The Expanding Universe-Use in School

Here are some more fantastic videos, which you generally can’t have access to in school so I’ve downloaded the videos for you. When at home please visit the original sources.

Dr Physics A is a fantastic communicator who makes all the content so accessible. He is working through the A level course and some of the content relates to A level material, and is done in a different manner to Higher and AH. The content isn’t wrong, it is just defined by different terms. Find his channel here.

Dr Physics A

Watch, if you check his equations for the special relativity topic he transposes t and t’ (as do many texts etc. Scotland always does things differently)! Check off each of the content points from the outcome booklet.

Parallax

Hubble’s Constant The Big Bang Theory- Part 1

Hubble’s Constant The Big Bang Theory- Part 2

Hubble’s Constant The Big Bang Theory- Part 3

From the Big Bang to Now

Olber’s Paradox

Dark Energy

BBC Dark Energy

 

 

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Special Relativity

Resources for Special Relativity

Here is a link to a fantastic little book that started me on my “very short introduction” library. It has been uploaded as a pdf file, but if you enjoy it give the author some credit and pay the guy (Russell Stannard) by buying it!

Relativity-A-Very-Short-Introduction.pdf

Frames of Reference

You should all try to make your holiday videos so useful in showing Physics ideas! Who is in motion? Does it remain the same throughout the sequence?


This is covered in the web-based research post but I’ve uploaded it here as an MP4 file.

Just check this off against the content as it isn’t all covered at Higher (some is the AH and some isn’t covered at all).

Neil deGrasse Tyson with his inimitable style explains the Michelson-Morley experiment and shows that despite getting a rubbish result it doesn’t say your results are rubbish! This was big Science progress and it wasn’t explained until Einstein came along. It was the turning point that transformed Science.

Here are further explanations of the Michelson-Morley experiment and a hint of more of the course to come.

Evidence for Special Relativity

Sixty symbols- Nottingham University

Sixty Symbols by Nottingham University are an amazing set of videos, although far more than sixty by now. Check out and keep watching.

…. and here at the end I have uploaded the worked answers (thanks to whoever wrote these excellent questions) so that you can check off your tutorials.

ODU worked ANSWERS_5

Our Universe tutorial solutions

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Perfect Answers (according to the SQA)

I will add and adapt these as I go through the past papers. If you’ve got additional definitions do pass them on. These would be great written on cue or flash cards. Go through past papers and record any common phrases or answers.

  Term Definition
1 acceleration Acceleration is the rate of change of velocity
2 acceleration of X ms-2 The velocity of the body increases/changes by X m s-1 every second.
3 Air bags / crumple zones / seat belts Time (of collision) increased, change in momentum is the same, (Average) force (acting on passenger) is decreased/reduced/smaller
4 Big Bang Description The Universe was initially in a hot and very dense state and then rapidly expanded. The universe started from a point/singularity and rapidly expanded.
5 Big Bang Evidence Cosmic Microwave Background Radiation, Redshift of galaxies, Olber’s Paradox (and darkness of the skies), H-He Problem (relative abundance of hydrogen/helium)
6 Closed universe The universe will slow its expansion and eventually begin to contract.
7 Collisions- law of conservation of momentum During any collision, in the absence of external forces momentum is conserved, total energy is conserved. In an elastic collision – Ek is also conserved In an inelastic collision- Ek is transferred into other forms.
8 Component of weight down a slope W sin θ, or mg sin θ
9 Cosmic Microwave Background Radiation. CMB Give a reason why the existence of this radiation supports the Big Bang Theory. is pervasive throughout space. It is the dominant source of radiation in the Universe. It is very uniform (throughout the Universe). It is isotropic (throughout the Universe). It shows the characteristics of blackbody radiation. It has a temperature of approx 3 K (2·74 K) due to cooling on expansion. It corresponds to a redshift of 1000, so the early temperature of this radiation was approx 3000 K. CMBR is thought to be the “afterglow” of the Big Bang, cooled to a faint whisper in the microwave region.
10 Dark Energy a hypothetical form of energy whose negative pressure counteracts gravity and is assumed to be responsible for the universe expanding at an accelerating rate. Dark Energy repels.
11 Dark Matter a hypothetical form of matter invisible to electromagnetic radiation, postulated (suggested) to account for gravitational forces observed in the universe. Dark Matter is attractive
12 Doppler Effect The Doppler Effect is the apparent change in frequency of a wave when the source and observer are moving relative to each other.
13 Doppler explanation There are more wavefronts per second observed due to the forward motion of the vehicle. (NB not wavefronts produced as there are not!)
14 Evidence for the big bang The cooling of the Universe and cosmic microwave background radiation provide evidence for the Big Bang
15 Explain why a greater number of muons are detected on the surface of the Earth than would be expected if relativistic effects were not taken into account. For an observer on Earth’s frame of reference the mean life of the muon is much greater OR The distance in the muon frame of reference is shorter
16 Explain why star is redshifted. The star is moving away from the Earth • The apparent wavelength of the hydrogen spectra from the star has increased • The apparent frequency of the hydrogen spectra from the star is less than the actual frequency on Earth • The frequency of the light from the star has shifted towards the red end of the spectrum • Light from the star is experiencing a Doppler shift.
17 Explain why the driving force must be increased with time to maintain a constant acceleration. The faster it goes, the greater the air resistance. or frictional forces / friction / drag then F(drive) constant, the unbalanced force would decrease or increasing F(drive) keeps the unbalanced force constant or overall/net force – must have
18 Explain, in terms of the forces, why there is a maximum angle of slope that the cart can ascend. As angle (of slope) increases mgsinθ increases When mgsinθ ≧ engine force – friction, the vehicle cannot move up the slope
19 F-t graphs The Area under a F-t graph is equal to impulse or change in momentum of the object.
20 Hubble Constant Ho and 1/Ho the ratio of the speed of recession of a galaxy (due to the expansion of the universe) to its distance from the observer. The reciprocal of the constant is called Hubble time and represents the length of time for which the universe has been expanding, and hence the age of the universe.
21 impulse This quantity Ft is called the IMPULSE and it is equal to the CHANGE IN MOMENTUM of the object. Impulse = change in momentum
22 inertia Inertia is the tendency of a body to remain at rest, or if moving, to continue its motion in a straight line
23 inertial reference frame two objects that are moving at constant speed with reference to each other
24 Law of conservation of momentum Total momentum before (a collision) is equal to the total momentum after (a collision) in the absence of external forces
25 Length contraction The decrease in length (in the direction of motion) of an object moving relative to an observer. N.B. it must be clear that the observer is in a different frame of reference.
26 Lorenz transformation not noted at low speeds. Lorentz factor is (approximately) unity/equal to one negligible change in length/time/mass observed
27 momentum the product of mass times velocity
28 Newton- definition One Newton is equal to the force which causes an acceleration of one metre per second squared when applied to a mass of one kilogram.
29 Open Universe The universe will continue to expand forever.
30 Radiation of peak wavelength 1·06 mm can be detected on Earth coming from all directions in space. Cosmic Microwave Background All three words required (Radiation) “CMBR” – Not acceptable, as this is not “naming”.
31 Redshift example More distant galaxies are moving away at a greater velocity/ have a greater recessional velocity
32 Redshift explanation Light from objects moving away is shifted to larger wavelength or the rate of change of wavelength/emitted wavelength as the galaxy moves away
33 Redshift, z Redshift, z, of a galaxy is defined as the change in wavelength divided by the original wavelength, and given the symbol z. It has no units.
34 Reference Frame The background frame against which measurements are made. There is no absolute reference frame.
35 Resultant force A single force that has the same effect as the forces actually acting on an object
36 Satellites a curved path Constant horizontal speed but are accelerating in the vertical direction under the influence of a gravitational field.
37 scalar and vector A vector is a quantity which has both a magnitude and direction. A scalar is fully described by its magnitude.
38 Spectral lines A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range. Spectral lines are often used to identify atoms and molecules from their characteristic spectral lines. These “fingerprints” can be compared to the previously collected “fingerprints” of atoms and molecules, and are thus used to identify the atomic and molecular components of stars and planets.
39 Terminal Velocity A constant velocity of an object when the driving force acting on an object is balanced by the frictional force.
40 Time dilation Time dilation is a difference in a time interval as measured by a stationary observer and a moving observer.
41 twin paradox Special Relativity would suggest one twin who has been out in space or travelling at high speed relative to one remaining on Earth should come back younger, but to the travelling twin they could consider themselves stationary as the Earth moved away fast, so to the astronaut twin the twin on Earth should be younger. This paradox is resolved as during the journey in space the travelling twin would have had to return, during which time they would be in a non-inertial reference frame, so they would have experienced the speed/acceleration. Therefore been in a non inertial reference frame and hence special relativity does not apply.
42 Speed of light is the same for all observers / all (inertial) frames of reference
43 Correct – from the perspective of the stationary observer there will be time dilation Incorrect – from the perspective of the students they are in the same frame of reference as the clock Not possible to say/could be both correct and incorrect – frame of reference has not been defined
44 light is redshifted/ shifted towards red

Proving the equations of motion

Equation 1

v u at

Equation 2

v-t graphs ut 12at2

 

Equation 3

EOM equation 3

If you don’t like proving v2=u2+2as from v=u+at then use this neat little sheet from Mr Mackenzie.

using displacement equation to prove the last equation

Below are the 16 graphs to try to learn. Going across a row from L to R shows graphs drawn from the gradient of the previous graph. Therefore if you write the axes on for s-t, v-t and a-t you can work backwards and forwards to quickly picture the shape of the graph you require.16graphs

Friction always acts to oppose motion. If the object is sliding down the slope then friction must act up the slope, but if the object is being pushed up the slope then friction acts down the slope.friction down slopefriction up slopeThe component pushing into the slope (mg cosθ) is balanced by the reaction force from the slope.

Lifts

lifts

Collisions Seatbelts, crumple zones, airbags, helmets etc are all designed to reduce the force on a person, by increasing the time of contact. In all cases the change in momentum or impulse remains the same as the vehicle/ object still has to come to rest from its initial speed.lower force

F=GMm/r=mg

finding g

Show that the frequency f of the sound heard by the passenger is given by where symbols have their usual meaning.Doppler proof

Although we talk about the Big Bang, it is important to emphasise that the universe, ie space, is expanding. There are a number of characteristics that indicate it is an expansion and not the result of an explosion.

Explosion Expansion
Different bits fly off at different speeds Expansion explains the large-scale symmetry we see in the distribution of galaxies
Fast parts overtake slow parts Expanding space explains the redshifts and the Hubble law
Difficult to imagine a suitable mechanism to produce the range of velocities from 100 kms–1 to almost the speed of light Expansion also explains redshifts and the Hubble law even if we are not at the centre of the universe

 

Type of Collision Momentum Kinetic Energy Total Energy
Elastic Conserved Conserved Conserved
Inelastic Conserved Reduced Conserved
Explosions Conserved

zero at start and finish

here Ep is converted to Ek so Ek increases Conserved

Hope these are helpful. Let me know if you want me to add anything further.

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Dark Matter v Dark Energy

Here are some links for a more in-depth experience of Dark Matter and Dark Energy. (remember Energy ⇒Expansion, Matter ⇒sMaller, or MAtter⇒ Attracts)

http://www.sixtysymbols.com/videos/ed_dark_energy.htm

34 mins interesting video.

http://www.sixtysymbols.com/videos/darkmatter.htm

11 mins on Dark Matter

Brand New Research- could you be a part of this?

https://science.nasa.gov/astrophysics/focus-areas/what-is-dark-energy

https://home.cern/about/physics/dark-matter

http://www.space.com/20930-dark-matter.html
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The Expanding Universe

Try the following practical

http://www.schoolsobservatory.org.uk/astro/cosmos/uniball

expanding universe school observatory

 

Expanding Universe Experiment

To understand how the redshift of galaxies is due to the expansion of the Universe, try the following experiment.

You will need the following items:

  1. A round balloon (do not use a long, thin one).
  2. Some coloured stick-on dots (at least 5 different colours).
  3. A piece of string about 50cm long.
  4. A ruler.
  5. A stopwatch or other timer.

Step 1 : Setting Up

You will need to work in teams of at least two, one to blow up and hold the balloon and the other to make the measurements.

Before you start, draw a table for your results like the one below with the colours of your five dots in the 1st column:

Colour of Dot First Distance D1 in cm Second Distance D2 in cm Change in Distance        D2 – D1 in cm Speed v in cm/second
Red
Green
Blue
White
Yellow
Time to fully inflate the balloon:        seconds.

Step 2 : Making the Measurements

Putting dots on the small balloon

Blow up the balloon a little bit and hold the “nozzle” closed, but do not tie it up.

Stick your five dots onto the balloon. Try to spread them out over the whole balloon.

stick dots

Each of the dots represents a whole galaxy, with the surface of the balloon being the Universe that they exist in.

Choose one of the dots to be your “home”. You can choose any of them.

Step 3

Use string to measure the distance between two dots

measure dots

While one of you holds the balloon, the other one can use the string to measure the distance from your “home” dot to one of the other dots.

Now measure the string distance with a ruler.

When you have measured the distance, write it down in your table in the D1 column.

Step 4

Measure the distances from the “home” dot to all the other dots as well and fill in that column of the table.

Note: The distance from your “home” dot to itself is zero.

Step 5

Now carefully blow the balloon right up, using the stopwatch to time how long it takes. Write down the time in seconds.

Step 6

Now re-measure all the distances from “home” to all the other dots and write then down in the D2 column of your table. Don’t forget that the distance from your “home” dot to itself is zero.

You now need to work out the speed of each galaxy. Remember that:

Here, the Distance travelled is the difference between D1 and D2, so calculate D2 – D1 for each of our dots and write them in the 4th column on the table.

Step 7

The Time taken is the time to blow the balloon up. Work out the speed V for each dot and put it into the 5th column. Because your “home” dot has not moved, its speed will be zero.

Step 8

We are studying how the speed that galaxies seem to have gets larger for galaxies that are further away.

The best way to see this is to plot a graph showing the distance along the bottom axis and with the speed up the side.

This means that you need to plot a graph with axes like the one below:

speed v distance

Put the points for all your dots on the graph using D2 as the Distance.

Step 9 : What does it all mean ?

Use the ruler to draw a straight line that goes as close to as many of the points as possible (don’t forget the “home” dot!)

Think about the following questions and discuss them:

  • Are the speeds of all the dots the same?
  • If not, do they get faster or slower as they get further from the “home”?
  • What would be different if you had chosen a different “home”?
  • What would have been the same?
  • What do you think this tells you about the way that the Universe expands and the redshift of galaxies?

If you are not sure about some of the questions, can you think of a way changing the experiment to make them easier to answer?

 

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The Twin Paradox

Citation for this article:
Markus Pössel, ” The case of the travelling twins ” in: Einstein Online Vol. 04(2010), 1007

The case of the travelling twins- let’s call them Pat and Mike!- pictures to come!

An article by  Markus Pössel

In Einstein’s special theory of relativity, there is no such thing as “time” in the singular. Time passes differently for different observers, depending on the observers’ motion. The prime example is that of the two hypothetical twins: One of them stays at home, on Earth. The other journeys into space in an ultra-fast rocket, nearly as fast as the speed of light, before returning home:

zwillinge

Afterwards, when the twins are reunited on Earth, the travelling twin is markedly younger, compared to her stay-at-home sibling. The exact age difference depends on the details of the journey. For example, it could be that, aboard the space-ship, two years of flight-time have passed – on-board clocks and calendars show that two years have elapsed, and both spaceship and travelling twin have aged by exactly that amount of time. On Earth, however, a whopping 30 years have passed between the spaceship’s departure and its return. Just like all other humans on the planet, the twin on Earth has aged by 30 years during that time. Seeing the two (ex?) twins side by side, the difference is striking.

So far, so strange, but undoubtedly real. Space-travel with speeds close to that of light may be unfathomably far beyond the reach of current technology. But sending elementary particles on round trips in a particle accelerator at 99.99999 percent of light speed is routine. The result is in precise agreement with the predictions of special relativity – the “inner clock” of such a travelling particle runs much slower than that of a particle of the same species that remains at rest.

Turning the tables?

The reason the case of the travelling twins is also known as the “twin problem” or even the “twin paradox” is the following. From the point of view of the twin on Earth, one can explain the age difference by appealing to time dilation a basic concept of special relativity. It involves an observer (more precisely: an inertial observer), for instance an observer that lives on a space station floating through empty space. For such an observer, special relativity predicts the following: For any moving clock, that observer will come to the conclusion that it is running slower than his own. Whether it is a clock on another space station floating past or a clock on an engine-driven rocket, in the time it takes for a second to elapse on the observer’s own clocks, less than a second will have elapsed on the moving clock. This slowdown is true not only for clocks, but for everything that happens on the moving space station or in the flying rocket. All processes taking place on these moving objects will appear slowed down for our observer.

Characteristically, there are situations where time dilation is mutual. For instance, if there are two observers drifting through space, each on his or her own space station, and if those two space stations are in relative motion, then for each observer, the time in the other space station appears to run slower than for himself. (If that already sounds like a paradox to you, you might want to read the spotlight topic The dialectic of relativity.)

With the help of time dilation – often abbreviated to “moving clocks go slower” – one can try to explain what happens to the twins. No wonder the travelling twin ages less! After all, the twin on Earth can invoke time dilation: Moving clocks go slower, and so do the clocks of the moving twin. On these slower-moving clocks – and, by extension, in the whole spaceship – less time passes than on Earth, in other words: when the travelling twin returns, he is younger.

No paradox so far. But why can’t the travelling twin turn the tables on her sibling? After all, motion is relative. Why can’t the twin in the spaceship define herself as being at rest? From that point of view, it would be the Earth that moves away before returning to the spaceship. And if that is so, couldn’t the travelling twin apply time dilation (“moving clocks are slower”) to everyone who remained on Earth? By that argument, shouldn’t it be the humans on Earth that are younger than expected once the twins are reunited? If both twins are on an equal footing, then each one should be allowed to consider herself at rest and invoke time dilation. But in the end, when the twins meet again, only one of them can be right – then, there cannot be any ambiguity: either the one twin is younger, or the other (or, of course, both twins’ arguments are wrong, and they have aged exactly the same). A contradiction – a twin paradox?

The importance of inertial observers

To resolve the contradiction, a closer look at time dilation is needed – in which situations do moving clocks indeed go slower? In the above text, the key criterion was hidden in parentheses: For the dictum “Moving clocks go slower” to hold, you must be an inertial observer. The example of freely floating space stations above gives a flavour of what this qualification means: In an inertial reference frame, all objects are perfectly weightless. For such observers, an object upon which no external forces act (for instance, that is neither pushed nor pulled) either remains at rest or moves with a constant speed along a straight line.

There’s the litmus test for each twin: Is she an inertial observer, and thus entitled to apply the time dilation formula, concluding that moving clocks go slower?

An unfortunate complication: The twin that remains on Earth is no inertial observer. She’s in a gravitational field in which objects fall down instead of remaining at rest. There are two possible ways to proceed. Either one can use Einstein’s theory of gravity, general relativity, and calculate how the gravitational field influences the twin on Earth. The result is that, in the given situation, the Earth’s gravity does not make an appreciable difference. If we ignore Earth’s gravity and treat the twin on Earth as an inertial observer, our results regarding the relative aging of the two twins will be correct, give or take a few fractions of a second. If we choose situations in which the twins eventual age difference is counted in years, gravity will not matter.

Alternatively, one could re-define the situation by having the non-travelling twin wait not on Earth, but in a freely floating space station in deep space, far away from any massive objects. That would definitely make her an inertial observer.

In both cases, the result is that the non-travelling twin has the right to apply the simple time dilation formula, and to conclude that her travelling sibling will be younger when they meet again.

What about the travelling twin? She’s not an inertial observer, either, at least not the whole time. If she simply would simply coast along with constant speed along a straight line, she could never return to Earth (or, in the alternative version, to the other twin’s space-station). In order to return, it is crucial that the travelling twin either come to a stop and accelerate towards Earth or, alternatively, fire her engine to force her spaceship onto a tight curve to point it back towards Earth. In both cases, the travelling twin feels the acceleration – decelerating, her body feels a pull in the direction offlight, re-accelerating, she is pressed into her seat, in flying a turn, she is pulled sideways. Acceleration is inevitable – and while she is accelerating, the travelling twin definitely isn’t an inertial observer. For instance, during a braking phase, objects afloat inside the spaceship’s cabin will not just float or move with constant speed – they will be accelerated toward the front of the spaceship. And in contrast with the twin on Earth, there is no slight redefinition that will do away with these acceleration phases. There’s no way around it: At least for some of the time, the travelling twin isn’t an inertial observer.

Thus the apparent paradox is resolved. The twins are not on an equal footing. The accelerated twin cannot just apply the simple time dilation formula, while her sibling on Earth can. The latter twin’s conclusion that the clocks of the travelling twin run slower, and that the travelling twin is thus younger when they meet again, is valid. (So what role does the acceleration play in this? Find out more in the spotlight topic Twins on the road.)

Further Information

The basics of special relativity – the proper theory to answer all questions about these twins – can be found in Elementary Einstein in the section Special Relativity.

Related Spotlight topics on Einstein-Online an be found in the section Special Relativity.

This is just a draft, I will sort it when my burnt fingers recover!
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Special Relativity & Web-based Research

Communicating Scientific Results

Here is a chance for you to practice some of the skills required for your Investigation. This task gives you some practice to help with your Researching Physics topic. It is to help you look at ways of communicating and think who you are communicating to.Log all the work that you do for this section in your Researching Physics Log Book.

Objective

You will look at the various ways in which findings can be presented, and appreciate the possibility of using other media such as video clips, articles, papers, posters etc.

Learning outcome

You will be more informed about the different ways in which one topic can be presented. You will begin to think about how to present your own work.

Learning activity

You can work independently or in groups. There are three different resources:

  1. A video clip entitled ‘Two postulates’ (http://www.youtube.com/watch?v=WdfnRWGgbd0).

    If you can’t read the file above it has been uploaded here as an MP4 file.

  2. A physicsworld article entitled ‘Slowed Light Breaks Record’ (http://physicsworld.com/cws/article/news/41246)
  3. The paper

‘On Velocities Beyond the Speed of Light c’ (On Velocities beyond the speed of light c.pdf) On Velocities beyond the Speed of Light

You should examine and discuss the three resources. Teachers should point out that even though the physics content may not all be at the students’ level of understanding, it is still possible to take information from it with their level of knowledge. This is emphasised by you completing the work below.

‘Two Postulates’

This clip discusses how to tell if an object is moving or not by way of an animation.

‘Slowed Light Breaks Record’

This is an article published in physicsworld in December 2009. It is not particularly long, although does contain a lot of information.

‘On Velocities Beyond the Speed of Light c’

This paper was published in 1998 from CERN. It has the more traditional scientific report structure and is a good example for you.

After completing the table on the sheet, you should find that all boxes are ticked – highlighting that even though the information is presented in different ways, all the resources contain what the students will have to put into their own reports.

There are many ways to present scientific findings. You might have written a report in the past but universities may ask you to present a poster of your work.

Here we will look at three different ways of presenting findings on special relativity.

On your own or in groups/pairs, have a look at the three examples of how findings on special relativity have been presented.

Copy and complete the table, either with a few notes or a tick or cross, to show if the example meets the criteria.

‘Two Postulates’ ‘Slowed Light Breaks Record’ ‘On Velocities Beyond the Speed of Light’
Is there mention of the objective for the investigation/experiment?
Is there information given on the experiment/s conducted?
Is there mention of the data (perhaps not all) and any analysis of the findings?
Does the article discuss the conclusion for the experiment/investigation?

Now you have looked at the three examples, ask yourself the following questions.

First impressions
  1. Was one resource more eye-catching than the others?
  2. Does one look like it will be easier to read/understand than the others?
  3. Which one looks most credible?
Down to the nitty gritty
  1. Which resource was the most interesting?
  2. Which one was the best presented?
  3. Which gave the most information?
  4. Did you need to understand everything mentioned to gain an understanding of the experiment?

Which format might you consider for your Communicating Physics investigation?

More information on Web-Based Research

Web-Based Research HApr16 A powerpoint presentation showing how to help you find viable websites

Web-Based Research Student Materials Some materials to give you advice on using websites.

Physics Web-Based Research Worksheets Material that you can work through to give you practice at completing web-based tasks.

 

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ODU Resources

I’ve uploaded the final copy and in both word and PDF versions. The word version needs you to enable macros to work, and your settings might not like that.

OUR DYNAMIC UNVERSE part 1 These are part 1 of the notes in pdf format, so you all ought to be able to open them.

OUR DYNAMIC UNVERSE part 1 These are part 1 of the notes in word format, you can adapt these if you can open them. As they are macro-enabled, you will need to ensure that your security isn’t locked beyond opening!

OUR DYNAMIC UNIVERSE part 2  These are part 2 of the notes in word format, you can adapt these if you can open them.

OUR DYNAMIC UNIVERSE part 2 These are part 2 of the notes in pdf format, so you all ought to be able to open them.

ODU worked ANSWERS_4 Currently the most up to date version of the worked answers.

ODU worked ANSWERS_4 The pdf version of the most up to date version of the worked answers.

I’ll get corrections up as soon as possible, just a bit hard to get it all done.

For those struggling with the vectors try these to give you some practice Great Resource from Mr Crookes. Set up your 2 vectors, either use a scale diagram or components and compare to the given answer. Enjoy!

AH (Doppler)– some of this is relevant to Higher.

africanfastfood This is an introduction to the momentum topic; think about the collision and where the energy is transferred.

4.4 ODU EqoM 2012 this document has the macros enabled. It allows you to check your answers for the acceleration time graphs that you drew from the velocity time graph diagrams.

If you don’t like proving v2=u2+2as from v=u+at then use this neat little sheet from Mr Mackenzie.

using displacement equation to prove the last equation

Collisions- Think Safety before buying a car!

OnVelocities_ This is a document referred to in the Research Task in the ODU part 2 notes.

PHYSICS WORLD ARTICLE DECEMBER 2009 This is a document referred to in the Research Task in ODU part 2 notes

Projectiles thanks to Mr. Rossi for this one.

Battleships & AWACS Projectiles thanks to Mr. Rossi for this one too.

Introduction to the Doppler Effect.

Chapter 1 exam questions B for CFE higher

Chapter 1 exam Answers B for CFE higher

The Expanding Universe

Are we missing something in the Expanding Universe?

HOMEWORK

The homework booklets are now in the HOMEWORK section.

Homework Booklet Complete pp6-8 (first question), 10-16, 18. Complete notes on Units prefixes and Sci Notation, Uncertainties, Equations of Motion. Read up on Forces.

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