particle accelerators

An electric field can be used to accelerate charged particles.

Conservation of energy tells us that

work done by the electric field = change in the particle’s kinetic energy

The speed of the particle can be determined if its charge and the accelerating voltage (potential difference) are known.  The notes attached to the end of this post will show how to perform the calculation.

These short video clips show how to draw electric field lines for point charges and parallel plates, with example calculations for the work done by electric fields and the final speed of charged particles in electric fields.

Q1(a) Electric fields lines around point charges from mr mackenzie on Vimeo.

Q1b – Electric field between parallel plates from mr mackenzie on Vimeo.

Q2 – Work done in moving a charged particle through a potential difference from mr mackenzie on Vimeo.

Q3 – Calculating the speed of a charged particle in an electric field from mr mackenzie on Vimeo.

quarks, leptons and antimatter

At the end of Our Dynamic Universe, we considered big things like stars, galaxies and the Universe itself.  Now the Particles and Waves unit brings us to particles so small we need groups of them just to make a single atom.  Is there a connection?


Why do we study particles? from mr mackenzie on Vimeo.
 

The Standard Model

An elementary (or fundamental) particle is a particle that is not built from other, smaller particles.  Until the start of the 20th century, scientists had believed that atoms were elementary particles.  However, the discovery of the electron (J.J. Thompson), proton (Rutherford), and neutron (Chadwick), together with Rutherford’s evidence for a heavy, positively charged nucleus at the centre of the atom suggested the atom was not an elementary particle after all.

Brian Cox explains in this video clip…

To go further, we have to introduce some particle physics vocabulary.

These new elementary particles are part of our Standard Model of how the building blocks of the universe interact with one another.  The particles that form “matter” are called fermions, after Enrico Fermi  (Fermi has an incredibly long list of things named after him).  The fermions are divided into two groups; quarks and leptons, as shown in the diagram below.

standard model


The Standard Model of Particle Physics. image: The University of Tokyo

Read morequarks, leptons and antimatter

Hubble discovers our universe is expanding

edwin_hubble_with_pipe

In the 1920s, Edwin Hubble had access to the Hooker telescope on Mount Wilson, Los Angeles.  This was the largest telescope in the world at that time.  His first breakthrough was the discovery of a cepheid variable star in the Andromeda nebula.  This enabled him to calculate the distance to Andromeda and he quickly realised this was not a nebula but a galaxy outside the Milky Way.
This video follows his work.

Hubble – nebulae or galaxies? from mr mackenzie on Vimeo.

Hubble then turned his attention to other galaxies, looking for cepheid variable stars that would allow him to determine their distances from the Milky Way.  He used redshift to calculate their recession velocity and plotted a graph against distance.

hubble_plot

He found that the recession velocity (v) was directly proportional to distance (d).  We can express this relationship as

v~=~H_o~d

where H_o is the Hubble constant.  Astronomers agree that the current value of the constant is

H_o~=~72 kms^-1Mpc^-1.

Since this is a  SQA course, we need to convert into SI units – giving

H_o~=~2.3 * 10^-18~s^-1

In this video, Professor Jim Al-Khalili looks at Hubble’s work on the expanding universe.

Hubble’s discovery of the expanding universe from mr mackenzie on Vimeo.

Although he was American, Edwin Hubble transformed himself into a tea drinking, pipe smoking, tweed wearing Englishman during his time as a Rhodes Scholar at Oxford.  He probably wouldn’t approve of this last video.

Unfortunately, astronomers were not eligible for the Nobel Prize for Physics.  The rules have now been changed.

 

redshift

more redshift

 

and Yoker Uni’s video about Doppler and stuff

 

While redshift can be used to tell us about the recession velocity of (non relativistic) galaxies, we also need to find a way to measure the distance to these galaxies.  Astronomers have two main methods to measure these distances; parallax (more parallax here) and cepheid variable stars – there’s a Khan Academy video on cepheid variable stars.

using redshift to map the expanding universe from mr mackenzie on Vimeo.

special relativity

Special relativity is tricky get get your head round.  Let’s start with a video about the speed of light.

This video follows Einstein’s thought process as he worked through his special theory of relativity.

special relativity from mr mackenzie on Vimeo.

time dilation

A Tale of Two Twins from Oliver Luo on Vimeo.

another take on special relativity and the twins paradox

 

…and the Glesga Physics version

 

length contraction

This video has helpful examples to explain length contraction.

Sometimes it’s easier to imagine we’re a stationary observer watching a fast moving object go whizzing past.  For other situations, it’s better to put yourself into the same frame of reference as the moving object, so that everything else appears to be moving quickly, while you sit still.  The muon example in this video shows how an alternative perspective can work to our advantage in Special Relativity.

Another way to think about this alternative frame of reference is that it’s hard to measure distances when you yourself are moving really quickly.  Think about it, you’d get tangled up in your measuring tape like an Andrex puppy.

Screen Shot 2016-02-09 at 23.44.47

image: trotonline.co.uk

It would be far easier to imagine you’re the one sitting still and all the objects are moving relative to your position, as if your train is stationary and it’s everything outside that’s moving.  That keeps everything nice and tidy – including your measuring tape.  Got to love Einstein’s postulates of special relativity.

Screen Shot 2016-02-09 at 23.47.59

image: mirror.co.uk

 

capacitors

You recently completed the topic on capacitors in dc circuits, finishing off with a detailed study of the graphs obtained for current & voltage against time when a capacitor is charged or discharged through a series resistor. There are some additional notes and practice questions at the end of this post but please watch the embedded video clips first.

This introduction to capacitors from the nice people at Make Magazine is a good starting point.

The S-cool revision site has some helpful notes and illustrations on capacitor behaviour; try page 1 (how capacitors work) and page 2 (charging and discharging).

There is information on charging and discharging capacitors on BBC Bitesize.

 

Use your knowledge of capacitor behaviour to explain how a flashing neon bulb can be controlled using a capacitor & resistor arranged in series. Here is a short video introduction to help with that.

Blinking Neon Bulb (5F30.60A) from Ricardo Alarcon on Vimeo.

There are people working to replace heavy battery packs with modern, high capacitance devices called supercapacitors. These supercapacitors have superior energy storage compared to the normal electrolytic capacitors you will have used in class. This video goes one step further and shows the fun you could have with an ultracapacitor. Do not try this at home!

Of course, you can always make your own capacitor with paper and electrically conductive paint.

Finally, you looked at capacitors in ac circuits. You need to know that a capacitor will allow an ac current to flow. The current in such a circuit will increase as the current increases. Mr Mallon’s site has a revision activity about capacitors in ac circuits.

Now download the pdf below. It contains notes to help with your prelim revision and some extra capacitor problems.

Thanks to Fife Science for the original pdf from Martin Cunningham.

internal resistance

Last week, we learned about internal resistance of cells. Page 24 of your printed notes explains how to use a simple series circuit containing a cell, resistance box, ammeter and voltmeter to determine the internal resistance of the cell.  By plotting a graph of your dat, with current on the x-axis and voltage on the y-axis, you can find the internal resistance of the cell.

The video below shows the same type of experiment, but uses a potato and two different metals in place of a normal cell.  Watch the video and note the values of I and V each time the resistance is changed – remember to pause the video each time so you can write the results.  Just scroll back if you miss any.

Now plot a graph with current along the x-axis and TPD along the y-axis.  If you don’t have any sheets of graph paper handy, there is a sheet available to download using the button at the end of this post.  Alternatively, print a sheet from a graph paper site or use Excel to plot your results.

Draw a best-fit straight line for the points on your graph and find the gradient of the line.  When calculating gradient, remember to convert the current units from microamps (uA) to amps (A).

The gradient of your straight line will be a negative number. The gradient is equal to -r, where is the internal resistance of the potato cell used in the video.

You can obtain other important information from this graph;

  • Extend your best fit line so that it touches the y-axis.  The value of the TPD where the line touches the y-axis is equal to the EMF of the cell. (Explanation: on the y-axis, I is zero so TPD = EMF)
  • Now extend the best-fit line so that it touches the x-axis, the current at that point is the short-circuit current – this is the maximum current that the potato cell can provide when the variable resistor is removed from the circuit altogether and replaced with just a wire.