the variation in stretchiness (or spring constant) within a packet of fruit laces. Terms such as variation and range could be introduced and used, if appropriate.
• Students could carry out a similar process as seen in the experiment Investigating simple steel springs and possibly go on to compare the variation in springs behaviour with the variation in confectionery laces.
• This experiment comes from Salters Horners Adanved Physics©, University of York Science Education Group.

This experiment was safety-checked in January 2007

Class practical

Students observe brittle fracture during compression of a Crunchie bar, and take measurements to calculate its breaking stress. They appreciate that estimates can be useful.

Apparatus and Materials

For each student group

• Crunchie bar
• Saw-toothed knife or modelling saw, sharp (avoid a pointed type)
• Bathroom scales (1,200 N or 120 kg )
• Testing rig (see technical notes)

Health & Safety and Technical Notes

Make sure that students do not eat the Crunchie bars, since eating anything in the laboratory is hazardous.

Take care when using the sharp saw.

Read our standard health & safety guidance

• Wooden beams, approx 35 cm x 5 cm x 2 cm, 2
• Lengths of studding, 15 cm long x 1 cm diameter, 2
• Lock nuts to fit studding, 2
• Wing nuts to fit studding, 2

Construct the rig as shown in the diagram.

Procedure

1. Saw a slice from the Crunchie, about 1.5 cm long. Try to keep the cut as ‘square on’ as possible. (Do not cut the slice in advance, as it goes gooey.)
2. Place the slice in the testing rig with the cut faces at top and bottom. Carefully and gradually tighten both wing-nuts.
3. Record the maximum load reached before the sample breaks.
4. Crunchie has a ‘honeycomb’ structure similar to bone and fractures in a similar way under stress. Observe the way in which the Crunchie sample fractures.
5. Measure the cross-sectional area of the Crunchie bar. Calculate the stress required to break the sample.
6. Compare this breaking stress with the stress on human leg bone in normal use. How do the properties of Crunchie compare with those of bone?

Teaching Notes

• This activity was originally developed as part of a teaching sequence based around ‘spare part surgery’ (replacement hip joints). The Crunchie is used as a physical model for bone.
• The maximum load will vary considerably between samples. The reasons for this can be discussed with students and include:
• it is difficult to tighten both wing nuts evenly
• the sample breaks more easily if the cut face is not exactly square-on
• a Crunchie bar contains many irregularities and is not manufactured as a uniform material
• Breaking stress = load that breaks the sample/cross-sectional area.
• The stress calculation can be challenging for many students, particularly if you ask them for an answer in N m ^-2 , rather than N cm ^-2 .
• Guide them to express the linear dimensions of the Crunchie in metres before calculating the area – this approach is much less prone to error than attempting to convert between cm ² and m ² .
• To compare the stress in human bones with that required to break a Crunchie, students will need to estimate the cross-sectional area of their own leg bones. If your school or college biology department has a skeleton, it would be useful to borrow it so that students can measure the relevant bone thickness. As the area is neither circular nor rectangular, and varies along the length of a bone, students will need to make a sensible estimate rather than an exact calculation.

This experiment comes from University of York Science Education Group:

Salters Horners Advanced Physics©

Diagrams are reproduced by permission of the copyright holders, Heinemann.