## 8 Equations of Motion…

A common problem for teaching Physics when you are not a Physics teacher is that you make many mistakes with complex ideas which appear simple on the surface.

I drop a ball to the earth and want to work out the distance fallen in a certain time. I then do a calculation of..

distance x speed = time

Oh dear but when I do the experiment it does not work like that but it works like this…

[latex size=”3″]s =\frac{1}{2}at^{2}[/latex]

Now we can reason this out. If I allow a ball to fall to earth it must accelerate due to the field of gravity around the earth 9.81N/kg. Or 9.81 m/s/s.

But where does the formulae  come from that we general use?

[latex size=”3″]s = ut+\frac{1}{2}at^{2}[/latex]

1. s = the distance between initial and final positions (displacement) (sometimes denoted as x)
2. u = the initial velocity (speed in a given direction)
3. v = the final velocity
4. a = the constant acceleration
5. t = the time taken to move from the initial state to the final state

So the question is what is it all about.

Well we need to think way back to the idea of a simple idea of how to work out the distance travelled by  a runner in a race.

Think of an athlete travelling 100m in 10s at a constant speed. His velocity or speed is…

[latex size=”3″] \frac{d}{t}= speed[/latex]  OR  [latex size=”3″] \frac{s}{t}= v[/latex]

Now this works fine if we are travelling at a constant speed but hey as you know this is not always the case and sometimes an object has a constant acceleration or deceleration. If you think about a graph of a person who got faster and faster then we would have a slope or triangular area on a speed-time or velocity-time graph. Now the area under the graph would be the distance travelled on the journey. But if our speed changed s=vt (for constant speed) becomes….

[latex size=”3″] s=\frac{vt}{2}[/latex]

Now you have an expression for the average speed but only from a standing start. Imagine now the same velocity time graph but this time the runner was already travelling at a velocity at the start of timing. Our area would become a triangle and rectangle…

[latex size=”3″] s=\frac{(v-u)t}{2}+ut[/latex]

Simplifies to

[latex size=”3″] s=\frac{(v+u)t}{2}[/latex]  – Eq 2

This is the formulae for average speed that takes care of all situations even when u or v is 0. Now then think graphically again if we are travelling at an initial velocity and then accelerate we are back to triangle and square again when looking at a vt graph. Hence…

[latex size=”3″] v=u+at[/latex]  – Eq 1

Now we can use this in a rearranged form..

[latex size=”3″] t=\frac{(v-u)}{a}[/latex]

Substitute into Eq 1 in new form into 1 to remove t so we now have an expression…

[latex size=”3″] s=\frac{(v+u)}{2}*\frac{(v-u)}{a} [/latex]

Which simplifies to..

[latex size=”3″] s=\frac{(v^{2}-u^{2})}{2a} [/latex]  – Equ 4

Now we have this we can work also work backwards to get Eq 3 …

[latex size=”3″] v=u+at[/latex]  – Eq 1

And *t gives..

[latex size=”3″]vt = ut+at^{2}[/latex]

Divide both sides by two…

[latex size=”3″]\frac{vt}{2} = \frac{ut}{2} +\frac{ at^{2}}{2} [/latex]

Add ut to both sides, multiply by 2 and tidy up..

[latex size=”3″]s = ut+\frac{ at^{2}}{2} [/latex] – Eq 3

So we now have the four equations of motion for an object which is travelling at a constant velocity or accelerating at a constant rate. As shown you can reason them all out with very simple ideas from first principals. You can also call them whatever number you want as some people label them differently.

So hopfully we have now understood where the formulae comes from and realise that if we drop a ball we must apply the formulae to work out the distance fallen in a more complex way.

Then it gets really interesting when you think about a tanker travelling at a constant velocity which then slows down. How far does it travel as it slows…

[latex size=”3″]s = ut-\frac{ at^{2}}{2} [/latex]

Of course, it will be ut for the whole time and then you take away a little bit of “s” from the other term as you slow.

## The Electron a “charged particle”

The story of cathode rays begins in 1855. In that year, Heinrich Geissler invented the mercury vacuum pump. With the pump he could remove almost all of the air from a sealed glass tube.  Geissler’s friend Julius Plucker used the pump to evacuate a special kind of tube. Inside the tube were two electrodes. Plucker attached one electrode, called the anode, to the positive terminal of a battery. He attached the other electrode, the cathode, to the negative terminal. He noticed that the glass near the cathode glowed with greenish light. When Plucker held a magnet near the tube, the glowing spot moved.  Plucker’s student, Johann Wilhelm Hittorf, put solid objects inside the tube between the cathode and the glow. The objects cast shadows. Hittorf concluded that the cathode was emitting something that travelled in straight lines, like light rays. The German physicist Eugen Goldstein named them “cathode rays.”

The English scientist William Crookes thought cathode rays were streams of molecules that had picked up a negative electric charge. Crookes knew from the laws of electricity and magnetism that a charged particle in a magnetic field would move in a circle. Since a magnetic field caused cathode rays to move in a circle, Crookes reasoned, they must be made of charged particles.

If cathode rays were streams of charged particles, an electric field also should have deflected their path. The German physicist Heinrich Hertz tested this hypothesis. He set a cathode ray tube between two metal plates. One plate was positively charged and the other was negatively charged. Negatively charged molecules should have been attracted to the positive plate. When Hertz connected his tube to the battery, the cathode rays kept going in a straight line. Hertz concluded that the cathode rays were a new kind of electromagnetic wave.  Hertz’s student, Philipp Lenard, designed a cathode ray tube with a thin foil at one end. The cathode rays went right through the foil. Since molecules of gas could not go through the foil, Lenard knew that cathode rays could not be charged molecules. He agreed with his teacher that they must be electromagnetic waves.

Then Jean-Baptiste Perrin conducted a very simple but very clever experiment. He accelerated a beam of electrons in a glass tube. You can see at the start of my video how the spot on the glass tube is the impact of the electrons causing fluorescent on paint on the inside of the tube. He then setup a magnetic field at 90 degrees to the beam using coils of wire (Helmholz coils). As you increase the current flow inside the coils the field becomes stronger causing the beam to curve according to Flemings LH rule of FBI. Now as the beam is directed down to a collector which is connected to a gold leaf electroscope the leaf rises. This shows us that the beam is in fact charged. Further experiments show the charge is also negative. This is evidence that cathode rays are in not part of the EM Spectrum.

[hana-flv-player video=”https://www.animatedscience.co.uk/wp-content/uploads/2011/01/charged-electron.flv” width=”400″ height=”330″ description=”Charged Electron” player=”4″ autoload=”true” autoplay=”false” loop=”false” autorewind=”true” /]

## GCSE Science A Journey!

I was thinking recently about the changes we have seen to GCSE science in the past 10 years. I cannot comment before this but for the past 10 years I have taught AQA Core Science and Additional Science for Y11. Also before this the AQA double award which was split into Y10/Y11 so you had two grades.

The first thing that amazed me is when the “How Science Works” agenda came into play AQA changed the science content by mixing half of Y10 with half of Y11 then removing some content and making it the “Triple” part so I would say that pupils after the changes covered less than before unless they did triple science.

This was not the worst part. Take for example Y10 Electricity pupils would have to do a two stage calculation for working out the energy loss in a transformer in the multichoice exam. It was very difficult to get 36/36 in the exam. However, now most of the maths has come out of the exams and they are much easier for pupils (who can read) to access.  What has changed is that there are now a lot of trick questions based more in English tricks than science tricks.

It was very interesting that for the past few years I keep raising the issue within science forums and nobody wanted to admit that things had got easier. However as more changes came in for 2010 Y9 students….

The exams watchdog, Ofqual, said the new papers – designed to address concerns that science exams had become too easy – had “not gone far enough”.

Last year Ofqual said science GCSEs taken in 2007 and 2008 had contained too many multiple choice papers and had failed to challenge the brightest.

Ofqual previously ordered an overhaul of GCSE science qualifications and immediate action was taken to toughen them up for students sitting them last year and this year.

Now the watchdog says the new-look qualifications, due to be introduced in autumn 2011, have been sent back to the exam boards for more work.

A spokesman for the exam board AQA said: “We are addressing the issues that Ofqual has raised, and will be re-submitting our specifications for accreditation, whilst maintaining the innovations that teachers and subject communities have

In view of the issues that Science is having I would appeal to all students and teachers to look for a guide from history. Just thumb though the exams and the textbooks from 20 years ago for Physics, Chemistry and Biology. You will see the standards and what is expected. The gap between GCSE and AS is getting wider and you will need to make sure that if for example you wish to study AS Physics you keep to the old standards. Mathematics is constantly removed from the subject to “make is more accessible” to pupils who cannot access maths as really the subject is dying as it is so hard compared to some others. But in reality Mathematics is the language of Physics and was invented by Physicists trying to understand the world around them. If you cannot express things mathematically Physics simply becomes a talking shop and more like philosophy.

Also why when you look through these is books is so much taken out of the modern AS/A2 exams. I am now teaching about 2/3 of what I did for my A-level 15 years ago so why has it been dropped? Don’t we use op amps, rectifying circuits and transistors in our circuits any more?  Well of course we do but now they are in the 1st year of a Physics or Electronics degree? Draw your own conclusions and remember you can learn more than the exam board wants and better than the rest. Learning about science is not dictated by the exam board and we can do much more than them.

## Parma Ham Dry Cure

Parma Ham the holy grail. Well I think I almost found it. I just used an off the shelf cure from https://www.sausagemaking.org/acatalog/Parma_Ham.html
This worked really well the instructions on how to use it are all there and it works. What is important is that you cannot eat this meat right away it must cure for a long time. The nitrates turn into nitrites by bacterial processes. If you eat it right away like bacon you are DEAD! Slowly the meat drys and cures until is it not raw but cured and tastes good.

The basic method is…

1)         Chill the meat overnight

2)         Rub the meat with half of the cure mixture, if using a boned joint ensure that the inner surface of the meat is properly coated, massage the cure into any crevices. I suggest you try a couple of kg of meat to start with. I did a piece with skin on from a leg but a loin works really well as it is so tender.

3)         Vacuum pack. (I did cling film which works but can leak)

4)         Leave the meat to cure in the fridge for 15 days. (yes seems like a long time)

5)         Unwrap the meat and repeat step 2 with the remaining cure mixture. Reseal

6)          Leave the meat to cure for another 15 days.

7)         Unwrap the meat and leave to soak in tepid water for half an hour.

8)         hang the ham for 3 hours in a draughty cool room can leave on a metal drying rack. (the skin looks very wet and horrible now)

9)         Smear the meat side of the ham with a mixture of lard and black pepper. Hang the ham in a warm room for 3 days, (an airing cupboard is ideal). Best to warm lard before it goes on, use a bag over your hand and seal any cracks. I hang in fishnet stocking large open weave.

10)       Hang the ham for a minimum of 30 days at 15 degrees Celsius with a 70% relative humidity.

11)        For smaller cuts of meat reduce the cure time by a third and the hanging time by 20%

I suggest you take good care of ham any cracks move over the lard to close. You should get a white mould form that is good and healthy. Any green mould cut off and wipe with vinegar. Any drips wipe away
Try and make sure the place you hand is dark, cool, medium humidity. Any extremes and will not work. You can wrap it in muslin as well to try and stop drying out too much. Also you can take off the skin first as it becomes very very hard, really depends on how the meat is cut to the benefit. If you are doing belly pork this way then reduce drying time and remove before curing.

## Dry Cure Bacon

Loin Bacon or Belly Pork Bacon is the easiest of all to make. Simply take a piece of free range pork like Gloucester Old Spot. You want a thick slab from an older animal which has been allowed to gain a medium to thick layer of fat on it.

Method is easy…

1)      Prepare correct size of vacuum pack with double sealed end, roll over the top to stop it getting wet

2)      Add pork and cure mixture then shake to distribute.

3)      Seal end with vacuum seal and double seal end.

4)      Leave in cold fridge and turn daily.

5)      You need to leave it for (at least) 24 hours per ½ inch or 13mm then add on 2 days. This means belly at least a week and loin more.

6)      When ready sometimes you can tell when it is really firm, wash off in cold water, pat dry with kitchen towel. Put on metal drying rack in fridge for a few hours.

7)      Can be cold smoked as well at this point or packed and frozen. Can eat right away or leave for a day to get more flavour.

I would say that these figures are conservative and you could add a little more normal salt and cure longer and it will taste fine. Also this bacon will not last like commercial bacon so best to freeze in vacuum packs and eat on defrost. Also if freezing leave in large pieces for belly then cut to lardons later.

Ingredients…

• Bacon Loin or Belly 2825g
• Old English Bacon Cure Ready mixed (30g per 1000g) 84.75g
• Brown Sugar 16g (balances salt adds flavour and helps preserve)
• Spices – mix what you want. Why not try out…Juniper berries, bay leaf, black pepper, mace, oregano, sage for a range of flavours. You cannot do any harm as long as they are not indian spice mixes which are too harsh.

## The Problem with Teaching Physics in modern times….

I am starting to worry about how we teach Physics to the pupils of today. It seems increasingly obvious that we teach more and more about things that are really unimportant to science and less about the fundamentals.

For example we spent a lot of time on the new HSW curriculum on identifying the type of a variable i.e. categorical, continuous and similar. This allows the pupils to decide which graph type to draw in an ISA exam for AQA and similar boards. However, really is that a skill that they need in their everyday lives or society needs for scientists of the future?

Now try some of these video cartoon clips https://www.animatedscience.co.uk/flv/ from KOCE (also see list on that page).

When you start to think about it, why is school Physics not split like this for all pupils into five main sections. Then just look at the topics they are such simple fundamental things which everyone should know about for their everyday lives. Also the right way to teach for pupils who go onto to Uni and further!

How many pupils really know about how a wheel works or  simple lever, possibly mans greatest inventions. However, somehow written out by the QCA from KS3 and KS4. On the select few who take A-Level Physics are supposed to learn about these basic things of life?

Even more interestingly to really see if school science has failed is ask these question to a pupil. “What do stars do”. They will all answer “emit light”. Then you refine it…. “apart from emit light” which is obviously a secondary thing. Then 99% will not know and neither will most adults either. So in fact it seems the people who write the GCSE Physics for the nation as the missed it out of all the specs.

Stars in fact create all the elements in the Universe and of course those which make up our bodies. So what do we teach about stars…. well we teach about life and death cycles but forget the major important thing.

So what am I saying? Well if you can please slip into your teaching some of the really important things which will still give us pupils who can think for themselves and be creative. Also make sure that every pupil who goes through your hands regardless of if the QCA tells you to teach it or not understands the idea of a lever!

## New solar fuel machine “mimics plant life”

In the prototype, sunlight heats a ceria cylinder which breaks down water or carbon dioxide

A prototype solar device has been unveiled which mimics plant life, turning the Sun’s energy into fuel.

The machine uses the Sun’s rays and a metal oxide called ceria to break down carbon dioxide or water into fuels which can be stored and transported.

Conventional photovoltaic panels must use the electricity they generate in situ, and cannot deliver power at night.

The prototype, which was devised by researchers in the US and Switzerland, uses a quartz window and cavity to concentrate sunlight into a cylinder lined with cerium oxide, also known as ceria.

Ceria has a natural propensity to exhale oxygen as it heats up and inhale it as it cools down.

If as in the prototype, carbon dioxide and/or water are pumped into the vessel, the ceria will rapidly strip the oxygen from them as it cools, creating hydrogen and/or carbon monoxide.

Hydrogen produced could be used to fuel hydrogen fuel cells in cars, for example, while a combination of hydrogen and carbon monoxide can be used to create “syngas” for fuel.

It is this harnessing of ceria’s properties in the solar reactor which represents the major breakthrough, say the inventors of the device. They also say the metal is readily available, being the most abundant of the “rare-earth” metals.

Methane can be produced using the same machine, they say. Refinements needed  The prototype is grossly inefficient, the fuel created harnessing only between 0.7% and 0.8% of the solar energy taken into the vessel. Most of the energy is lost through heat loss through the reactor’s wall or through the re-radiation of sunlight back through the device’s aperture. But the researchers are confident that efficiency rates of up to 19% can be achieved through better insulation and smaller apertures. Such efficiency rates, they say, could make for a viable commercial device. “The chemistry of the material is really well suited to this process,” says Professor Sossina Haile of the California Institute of Technology (Caltech). “This is the first demonstration of doing the full shebang, running it under (light) photons in a reactor.”

She says the reactor could be used to create transportation fuels or be adopted in large-scale energy plants, where solar-sourced power could be available throughout the day and night. However, she admits the fate of this and other devices in development is tied to whether states adopt a low-carbon policy. “It’s very much tied to policy. If we had a carbon policy, something like this would move forward a lot more quickly,” she told the BBC. It has been suggested that the device mimics plants, which also use carbon dioxide, water and sunlight to create energy as part of the process of photosynthesis. But Professor Haile thinks the analogy is over-simplistic.

“Yes, the reactor takes in sunlight, we take in carbon dioxide and water and we produce a chemical compound, so in the most generic sense there are these similarities, but I think that’s pretty much where the analogy ends.”

The PS10 solar tower plant near Seville, Spain. Mirrors concentrate the sun’s power on to a central tower, driving a steam turbine

Daniel Davies, chief technology officer at the British photovoltaic company Solar Century, said the research was “very exciting”.

“I guess the question is where you locate it – would you put your solar collector on a roof or would it be better off as a big industrial concern in the Sahara and then shipping the liquid fuel?” he said.

Solar technology is moving forward apace but the overriding challenges remain ones of efficiency, economy and storage.

New-generation “solar tower” plants have been built in Spain and the United States which use an array of mirrors to concentrate sunlight onto tower-mounted receivers which drive steam turbines.

A new Spanish project will use molten salts to store heat from the Sun for up to 15 hours, so that the plant could potentially operate through the night.

## 3D Invisibility Cloak unveiled

3-D invisibility cloak hides gold “bump” The first device to hide an object in three dimensions has been unveiled by a group of physicists in the UK and Germany. While the design only cloaks micro-scale objects from near-infrared wavelengths, the researchers claim that there is nothing in principle to prevent their design from being scaled up to hide much larger artefacts from visible light. The origins of this design date back to 2006, when David Smith and colleagues at Duke University in North Carolina created a cloak that could bend microwaves around an object, like water flowing around a smooth stone.

This early cloak was made using a metamaterial – an artificially constructed material with unusual electromagnetic or other properties – which consisted of a cylinder built up from concentric rings of copper split-ring resonators. This first cloak, however, only worked in two dimensions – in other words, looking at the cylinder from above revealed the presence of the shielded object.

Carpet cloak Now Tolga Ergin and colleagues at Karlsruhe Institute of Technology in Germany, together with John Pendry of Imperial College in London, have overcome this problem by creating a “carpet cloak”. Proposed in 2008 by Pendry and Jensen Li, this involves hiding an object underneath a bump on the surface of an otherwise smooth material – just as something might be hidden under a carpet – and then smoothing out the resulting bump. This is achieved by creating a bump on a flat mirror and then placing onto the mirror a layer of metamaterial with optical properties such that light appears to reflect off the mirror as if the bump were not there. This technique was demonstrated experimentally at two different wavelengths last year, with Smith’s group showing that it worked in the microwave region while researchers at Berkeley and Cornell University near New York obtained similar results at infrared wavelengths. However, these cloaks were also limited to just two dimensions.

Ergin’s group has made a carpet cloak in three dimensions by stacking nanofabricated silicon wafers on top of one another in a “woodpile” matrix and then filling in the gaps between the wafers with varying amounts of polymer. This achieves the desired distribution of refractive indices within the structure. Hiding the bump The cloak structure was then placed on top of a reflective gold surface containing a bump, leading to a cloaking effect using unpolarized light with wavelengths between 1.4 and 2.7 µm – the near-infrared. Importantly, this effect held for viewing angles up to 60 degrees (with zero degrees representing viewing in just two dimensions).

The bump, however, was very small – just 30 µm (10–6 m) × 10 µm × 1 µm. Team member Martin Wegener says it should be possible to use existing technology to make the cloak bigger in order to hide larger objects, but that this approach would be extremely time-consuming. “Faster nanofabrication tools will have to be developed allowing for three-dimensional structures,” he adds. For Wegener the aim of the work is not about focusing all efforts on creating invisibility cloaks, but is about exploring a range of applications in transformation optics.

This involves calculating what kind of material is needed to bend light in a certain way, by considering light trajectories as the result of the warping of space. Wegener says that transformation optics should lead, for example, to the design of better antennas or smaller optical resonators. Smith describes the latest work as “very exciting” and agrees that its real importance lies in the development of transformation optics. “Demonstrations like these are paving the way for transformation optical design to become an established design methodology, like ray-tracing,” he says. The research is published in Science.