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Can you change the volume and pitch of sound in a variety of ways? This box has the equipment you will need to create, measure and change sounds scientifically in your classroom.

Year 4 could use this box to find patterns in the sounds that are made by tuning forks, and different lengths of boomwhacker tubes, to investigate pitch. They may use different materials in the sound boxes to investigate which provides the best insulation against sound. The sound level monitor could be used to investigate volume, and the slinkies to create a scientific model of how sound travels through different materials to your ear.

**Year 4 Science: Sound**

- identify how sounds are made, associating some of them with something vibrating
- recognise that vibrations from sounds travel through a medium to the ear
- find patterns between the pitch of a sound and features of the object that produced it
- find patterns between the volume of a sound and the strength of the vibrations that produced it
- recognise that sounds get fainter as the distance from the sound source increases.

- Sound Level Meter
- Tuning Forks
- Boomwhackers
- Sound Muffling and Insulation box
- Wire Helix Slinky
- Model ear

Download full contents list **here.**

An optical engineer researches and develops new technologies related to the science of light, which is called *optics*. So they’ll study how light behaves, how you can manipulate it using lenses and mirrors, and how the colour of light affects its properties. They’ll then apply that knowledge to sight and vision problems, or in electronic systems and equipment.

Optical engineers might design lasers, build telescopes, create fibre-optic communications systems; or they might work with microscopes, computer chips, or consumer electronics. Or they might work in healthcare, understanding the human eye.

**Attributes: **observant, hard-working, committed

The light we see is made up of the different colours of the spectrum. We see light split up into it’s different colours when we see a rainbow.

Each colour absorbs some light, but we only see the colour light reflected back to us. So while it is still, each area of felt tip pen on our spinner reflects a different coloured light back to us. When the spinner is moving, it is turning too quickly for your eyes to tell which area of felt tip pen each colour is coming from. Our eye treats this like all those different colours of light are coming from the same place. So it sees it as white.

You could try making a spinner at home by watching the video. What happens when you try different colours?

**How does a kaleidoscope work?**

The tube of a kaleidoscope contains mirrors. If there are three mirrors, this generates a pattern based on repeating triangles, if there were 4 mirrors the pattern would be based on rectangles and so on. One end of a kaleidoscope has the object chamber, which contains the shiny objects to be reflected. The object chamber must not only keep the objects contained, but allow light through to illuminate the chamber. The other end of the kaleidoscope has the viewing hole.

When you look through the hole, light filters through the object chamber and passes through or bounces off the shiny objects. The light then reflects off the mirrors, bouncing down the tube of the kaleidoscope until it emerges through the viewing hole, into your eye. Every reflection the light goes through adds a layer to the image you see. As you turn the kaleidoscope, the objects move in the chamber and the reflections change, which creates new patterns.

We came across this lovely activity to make rainbow light patterns using a CD. You’ll need strong, direct sunlight for a strong effect, so seize your moment in the five minutes of summer we get in the North-East.

Rainbow by William Welch (CC-BY from Flickr)

A zoetrope is a cylinder with a series of pictures on the inner surface, which you view through slits. When the cylinder spins, you get the impression that the images are continuous and moving. It’s very similar to an old-fashioned film projector, but with the movie on a loop.

Zoetropes work because the human brain is astonishingly good at recognising movement. So much so that it sees ‘movement’ even when there isn’t any. So if your eye sees a sequence of still images, your brain merrily glues those together as a movie. You see this every time you watch TV, go to the movies, or work with a computer screen or phone.

To make your own zoetrope, follow this guide from the CBBC Art Ninja.

To find out more about how it works, watch the video below… which will also tell you how to say ‘zoetrope’. Always tricky, that one.

Aerospace engineers design, build and maintain aircraft, spacecraft, satellites, and missiles. They may be involved in creating and testing prototypes, researching ways to make fuel efficient parts, developing navigation systems, or supervising the manufacture and maintenance of aircraft or spacecraft.

**Attributes: **creative, passionate, tenacious

To make a balloon rocket you need a balloon, a drinking straw, some tape and some paper or card to make the fins.

- Cut the end off your balloon and tape the opening around one end of your straw. make sure no air can escape between the balloon and the outside of the straw.
- Cut out three fin shapes and attach them to the other end of your straw. Make sure you leave enough room for your mouth to blow up the balloon.
- Blow up the balloon and let go!

**What’s happening?**

The balloon is moved forward by a force called **thrust.** This is a push that moves the balloon forwards. This comes from the energy of the balloon forcing the air out.

You could investigate these questions using your rocket:

Does the shape of the balloon (the round ones or the thin ones) change how far or how fast the balloon travels? Does the shape of the fins make a difference? What is the best shaped fin? What is the best material to use to make the fins?

If you have space in your house or garden, you could try making this rocket (click here for instructions).

- You will need 6 lollipop sticks and 4 elastic bands.
- Take four of the lolly sticks and place them on top of each other. Hold them together using an elastic band at each end.
- Using the two remaining lolly sticks, join them at one end using an elastic band. Put the stack of four lolly sticks in between them.
- Use the final elastic band to hold the stack in place. Your catapult is complete. Our simple catapult design fires table-tennis balls or (cheaper, but a bit gooey) marshmallows.
- The design can be modified using another elastic band and a spoon. You can also investigate how the position of the stacked sticks affects how well the catapult works.

**How does it work?**

The more force you apply to a catapult, the more force is applied in turn to the object being launched. More force means more speed and – you’d hope – more distance. If you make one of the catapults, you’ll find that pulling the lolly stick back harder shoots the projectile (the marshmallow) faster and further.

If you modify your catapult by adding a spoon, you can add more force by pulling the top of the spoon back further.

Here’s a more complex design of catapult using the same materials: rubber bands, lolly sticks, and a spoon:

Despite its size, the giant catapult in this video is simpler. See the instructions here, and remember that the more force you apply to pull back the catapult elastic, the greater the force applied to the projectile, and the faster and further it will travel.

Simple Harmonic Motion

(and a bit of error analysis)

Supporting notes for this film will follow shortly.

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As ever, no single film can encompass everything one might wish to say about a practical. Please, leave comments with your thoughts about the approach we’ve taken, and your suggestions for alternatives or improvements.

Inverse Square Law

Supporting notes for this film will follow shortly.

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As ever, no single film can encompass everything one might wish to say about a practical. Please, leave comments with your thoughts about the approach we’ve taken, and your suggestions for alternatives or improvements.

Force on a Current-Carrying Wire

Supporting notes for this film will follow shortly.

— to follow

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As ever, no single film can encompass everything one might wish to say about a practical. Please, leave comments with your thoughts about the approach we’ve taken, and your suggestions for alternatives or improvements.

Investigating Diffraction Using a Laser

All the new specifications include a required practical that asks students to measure the wavelength of light by diffraction. Some awarding bodies insist on the use of a laser, while others allow alternative light sources. Some expect the use of Young’s double slits, whilst others suggest a diffraction grating.

In both cases, the light diffracts as it passes through the slits, leading to a broader spread of light on a screen. The different beams diffracted by each slit interfere with each other, either constructively or destructively, depending on their relative path length between slit and screen.

This is a great opportunity to carry out careful measurements, to revise geometry and trigonometry, and to discuss the nature of light itself.

In this film, we show first the double slit method set up conventionally, and then a method using a diffraction grating arranged vertically. Both approaches use laser pointers. The vertical arrangement has advantages in terms of both space in the lab and experiment safety, which are covered in the film.

Many teachers are – quite rightly – concerned about the safety implications of using multiple lasers in a class, even with reasonably sensible students. Particular concerns include:

- With multiple sets of apparatus it can be hard to avoid having laser beams (or their reflections or diffraction paths) criss-crossing the lab.
- In many labs it’s hard to achieve a good blackout, and that carries its own classroom management issues: do you have appropriate places to store coats and bags, for example? What about trailing cables and other trip hazards, in a darkened environment?
- Lasers can be sourced for very little money, but they’re often more powerful than the claimed “<1 mW”. Christina started what turned out to be an interesting discussion about how one might check this, on Talk Physics (registration required).

As ever, one should check with CLEAPSS. Here’s their guidance on lasers (PDF link). Their recommendation is to purchase from an established office or IT supplier, and to ensure the specific unit you receive has a CE marking and a classification BS EN 60825 Class 2. But that’s a summary: **read the CLEAPSS advice in full**.

It *is* possible to avoid lasers by using a white light source with a coloured filter. However, to get good results the source needs to be very bright, ideally narrow (collimated), and as close to monochromatic as possible. In practice the filter often costs more than a suitable laser, but if you’d like to explore the option, here’s a write-up at Practical Physics.

As shown in the film, different exam boards and textbooks use different notation for the formula governing the diffraction of light using a double slit aperture:

\(\lambda = ax / D\)

where:

- \(\lambda\) = wavelength of light (to be found)
- \(a\) = slit spacing, between centres – this information is probably printed on a double-slit slide.
- \(x\) = fringe separation, between adjacent maxima or minima. Measure with a ruler or Vernier callipers, or use mm squares on graph paper as the screen.
- \(D\) = distance from slits to screen, which should be as large as possible (ideally 2 m or more).

Alternatively:

\(\lambda = ws/D\)

where:

- \(s\) = slit spacing
- \(w\) = fringe separation

A straightforward calculation can be done, or you can use the graphical method Alom describes in the film at 1’04”, plotting the fringe separation obtained for a range of different \(D\) values and using the gradient to calculate \(\lambda\). You can check the value you obtain against the value stated on the laser and see if it agrees, within your experimental uncertainty.

Questions you might ask your students:

- Why is a laser a particularly suitable light source for this experiment?
- What would happen to the fringe spacing if we used a green or blue laser? Why?
- Why do we want \(a\) (or \(s\)) to be as small as possible, and \(D\) as large as possible?
- What are the uncertainties in the measured quantities, and how do we combine those to arrive at an uncertainty in \(\lambda\)?

We have a PDF version of the above diagram available for download.

This is an alternative or additional method. The pattern obtained is easier to see, since the bright fringes (maxima) are well-defined ‘spots’. however, the mathematics involved is a little more involved, and students must use trigonometry to find the diffraction angle \(\theta\).

In the film, Christina sets up the apparatus vertically, which both requires less space in the lab and reduces concerns over laser safety. However, you will still need to be cautious for stray reflections.

The relationship here is

\(n\lambda = d \sin\theta\)

where:

- \(n\) = the order of the maximum, with \(n=0\) as the central maximum, \(n=1\) for the ‘first order’ to either side, and so on.
- \(\lambda\) = wavelength of light
- \(d\) = slit spacing. Usually a diffraction grating slide states the number of lines per mm. For example: 300 lines/mm implies 300,000 slits/m, so \(d = 1/300,000~\mathrm{m}\).
- \(\theta\) = angle between the straight-through direction (helpfully marked by the zero-order maximum) and the maximum being investigated. This must be found using trigonometry:

As stated in the film (at 3’15”), we cannot use the small angle approximation here, since the angles are too large. Hence:

\(\theta = \tan^{-1}(\frac{x}{D})\)Using the measurements in the film, Alom’s miraculous ‘off-the-cuff’ calculation went like this:

- Total distance = 191 mm, so \(x\) = 191/2.
- \(D\) = 225 mm
- So \(\theta = \tan^{-1}((191/2)/225) = 22.9985\) ≈ 23.0°

Now, to calculate the wavelength:

\(n\lambda = d\sin\theta\) or \(\lambda = \frac{d\sin\theta}{n}\)

Since we measured two fringes either side of the central maximum (for accuracy):

- \(n = 1\)
- \(d = \frac{1}{300,000}~\mathrm{m}\)
- \(\lambda = (\frac{1}{300,000}\sin 22.9985)/2 = 6.5118 \times 10^{-7} = 651~\mathrm{nm}\) (to 3 sf).

Again, students can compare this with the manufacturer’s stated value; the students should be able to assess their uncertainty to check that the manufacturer’s value falls within their uncertainty range. The same discussions as above can be had about how to minimise uncertainties, and what would happen if a different colour laser were to be used.

Christina suggests in the film that for an extension activity, students could be given an unmarked diffraction grating with a different (and unknown) slit spacing, and asked to use the laser wavelength they’ve calculated to measure the slit spacing. As set out earlier, white light could be used with a colour filter, and the comparisons of uncertainties would be interesting.

Double slit slides: can be bought for around £10 each, for example from Philip Harris.

Gratings: eg. 300 lines/mm for around £15, again from Philip Harris.

At the time of writing, the exam boards appear to agree that this practical might be used to address CPAC 3 and 4, or subsets of them. For example, AQA suggests:

- using appropriate analogue apparatus to record a range of measurements (to include length/distance, angle)
- using a laser or light source to investigate characteristics of light, including interference and diffraction.

We’ve drafted a student worksheet for this practical, which you may find useful:

- Diffraction Practical Worksheet (PDF, 1.7Mb)

Investigating the Discharge of a Capacitor

All the new specifications include a required practical that asks students to investigate capacitors charging or discharging through a resistor. The awarding bodies agree that this practical is an ideal opportunity for students to develop their skills in using ICT.

It’s possible to measure the changing potential difference across the capacitor using:

- A voltmeter and stopwatch.
- An oscilloscope (whether cathode ray or digital, for example a Picoscope).
- A datalogger.

The circuit will be similar whichever approach you use. A meter connected in parallel across the resistor *R* measures *V*. With the switch connected at *A*, the capacitor *C* charges (almost instantly, since there is negligible resistance in the circuit). When the switch is flicked to position *B* the capacitor discharges through the resistor, with both the current and voltage decreasing exponentially.

In their experiments, both Alom and Carol do without a two-way switch and instead simply disconnect the capacitor from the power supply to make it discharge through the resistor.

As Alom mentions in the introduction, the uses of capacitors are quite interesting for giving the students some context here. He refers to a previous film:

In core practical film, Alom uses Edu-lab data loggers (see below for approximate costings), but there are many alternatives. You could also use a digital oscilloscope which stores data, or a computer-based ‘Picoscope’ or similar which functions equivalently.

From 1’32” in the film Alom suggests that students can check the discharge curve is exponential by seeing if there is a constant half-life (the time taken for the potential difference to fall by a half). Or, better, to measure the time constant and if it that is… er… constant (the time constant is the time taken for the measured potential difference to drop to 1/*e* of its original value – see the graph above).

Earlier in the film, Alom chooses values for *C *and *R* which multiply to give a time constant which is measurable: neither too fast nor too slow. In this case:

\(C = 4700~\mathrm{\mu F}\)

\(R = 10~\mathrm{k\Omega}\)

So time constant \(\tau = 4700\times10^{-6} \cdot 10 \cdot 10^3 = 47~\mathrm{s}\)

The exponential equation:

\(V = V_{0}e^{-t/RC}\)

is one which students will need to be able to handle. Alom shows how to manipulate this into the form of a straight-line graph. First, take natural logs of both sides:

\(ln(V) = ln(V_0) – \frac{t}{RC}\)

Compare with:

\(y = mx + c\)

If \(ln(V)\) is plotted on the y-axis against \(t\) on the x-axis, then \(ln(V_0)\) will be the y-intercept and \(-\frac{1}{RC}\) the gradient, hence \(C\) if \(R\) is known.

This might be a useful opportunity to show students the resistor colour code:

- Wikipedia page.
- The best little web app we’ve found for calculating and interpreting resistor bands. —
*Seriously, this page is awesome. We have it as a shortcut on our browser toolbars.*

You might like to ask your students:

- Why is a datalogging method appropriate for this practical?
- Does it matter which way round we connect the capacitor? (
*see Carol’s comment at 3’21**”*). - For how long should we time the discharge?
- What would happen if we instead measured V while the capacitor charges?
- Why process the data so we get a straight line graph? Why is this better than a curve?
- What should the units of \(ln(V)\) be?

Carol uses a multimeter as a voltmeter and a stopclock to do the timing manually. She suggests measuring *V* every ten seconds: it’s hard to record it any more frequently, but take less frequent measurements and the graph will be hard to draw, with too few data points. Any voltmeter will do: digital, analogue, multimeter, or even an oscilloscope.

Students could be challenged to find an unknown capacitance by measuring the time constant obtained with a particular resistor. In the film, Carol explains that some preliminary runs will be needed to test the circuit and to ensure they have a suitably measurable time constant.

This method lends itself to the use of ICT, in that students can put their data into a spreadsheet and manipulate them into a straight line for (as shown above). Alternatively, data can be processed by hand.

You might as your students:

- Why do we not need to worry about starting the timing immediately the discharge begins? (This will test their understanding of the exponential decay function.)
- What are the causes of uncertainty in the experiment – not only our measurements, but the manufacturers’ tolerances for their components?
- How can we reduce the uncertainty in our readings?

Since \(Q = CV\), a large capacitor charged to a huge voltage stores a lot of charge, which will lead to a high initial charging or discharging current, with consequent heating effect. The values used in the film (and noted above) offer a good guide to what works well – and safely.

Capacitors should not be charged to a voltage higher than that stated on their labelling or product information sheets. Electrolytic capacitors should be connected with the correct polarity.

It’s also important to ensure the capacitor is discharged before touching it: disconnect the power, then operate the circuit to discharge the capacitor through the resistance before dismantling the apparatus.

The Edu-logger system used in the film sells for around:

- £45 for the voltage sensor
- £43 for the USB module to connect to a PC (standalone display/tablet/smartphone alternatives are available).
- £43 for a battery module.

Those figures are without VAT. Other systems are available for similar prices, or you can spend considerably more on systems with increasing levels of flexibility. Most suppliers will offer discounts on bulk orders.

The IOP’s Teaching Advanced Physics website has a series of articles about teaching topics around capacitance:

At the time of writing, the exam boards appear to agree that this practical might be used to address, in whole or in part:

- CPAC 3:
*Safely use a range of practical equipment and materials.* - CPAC 4:
*Makes and records observations*.

We’ve drafted a student worksheet for this practical, which you may find useful as a starting point:

- Capacitor discharge lab manual (Word .docx)

Measuring the EMF and Internal Resistance of a Cell

All the new specifications include “measure the internal resistance of a cell” as one of the practicals. This is probably a new bit of physics for your students, and although the practical is straightforward to set up, collecting and processing the data is more of a challenge. Comparing two different types of cell, as shown in this film, can make the practical more interesting, with potential for differentiation by ability.

The film starts (to 1:24) with the theory which you’ll probably introduce to students before carrying out the practical.

From 1:30 onwards, the film illustrates how you might go about conducting the practical with conventional cells, and also with a button cell (watch battery).

Christina and Alom do several things in the film to limit the current so the cell doesn’t overheat: they use a limiting resistor, start with low currents, and connect the circuit only momentarily. This represents safe working practice, but heating the cell would also affect the resistance we’re trying to measure.

We used a 10 Ω resistor to limit the current in the circuit. A simple fixed resistor would do, but make sure it can handle the maximum power you expect in the circuit – a few Watts. We didn’t have such a resistor to hand for filming, hence the huge switchable resistance box.

To vary the current to get multiple readings we used an old rheostat, rated at about 16 Ω. In practice anything with a range up to 50 Ω or so should work. It’s also possible to use a range of different fixed resistors, or a switchable resistance box.

Digital or analogue voltmeters or ammeters could be used instead of multimeters, but as Christina points out in the film, the use of multimeters is a skill your students will need to develop anyway. Students will need to select the most appropriate range, which is likely to be 20 V DC for the voltmeter and 200 mA DC for the ammeter (taking care to convert back to amps when processing the data).

Alom’s multimeter films may be dull, but they’ve had a third of a million views so… they may have some redeeming merit. Click through to YouTube or to maximise the film from these tiny windows:

Working in pairs, this experiment can be be done very quickly. Systematic data are nice, but as long as there’s a good spread of data points across the whole range of currents, students should get a good result.

From our data, we arrived at:

Gradient = -2.10

y-intercept = 1.415

so:

EMF = 1.415 V

Internal resistance = 2.10 Ω

We would normally expect an AA cell to have an EMF of about 1.5 V and an internal resistance of about 1 Ω. Ours was old and cheap, which probably explains our results: it’s worth noting that poorer-quality cells can make for a more interesting experiment!

You might ask your students:

- Is their result what they would expect from the cell packaging or label?
- How could they assess the uncertainty in their data?

Christina mentions *tolerance *at 4’11”, which is a concept with which students may not be familiar. All components have a stated manufacturer’s tolerance, which notes the ±% range which might be expected when the component is in normal use.

We used a standard CR2032 watch battery. The readings for this sort of cell vary much more wildly than for an AA cell. We’d assumed this is due to internal heating of the cell, but in writing these notes we’ve started to wonder if it’s more about the chemistry that’s going on inside – if there’s a limit to the reaction rate, that would explain why the voltage drops away rapidly (particularly with high current drain cases), before the cell recovers after ‘resting.’ Comments welcome, and for now we’ll move on…

Taking photos of the meters is one way of dealing with rapidly-changing readings. Another approach would be to use analogue meters, which can be easier to read by eye.

At 6’09” you’ll see Christina using a ‘best fit’ ruler – a clear ruler with a slot through the middle. We recommend these! Our results:

With the increased uncertainty in the readings, Alom suggests repeating the whole experiment twice. Each repeat could be plotted onto the same axes and the gradients and y-intercepts compared. Students could then find the mean EMF and internal resistance, together with their associated uncertainties.

We would normally expect a 3 V cell to have an EMF of about 3 V, and an internal resistance which is much higher than the AA cell – which indeed is what we found, measuring an internal resistance of 15 Ω.

You might ask your students:

- Is there a better way to record the fluctuating readings?
- Is a simple mean a legitimate way to combine repeat readings?
- What’s the best way to deal with data which looked bunched-up on a graph because you need to include the y-intercept? (You could investigate mathematical extrapolation methods here.)
- Why do cells have different EMFs and internal resistance? What chemicals do they contain and how are they structured inside? (a useful resource here is Battery University, though it gets a little… detailed, shall we say?)

- 50 AA cells should cost about £12.
- 40 3 V coin cells should cost about £5.

Some teachers like to challenge their students further by investigating the EMF and internal resistance of a cell made with copper and zinc electrodes and an item of fruit or a vegetable, for example: a ‘potato battery.’ Further guidance on this can be found at the Practical Physics website. Cutting the potato into different shapes can make for an interesting comparison.

At the time of writing, the exam boards appear to agree that this practical might be used to address, in whole or in part:

- CPAC 1: Follows written procedures
*Correctly follows instructions to carry out the experimental techniques or procedures*

- CPAC 4: Makes and records observations.
*Makes accurate observations relevant to the experimental or investigative procedure.**Obtains accurate, precise and sufficient data for experimental and investigative procedures and records this methodically using appropriate units and conventions.*

You can likely prioritise other CPACs should you so choose. There are some more notes on this in the draft student worksheet, below.

We’ve drafted a student worksheet for this practical, which you may find useful as a starting point:

- EMF and internal resistance worksheet (Word .docx).

Measuring g using a free fall method

A-level specifications from all the exam boards include “measure the acceleration due to gravity of a freely falling body” as one of the practicals. Students might be a bit uninterested in measuring the value of a constant with which they are already familiar. However, this practical is likely to be undertaken close to the beginning of an A level course. As such, it can be used to make a number of valuable points, each of which is worth introducing our students to at this stage:

- By comparing more than one method, students can practice thinking critically about experimental methods.
- Learn to assess and reduce uncertainty.
- Consider how to present and process data.
- Discuss what is meant by ‘constant.’

The film shows four different methods of measuring g using a falling object:

- Drop a ball and time its fall with a stopwatch.
- Drop a ‘g-ball’, which times its own fall.
- Drop a ball through light gates.
- Use an electromagnetic switch to release a ball bearing, with triggered timing.

Which of these methods you use might depend on your students’ skill, your own preference, apparatus availability, ease of data collection or processing, and class size. It’s good to compare at least two methods (even if one is shown as a demonstration only), to prompt and inform discussion about precision, accuracy and uncertainty.

Since we anticipate this practical being used early in the A level course, we’ve not included comments about how to do a full error analysis. There’s more error handling in some of the other films in the series, and we’re planning to complete a film specifically about error as the series continues.

The ASE book The Language of Measurement (£13.50/£8.50 members) refers to *precision* as:

A measurement is precise if values cluster closely.

In the film, at about 2:22, the word ‘precision’ is used to mean the timer’s smallest scale division. This is us showing our age! A better term might be ‘resolution’.

Other ASE definitions:

Accuracy: a result is accurate if it is close to the true value.

Uncertainty: the interval within which the true value can be expected to lie.

Methods 1, 2 and 4 give values of the time \(t\) for a ball to fall from rest at a height \(h\). From the equation:

\(s = ut + \frac{1}{2}at^2\)

we have:

\(g = \frac{2h}{t^2}\)

Measuring \(t\) for different values of \(h\) allows a graph to be drawn of \(h\) against \(t^2\). The gradient of that graph is \(g/2\).

In method 3 the ball falls through two light gates separated by a distance \(h\). Each gate gives a value for the average speed of the ball as it passes through, so we can use \(v^2 = u^2 + 2as\) to find its acceleration between the gates.

Uncertainties arise in four ways:

- Starting the timer.
- During the ball’s descent, due to air resistance or other factors.
- Stopping the timer.
- Determining the height of the fall.

Students can think about these as they compare the different methods. They can try to assess whether each uncertainty will make the values of \(t\) and \(h\) too big or too small, or just more uncertain. They can also discuss how each factor will affect the value of \(g\).

For example: if the measured value of \(t\) is too big, the calculated value of \(g\) will be too small, because t is on the bottom line of \(g = 2h/t^2\).

Eventually, students must be able to assess the overall uncertainty in their measurements. For example, they might state their measured value as \(g = 8.7 \pm 1~\mathrm{ms^{-2}}\). For now, however, it is a good start to be able to calculate the percentage error, e.g.:

\(\frac{9.8 – 8.7}{9.8} \times 100\% = 11\%\)

Drop a ball from a measured height \(h\); start and stop a timer to find \(t\).

Students should be able to comment on the problems with starting and stopping the timer at the correct instants. Reaction time here is not the same as the human response to a random stimulus, since we can watch the ball falling and anticipate the correct moment to stop the timer. It’s still, however, a poor way to measure \(g\)!

Repeated measurements for a fixed value of \(h\) will give a range of values for \(t\). Some students may be better at using a consistent technique, which will give a smaller spread in the values of \(t\). This reduces the random error, but there may still be systematic error, which itself may be revealed by repeating the experiment for different values of \(h\).

- What’s a better way to release the ball?
- What’s a better way to measure the time?
- Why don’t we try to reduce the uncertainty in measuring \(h\)?

These cost about £20 + VAT from education suppliers, one of which is Timstar (as of 2020-08-03 Timstar appear to have stopped selling the G Ball. We’ve found other UK suppliers: Philip Harris, Better Equipped, Breckland Scientific. Search for ‘G Ball’ to find others. There appear to be at least two manufacturers, Unilab and Mollic).

The g-ball starts timing when released and stops timing as soon as it hits the floor. Like most stopclocks, it measures to a resolution of 0.01 seconds. The switch release can limit accuracy, but overall the g-ball is a quick way to collect a large number of data points. In the film, Alom and Christina use an L-shaped bracket clipped to a metre rule to press the release switch, to aid a clean release.

- How is this better than using a stopwatch?
- How can they ‘average’ their data?

Your students could just repeatedly drop the g-ball from the same height and average all their data, then substitute their average \(t\) into \(s = \frac{1}{2}gt^2\) to find \(g\). Much better would be to exclude anomalous values first, and better still would be to plot a graph of \(h\) against \(t^2\) to spot those anomalies.

If you’re going to plot a graph, however, you might as well have two meaningful variables. In the film, Christina and Alom drop the ball from different heights and collect a lot of (not very good!) data quickly.

This approach:

- Helps to spot anomalies visually – an indication of random error.
- Shows that \(g\) is (more-or-less!) constant: the graph is a straight line.
- Allows \(g\) to be determined from a gradient, an important skill.
- Might lead on to a discussion about systematic errors (should the graph pass through the origin?).

Systematic errors can often be eliminated by plotting a graph. For example, if the height is measured 1 cm too short each time, the line on the graph will be shifted downwards. The gradient will be unchanged, and the systematic error should be easily detected.

Another approach, incidentally, would be to plot \(2s\) against \(t^2\), giving a simpler gradient of \(g\). This is a matter of personal preference.

Random error: a measurement error due to results varying in an unpredictable way.

Systematic error: A measurement error where results differ from the true value by a consistent amount each time.

Using light gates is a great way to get students familiar with data loggers. Watch out for the common misconception that using a computer will automatically give a better result! In this case, the timing typically does have a higher resolution, and it’s possible to collect lots of data quickly – both good reasons for using the apparatus.

With two light gates, there are three possibilities:

- Display values of \(u\) and \(v\), and calculate g using \(v^2 = u^2 + 2as\).
- Display values of \(u\), \(v\) and \(t\), and calculate g using \(v = u – at\).
- Position the top light gate just below where the ball is released so the initial velocity is close to zero, then proceed as above.

Note that the measured speeds are always average values, because the ball is accelerating during the time it takes to pass through the light gate.

- Can we be sure that the data logger determines accurate times?
- If we vary \(h\), what graph should we plot to determine \(g\)?
- How can a graph help to reveal problems with the experimental technique?

If you don’t have multiple sets of data loggers, you could have one set up and have students use it in turn. However, the experience of setting up the apparatus is itself valuable, as it prompts the student to think through the role of each piece of equipment rather than to approach the configured apparatus as a ‘black box.’

The commercially available apparatus that Alom and Ronan discuss in the film is available from Philip Harris, for about £100+VAT. Instructions for its use are available from the Nuffield Foundation, which also includes circuit diagrams for a DIY version. (*update 2020-08-03*: it looks like the old practicalphysics.org site has been taken down. The content has moved to spark.iop.org/practical-physics, and the resources on this particular experiment are: Acceleration due to gravity, and Measurement of g using an electronic timer).

Ronan’s version addresses several subtle issues, including that of releasing the ball cleanly, and using a plumb-line to confirm that \(h\) is being measured vertically. We’ll update this article with more details of Ronan’s apparatus when we have them.

- Between which two points should we measure the height of fall \(h\)?
- Can we be sure that the timer starts and stops at the exact moments we want it to?
- If we vary \(h\), what graph should we plot to determine \(g\)?

At the time of writing, the exam boards appear to agree that this practical might be used to address, in whole or in part:

- CPAC 2:
*Applies investigate approaches and methods when using instruments and equipment.* - CPAC 4:
*Makes and records observations*.

Each exam board has published a list of apparatus and techniques with which students much be familiar, along with suggestions as to which elements might be addressed by each practical. For example, Edexcel’s guidance for this practical suggests:

- 1. Use appropriate analogue apparatus to record a range of measurements (to include length/distance, temperature, pressure, force, angles, volume) and to interpolate between scale markings
- 2. Use appropriate digital instruments, including electrical multimeters, to obtain a range of measurements (to include time, current, voltage, resistance, mass).
- 4. Use stopwatch or light gates for timing.
- 11. Use ICT such as computer modelling, or datalogger with a variety of sensors to collect data, or use of software to process data.

Check your exam board’s resources: there should be a mapping document to help you decide which criteria to assess on each practical.

We’ve drafted a student worksheet for this practical, which you may find useful:

- Acceleration due to Gravity Worksheet (Word .doc file)

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