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

Class practical

To introduce ideas of energy transfer by heating and thermal capacity.

Apparatus and Materials

For each student group

• Datalogger with temperature sensor
• 1 litre beaker
• 250 ml beaker
• Insulating jacket
• Immersion heater
• 1 kg metal block (e.g. aluminium) with bores drilled for heater and temperature sensor
• Electric kettle or Bunsen burner to heat water rapidly
• Mug(s), ceramic OPTIONAL
• Cup(s), paper, polystyrene and plastic, with lids if possible OPTIONAL
• Different insulating materials (e.g. expanded polystyrene, newspaper, wool) OPTIONAL
• Instant coffee and tea bags OPTIONAL

Health & Safety and Technical Notes

An electric kettle is a much safer source of hot water than a Bunsen burner, tripod and gauze. However, immersion heaters also get hot and must be handled with care.

Read our standard health & safety guidance

Procedure

There are a number of things you can do with just temperature sensors.

1. Cooling curves. Fill a beaker with hot water from a kettle. Record its temperature once a second for a few minutes. If possible, produce a graph directly.
2. Compare cooling curves for beakers with different insulation, lids etc. Start each with water at the same temperature and record information from several sensors on the same graph.
3. Heating curves. Place sensors and heaters in beakers with 1 litre water and 250 ml water, and a 1 kg metal block. Start the heaters at the same time and with the same voltage and record the temperature-time graphs, all on the same display.

Teaching Notes

• These activities are excellent to emphasize the value of datalogging as the display is much easier to read than normal thermometers. Readings can be taken more often and with less chance of recording errors. Suitable software can produce an immediate graphical display to confirm that the data are being collected correctly.
Specific teaching points:
• This experiment can be used to calculate cooling rates in °C per second. The flattening curve shows that the rate of decrease of temperature is lower as the temperature falls.
• Without being quantitative, cooling curves which are produced live provide at-a-glance evidence for the effectiveness of different insulations.
• Comparing different masses of the same material (water is easiest) shows how the same amount of energy transferred causes different changes in temperature that depends on the mass. This is an introduction to thermal capacity and to the difference between energy transferred and temperature.
• Comparing the different materials (but same mass) is a further step on this road. The temperature of the aluminium will rise much more quickly than the 1 kg of water (1 litre). This is also partly because it will dissipate energy more slowly: it will take longer for energy to be transferred to the surface of the aluminium by conduction, and then be transferred to the surroundings by radiation, compared with time for convection currents to be set up in water. Hence the ratio of the rate of temperature rises is not the same as the ratio of the specific thermal capacities.
• If you want to use these methods to measure specific thermal capacities, then you need to ensure that you minimize energy dissipated to the surroundings with good thermal insulation.
• How Science Works extension: You could either set students a structured investigation and then follow with questions based on this or offer an open-ended investigation.
• Students could:
• identify and select the variables that they wish to measure and control
• produce their own experimental procedure, including the selection of appropriate time intervals.
• The amount of guidance given will very much depend on your students’ level of confidence and skills with designing their own experiments.
• Some groups could be set a very open-ended brief, ‘investigate cooling’. With others you might set the investigation in a real world context, suggesting some of the possible variables e.g. you could tell them that they are to investigate which is better to keep a cup of hot coffee warm for longest - a ceramic mug, a paper or a polystyrene cup? Most takeaway coffee cups have a lid, so this could be extended to investigating how effective the lid is at reducing energy dissipation. More advanced students could investigate whether tea and coffee behave in exactly the same way as water.
• Collecting data for cooling curves for cups of different materials is relatively straightforward, so students need only minimal guidance in the specifics of what they are to do.

Heating and cooling worksheet (Word, 58 KB)

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

A simple investigation of the factors affecting the resistance of a wire.

Apparatus and Materials

For each student group

• Cells, 1.5 V, with holders, 2
• Crocodile clips, 2
• Ammeter (0 - 1 amp), DC
• Leads, 4 mm, 5
• Wire available for class use (see technical notes)
• Power supply, 0 to 12 V, DC (OPTIONAL)
• Metre rule (OPTIONAL)
• Insulating tape (OPTIONAL)
• Digital and analogue ammeters, 0-1 A (OPTIONAL)
• Digital and analogue voltmeters, 0-12 V (OPTIONAL)
• Micrometer (OPTIONAL)

Health & Safety and Technical Notes

Modern dry cell construction uses a steel can connected to the positive (raised) contact. The negative connection is the centre of the base with an annular ring of insulator between it and the can. Some cell holders have clips which can bridge the insulator causing a short circuit. This discharges the cell rapidly and can make it explode. The risk is reduced by using low power, zinc chloride cells not high power, alkaline manganese ones.

When using a power supply, high currents will cause the safety cut-out on the power packs to automatically switch it off. If short lengths of wire are used with relatively high currents and voltages, then significant electrical heating may also occur. Students should be encouraged to adjust the voltage to keep currents small with every set of readings. At each stage they can connect the circuit, take readings quickly and then disconnect the power supply.

If you use a mains power supply, use one that is designed to limit the output current to about 1 amp, and preferably with a current overload indicator.

Read our standard health & safety guidance

The following apparatus should be available for class use:

• Selection of reels of Eureka wire (also known as Constantan or Contra) of different gauges, e.g. 0.71 mm (22 SWG), 0.46 mm (26 SWG), 0.32 mm (30 SWG) and 0.24 mm (34 SWG).
• Selection of reels of different wires (e.g. copper, Eureka, iron) of same gauge (e.g. 34 SWG).

Procedure

1. Connect up a series circuit of two cells, and the ammeter, with a 30 cm length of one of the wires closing a gap between two crocodile clips. Note the reading on the ammeter.
2. Replace the specimen of wire with another of the same length but different gauge or material.
3. Investigate how the current depends on the thickness of the wire, its length and the material from which it is made.

Teaching Notes

• Use fine gauge wires. If too thick a wire is used, the results may be affected by warming of the wires.
• If coils of copper and Eureka wires of the same gauge can be prepared so that they have equal resistances, the effect is very striking. However, this would then lose its value as an open investigation.
• Students should come to understand that the resistance of a wire depends on its length, its cross sectional area, and the material out of which it is made. With some students you could go further and introduce the concept of resistivity ρ, through the relationship R = ρ l / A where R = resistance, ρ = resistivity, l = length and A = cross-sectional area.
• This may also be an opportunity for a large scale demonstration of the effect by the teacher. But note: if the current is too large, the voltage of the cells will fall due to their internal resistance. For this reason, it is important to keep the current very low - copper wire is effectively a short.
• How Science Works extension: This experiment can be used as a more open-ended investigation. Students can select the variables, the ranges of results and the equipment used. The amount of guidance will depend greatly upon the teaching group. Investigating the effect of length on resistance is common but some students may wish to investigate the effect of the thickness of wire. In either case, different wires should be made of the same material. Students may need to know the conversion between SWG (standard wire gauge) and wire diameter/radius.
• Students will find it easier to measure at a prescribed length if they tape the wire to a metre rule with insulating tape and make connections with flying leads rather than crocodile clips.

This experiment was safety-checked in August 2007

Class practical

Students make a timer using a simple pendulum.

Apparatus and Materials

For each student group

• Pendulum (e.g. Plasticine bob on string/thread)
• Stopclock
• Chemical balance (0-100 g)
• Stand, clamp and boss
• Protractor

Health & Safety and Technical Notes

If large masses are used then the stands may need to be clamped to the bench.

Read our standard health & safety guidance

Procedure

1. Show a demonstration pendulum and ask students to think about the variables that may affect the time period for one oscillation.
2. Ask students to select one independent variable, collecting a set of data to investigate its effect on the oscillation time.
3. After students have completed an initial investigation and drawn conclusions, ask them to evaluate their method in terms of its accuracy and improve on it.

Teaching Notes

• You may need to explain what one oscillation for a pendulum is (motion there and back again). Variables to investigate include the mass of the pendulum bob, length of the pendulum (best measured to centre of bob), and initial amplitude (angle or displacement).
• A discussion following students' first attempts might lead to the following ideas for improving their measured value.
• Reduce the uncertainty in a measurement of periodic time by:
• measuring many oscillations to calculate the average time for one oscillation
• increasing the total time measured for multiple swings
• There is some uncertainty when measuring both the start time and also the stopping time, resulting from the experimenter's reflex time (as much as 0.2 s each, i.e. totalling 0.4 s ). The percentage uncertainty which this 0.4 s represents decreases as the total time measured increases. Students could carry out simple error calculations to discover, for example, the effect of a human reaction time of 0.2 s econds on timings of 2 s 20 s and 200 s.
• You may wish to get them to estimate the human reaction time or measure it as a separate activity. There are many web-based activities freely available.
• Improve the accuracy of a measurement of periodic time by:
• making timings by sighting the bob past a fixed reference point (called a fiducial point)
• sighting the bob as it moves fastest past a reference point. The pendulum swings fastest at its lowest point and slowest at the top of each swing.
• The periodic time for a swinging pendulum is constant only when amplitudes are small. Its period of oscillation is then T =2π √ _(l /g)_where
• T = Time period for one oscillation (s)
• l = Length of pendulum (m)
• g = acceleration due to gravity (m s^-2)
• Students investigating the effect of bob mass or pendulum length should keep the maximum angle of swing under 5 °.
• How Science Works Extension: This provides an excellent opportunity for planning, carrying out and evaluating an investigation using multiple skills. The number of variables is limited but there is enough scope to allow students to develop an approach and select appropriate ranges and intervals.
• Students often assume that any sensibly selected independent variable will always have an effect upon the dependent variable. Many may decide to investigate the effect of the mass of the bob, which yields an unexpected (counter-intuitive) result: the mass has no effect on periodic time. Proving that there is no link between two variables can be just as significant as finding one.
• The introductory discussion can put the pendulum into a scientific and historical context by describing the development of timing devices. Start with the hours of a day as one of the simplest units of time, easily measured with a sundial. Use this to introduce Galileo Galilei (1564-1642) and the (possibly apocryphal) story that his understanding of the behaviour of pendulums was spurred by observing the bronze chandelier or incense burner in the cathedral at Pisa. Galileo's pendulum introduced a method of measuring short periods of time that improved on the use of the human pulse. You could extend this timeline by describing further developments in timing devices, right up to the atomic clock (usually containing caesium) which is accurate to within 10-9 seconds per day.
• For students who take a particular interest in the measurement of time, suggest the book Longitude by Dava Sobel (ISBN 0007214227), which provides further background about the development of clocks and their use in navigation. It also has some examples of the struggles that can happen in the development of science and technology.

This experiment was safety-checked in January 2007

Class practical

Measuring many sheets to find the thickness of one.

Apparatus and Materials

For each student group

• Pack of paper containing a known number of sheets (e.g. 500)
• Sheet of the same paper
• Ruler with millimetre scale (e.g. a metre rule)
• Chemical balance
• Micrometer (OPTIONAL)
• Selection of rulers/tape measures with different scale divisions (OPTIONAL)

Health & Safety and Technical Notes

Read our standard health & safety guidance

Procedure

1. Attempt to measure the thickness of a single sheet of paper. Fold the paper in half, in half again, and so on, to obtain multiple thicknesses. Measure the thickness and calculate the thickness of a single sheet.
2. Measure the thickness of a pile of a known number of sheets (say, 100 or 200). Calculate the thickness of a single sheet.
3. Compare these two methods for measuring the thickness of a single sheet. Which is better?

Teaching Notes

• A book could be used instead of a pile of sheets of paper. Students should make a rough measurement of a pile of paper or the thickness of the book (remember the book is numbered on both sides of the paper).
• As well as the length, width and thickness of the paper, some students may attempt to measure its density. Often paper is sold with a g/m ² value on the packet (which is not a density) and so this may provide a value against which they could check their measured value.
• Alternatively, a textbook can be used, but beware of the factor 1/2 since a book has half as many leaves as pages.
• To encourage order of magnitude estimates, you could go on to give pupils a rough value for the diameter of an atom so that they can calculate how many atoms would sit next to each other in the thickness of a piece of paper. For paper made of cellulose (which contains carbon, hydrogen and oxygen) then the average atomic diameter is probably only about 1.5 x 10 ^-9 cm. Students who do not delight in using large numbers should not be dragged through these calculations.
• There are excellent books, videos and web sites on Powers of ten:

  Powers of ten

  Classroom displays of large and small distance measurements with pictures of the objects measured will create a good background to this work.
• You could follow this up with the activity Practice in using large and small numbers, which can be downloaded from:

  here

• How Science Works extensions: Although the measurement methods here are relatively straightforward, this provides an opportunity for students to design and carry out their own experiment. Emphasise that they should measure as accurately as possible and clearly explain how their method improves the quality of data collected. Get them to try and estimate the uncertainties in their results and to identify which measurement they feel has the greatest uncertainty.
• You could encourage students to write a full plan/method before they begin. If they are to do this, make relevant teaching points about the importance of clear and unambiguous instructions. Each group/student could write a procedure, which is then passed on to a different group/student to carry out, exactly as written. The second group/student can then evaluate the information that they have been given.

This experiment was safety-checked in October 2007

Class practical

Calculating the energy transferred per second from a lamp.

Apparatus and Materials

For each group of students...

• Power supply, LV
• Lamp 12V 6W
• Lamp holder on base
• Ammeter (0 - 1 amp), DC
• DC voltmeter (0 -15 volt)
• Variable resistor, optional

Health & Safety and Technical Notes

Read our standard health & safety guidance

The rating of the lamp is chosen so as to provide reasonable current and voltage readings. Any lamp that produces similar values to a (12 V 6 W) lamp is suitable. Remember that, on switch-on, a lamp draws several times the rated current: the power supply must be able to supply this.

Procedure

1. Connect the circuit shown and take readings of the ammeter and voltmeter. Calculate the energy transferred electrically each second.

Teaching Notes

• To give more practice in making calculations of power, a variable resistor can be included in the circuit. Students take a series of readings and compare them with the brightness of the lamp.
• The table could be labelled as shown:
• Current in amps (charge flowing in coulombs per second)
• Potential difference in volts (energy transferred in joules by each coulomb)
• Power (= energy transferred electrically from the power supply per second, in joules/second or watts (Power = VI)
• Working out the units is a useful check on what is happening in the circuit in terms of the physics.
• How Science Works extension: Students could be asked to design an experiment whereby they calculate the efficiency of the energy transferred electrically to light. Discussion will likely identify the difficulty in quantifying the amount of light produced. What should also emerge is that the amount of light radiated can be inferred by calculating the energy stored thermally. A possible approach is to put the lamp in a sealed polystyrene cup filled with air (or even water) and measure the temperature rise.
• The specific thermal capacity of air at constant pressure is about 1,000 J/kg 'C, and that of water is 4,200 J/kg 'C

This experiment was safety-checked in January 2007

Class practical

Using an aluminium block and immersion heater to estimate the specific thermal capacity (also called the specific heat capacity) of aluminium.

Apparatus and Materials

For each group of students

• Aluminium calorimeter with holes for heater and thermometer (see discussion below)
• Thermometer -10°C to 110°C
• Stopwatch or stopclock
• Immersion heater, 12 V 100 W (older, 60 W types will do)
• Low voltage power supply or transformer (to supply 8A)
• Lever-arm or domestic balance (+/- 2g)
• Insulation/cladding for the metal block OPTIONAL

Health & Safety and Technical Notes

The immersion heaters should have been allowed to cool in air after heating water, to eliminate the (small) risk that water has been drawn inside through a cracked seal.

Read our standard health & safety guidance

If bespoke insulation is not available, then scraps of material and or newspaper can be held on with string/elastic bands to provide a thick insulating jacket for the block.

If you drop some paraffin-oil into the thermometer hole it will ensure good thermal contact between the block and the thermometer. It is not necessary to use oil with the immersion heater. In fact, as there is a danger of cracking any oil which is left on the heater when it is removed from the block, it is wiser not to use it.

Procedure

1. Find the mass of the aluminium block on the balance. Place a small drop of oil in the thermometer hole. (This will provide good thermal contact between the block and the thermometer bulb.) Insert the thermometer and immersion heater in the appropriate holes. Read the thermometer. Connect the heater to the 12 volt supply and switch it on for 5 minutes. Note the maximum temperature rise obtained after the supply has been switched off.
2. Many suppliers can provide similar 1 kg blocks made of steel, copper, brass etc. If these are all set up at the same time they will show that different materials of the same mass will achieve different temperature rises when the same amount of energy is transferred to them.

Teaching Notes

• Change in energy stored thermally (due to the temperature rise) = mass x specific thermal capacity x temperature rise
• The temperature of I kilogram of aluminium rises about four times that of a kilogram of water. If the heater does not behave differently in aluminium compared to water there must be another factor which is peculiar to the aluminium. This is the specific thermal capacity (also called specific heat capacity) of the aluminium.
• The specific thermal capacity of aluminium is 900 J/kg °C
• The specific thermal capacity of water is 4200 J/kg °C
• It takes more energy to raise the same temperature of water by each °C than it does to raise the temperature of the same mass of aluminium.
• How Science Works extension: After collecting data, students calculate the specific thermal capacity of the aluminium (or other material) used. To assess the accuracy of their measured data, they can compare their value of specific thermal capacity with its accepted (true) value from data tables. You can also ask them to calculate the percentage difference between the two values, to show how the accuracy of measurements can be expressed quantitatively. Differences between the two values can also be used to prompt a discussion about errors and uncertainties in their measurements, identifying the main sources.
• Energy dissipated so that it is stored thermally in the surroundings is something that students can investigate further, to obtain a more accurate value of the specific thermal capacity. The Guidance note:

  Cooling corrections

  suggests a procedure for controlling such transfers. A less sophisticated, but equally valid, approach is to repeat the experiment (the block needs time to cool}, using insulation around the block. Their second set of data will enable them to assess whether this gives a more accurate result for specific thermal capacity.
• Before you make this comparison remember that power supplies may only give unidirectional potential differences and not fully smoothed values. The power measured is on DC meters as VI is only 0.8 of what it should be. See the guidance note...

  Explaining rms voltage and current

This experiment was safety-tested in December 2006

Class practical

Introducing the idea of measuring multiple objects and finding an average.

Apparatus and Materials

For each student group

• Large supply of coins (all of one denomination)
• Ruler with graduations in mm (e.g. metre rule)
• Micrometer (OPTIONAL)

Health & Safety and Technical Notes

Read our standard health & safety guidance

There is a significant risk that the coins will go missing! You could use steel washers as an alternative if you are concerned about this.

Procedure

1. Estimate the thickness of a single coin.
2. Measure one with a ruler.
3. Measure a pile of coins stacked on each other. Calculate the average thickness.

Teaching Notes

• Each student should try to measure the thickness of a single coin with a ruler with millimetres marked on it. The teacher should ask for results and also ask how reliable students think they are. Then ask for suggestions of improvement. Some may suggest measuring the height of a pile of coins and then calculate the thickness of one.
• Discuss the general idea of accuracy behind the method by saying:
• "Suppose you have just one good coin and this ruler marked in millimetres, how thick would you find the coin if you could measure it very carefully? Yes, we do now know that the thickness is, say, 1.3 mm but could you really see that if you had just one coin to measure? Even if you thought you could see it, would that be a safe and fair answer to give? With just one coin what would be the fairest thing to say? If you wanted to be quite safe, what would you say? Yes I agree; all we can say is somewhere between 1 and 2 millimetres. Now suppose you have 10 coins in a pile and you measure the pile. Even if you make a mistake of 1 millimetre in that measurement, how much of a mistake is that in the thickness of one coin? So if you measure 10 coins you could say that you think each coin is 1.3 millimetres thick. What would you say if you measured 100 coins in a pile?"
• At an introductory level, you might leave this problem there and come back to it later. Big numbers and small decimals are not easy, and the problem of accuracy is not a particularly interesting one yet.
• If a student points out that worn coins are thinner than new coins, then it might be worthwhile sorting them into two stacks, using the faces on the heads and the date on the coins. Compare the heights of the stacks. Of course, this kind of experiment is of far greater value if pupils suggest it themselves, or even if the teacher can coax it out of them in a way that makes them feel it is their own suggestion. Then they are doing science. Measuring many atoms in order to find the size of one atom is a skill which scientists have.
• How Science Works extensions: Point out that it is worthwhile changing and improving an experimental method as you carry out an experiment and that deciding on a method does not preclude subsequent changes.
• Collecting the data from the class for the three different measurements of the thickness can be used to prompt discussion about data spread, variation and accuracy.
• You could ask students to use the micrometer on a single coin and compare the value measured this way with the value obtained from the stack of coins. If students have not used a micrometer before, allow time for teaching them how it works and have them take sample readings before expecting them to use it confidently.

This experiment was safety-checked in July 2007

Class practical

This is an introduction to the language of measurement, including concepts of range, reproducibility, mean value, true value, accuracy, instrument resolution and, most important, measurement uncertainty.

Apparatus and Materials

For each student or student group

• Stopwatch or stopclock
• String
• Statistics board (see technical notes)
• Masses, 50 g, 5 or 6
• Cones/track markers, 10 OPTIONAL
• Video camera OPTIONAL
• Tape measure, long (at least 10 m) OPTIONAL

Health & Safety and Technical Notes

If working outside, students must be appropriately supervised.

If a trolley is used in the lab, ensure that the trolley cannot land on anyone's feet or legs.

Read our standard health & safety guidance

A statistics board is made from a piece of wooden board about 0.5 m square. Ten slotted channels are glued to it and metal (or other suitable material) discs are cut so that they fit into the channels. The board is supported vertically.

Assign values to each channel. Students drop in a disc for the value they achieve. The distribution of results grows as results are added.

Procedure

1. One student runs a distance of 100 metres. You, and other students, all independently time the run.
2. Compare all of the measurements. What is their range (the difference between the highest and the lowest measured values)? What does this tell you about the reproducibility of the measured values of time?
3. What is the mean of all the measurements? A mean is a kind of average. Work this out by adding them all together and then dividing by the number of measurements. How closely do you think the mean value agrees with the true value of the run time? In other words, estimate the accuracy of the mean value.
4. Did everybody use stopwatches with the same resolution ? For example, were everyone’s stopwatch time indications in tenths of seconds or hundredths of seconds? (0.1 s econd is a tenth of a second; 0.01 s econds is a hundredth of a second).
5. Try to estimate the reaction times involved in pressing a stopwatch to both ‘start’ and ‘end’ the run. The sum of these reaction times is very likely larger than the resolution of the stopwatch.
6. How certain can you be about the actual time taken for the run? You can’t be perfectly certain! There must be some uncertainty in the measurements. The mean measurement could be 14.8 s econds. Perhaps you think that the ‘true’ time for the run is in between 14.6 s econds and 15.0 s econds. Then you can say that the uncertainty is ± 0.2 s econds.

Teaching Notes

• The most important term here is measurement uncertainty, a concept that can be introduced early in science education. Additional terminology about measurements should enhance its meaning and not distract from it. For example, you may decide to omit steps 4 and 5 from the Procedure (above).
• In more advanced work, measurement uncertainty is sometimes called measurement ‘error’. Here, the word uncertainty more clearly describes a reasonable doubt about the result obtained.
• Precision is a quality denoting the closeness of agreement between measured values obtained by repeated measurements. If values cluster closely, measurements are called ‘precise’. Reproducibility is the precision obtained when measurements are made by different operators using different instruments.
• Statistical treatment plays very important parts in modern science. In advanced experiments students are expected to treat errors with some statistical care. In kinetic theory the steady pressure of a gas is recognized as an average of innumerable individual bombardments. Statistical methods are used to delve into details of molecular speed or sizes. In modern atomic physics statistical views are of prime importance. So you might well make a gentle start to later science studies by showing how scientists look at a number of measurements of the same thing.
• The times could be collated as lists of numbers or, using a computer, as bar charts, or using a statistics board. Bar charts enable students to understand range, mean and uncertainty visually.
• It is worth pointing out that there is such a thing as too many digits in a quoted value. A student who uses a stopwatch and gives a time of 14.77 s econds is crediting the timing process with less uncertainty than it actually has. Answers of 15 seconds or 14.8 s econds may be acceptable (depending on the timing procedure and the stopwatch).
• ‘Mean’ is here used to indicate a particular kind of average – that found by dividing the sum of values by the sample size.
• You could repeat the activity for a different motion, such as for a trolley pulled across a metre distance on a table, or the fall of a mass. Again, all students should measure the time for the same motion. Range, mean value, and measurement uncertainty can be compared with those for the student’s 100 metre run.
• You may want to compare timings for real sports races. Information on sporting records can be found on the Internet. For example see Usain Bolt's record breaking 100 m run in the 2008 Olympics. Instrument resolution for different sports could be compared, and students could discuss the idea of uncertainty in the measured values...

  watch Usain Bolt break record

• How Science Works extension: This experiment covers concepts of accuracy and precision of data, as well as measurement uncertainty. The scope could be increased further, as follows:
• Arrange pairs of students every 5 m or 10 m apart along the 100 m running path. Use some kind of signal (e.g. dropping a raised arm) to start both the runner and everyone’s timers. As the runner passes each student, they stop their timer and record the time taken to reach them.
• Students then plot this data graphically (distance against time). This will make it easier for students to understand average speed and get a feel for the variation in measurements. A true value of velocity can be calculated from the gradient of the best fit line.
• If you placed cones/markers along the track, you might be able to video each student running, with a stopclock also in the camera view. This would generate a second set of results that could be compared numerically or graphically to the class set. Students could comment on whether this method improves on the previous one.

This experiment was safety-checked in January 2007

Class practical

Students make a timer using a simple pendulum.

Apparatus and Materials

For each student group

• Pendulum (e.g. Plasticine bob on string/thread)
• Stopclock
• Chemical balance (0-100 g)
• Stand, clamp and boss
• Protractor

Health & Safety and Technical Notes

If large masses are used then the stands may need to be clamped to the bench.

Read our standard health & safety guidance

Procedure

1. Show a demonstration pendulum and ask students to think about the variables that may affect the time period for one oscillation.
2. Ask students to select one independent variable, collecting a set of data to investigate its effect on the oscillation time.
3. After students have completed an initial investigation and drawn conclusions, ask them to evaluate their method in terms of its accuracy and improve on it.

Teaching Notes

• You may need to explain what one oscillation for a pendulum is (motion there and back again). Variables to investigate include the mass of the pendulum bob, length of the pendulum (best measured to centre of bob), and initial amplitude (angle or displacement).
• A discussion following students' first attempts might lead to the following ideas for improving their measured value.
• Reduce the uncertainty in a measurement of periodic time by:
• measuring many oscillations to calculate the average time for one oscillation
• increasing the total time measured for multiple swings
• There is some uncertainty when measuring both the start time and also the stopping time, resulting from the experimenter's reflex time (as much as 0.2 s each, i.e. totalling 0.4 s ). The percentage uncertainty which this 0.4 s represents decreases as the total time measured increases. Students could carry out simple error calculations to discover, for example, the effect of a human reaction time of 0.2 s econds on timings of 2 s 20 s and 200 s.
• You may wish to get them to estimate the human reaction time or measure it as a separate activity. There are many web-based activities freely available.
• Improve the accuracy of a measurement of periodic time by:
• making timings by sighting the bob past a fixed reference point (called a fiducial point)
• sighting the bob as it moves fastest past a reference point. The pendulum swings fastest at its lowest point and slowest at the top of each swing.
• The periodic time for a swinging pendulum is constant only when amplitudes are small. Its period of oscillation is then T =2π √ _(l /g)_where
• T = Time period for one oscillation (s)
• l = Length of pendulum (m)
• g = acceleration due to gravity (m s^-2)
• Students investigating the effect of bob mass or pendulum length should keep the maximum angle of swing under 5 °.
• How Science Works Extension: This provides an excellent opportunity for planning, carrying out and evaluating an investigation using multiple skills. The number of variables is limited but there is enough scope to allow students to develop an approach and select appropriate ranges and intervals.
• Students often assume that any sensibly selected independent variable will always have an effect upon the dependent variable. Many may decide to investigate the effect of the mass of the bob, which yields an unexpected (counter-intuitive) result: the mass has no effect on periodic time. Proving that there is no link between two variables can be just as significant as finding one.
• The introductory discussion can put the pendulum into a scientific and historical context by describing the development of timing devices. Start with the hours of a day as one of the simplest units of time, easily measured with a sundial. Use this to introduce Galileo Galilei (1564-1642) and the (possibly apocryphal) story that his understanding of the behaviour of pendulums was spurred by observing the bronze chandelier or incense burner in the cathedral at Pisa. Galileo's pendulum introduced a method of measuring short periods of time that improved on the use of the human pulse. You could extend this timeline by describing further developments in timing devices, right up to the atomic clock (usually containing caesium) which is accurate to within 10-9 seconds per day.
• For students who take a particular interest in the measurement of time, suggest the book Longitude by Dava Sobel (ISBN 0007214227), which provides further background about the development of clocks and their use in navigation. It also has some examples of the struggles that can happen in the development of science and technology.

This experiment was safety-checked in January 2007