Faraday and Lenz’s Law

Updated website at: http://sciencehsc.com.au 

 

Faraday’s Law of induction states that “The induced electromotive force in any closed circuit is equal to the negative of the time rate of change of the magnetic flux enclosed by the circuit.”
i.e if there is relative motion (or change in flux) between a magnet and a conductor, then an electromotive force (emf) is induced.LightningBoltGeneratesElectricity3
Lenz’s Law says that if an induced current flows, its direction is always such that it will oppose the change which produced it.

The importance of Lenz’s law
Set up an experiment where the north pole of bar magnet is moving into a coil. As there is relative motion between the magnet and the conductor (the coils), an emf is induced by Faraday’s Law. Lenz’s law tells us that the induced emf will flow to oppose the change in flux that induced it, thus it would flow anticlockwise as viewed from the magnet. Now let us consider if the induced current flowed clockwise!

IF the induced current flowed clockwise then the coil would form a south pole (at the end the magnet is entering), and thus attracts the bar magnet, accelerating it. As the bar magnet increases in velocity, so does the magnitude of induced emf, and again it accelerates the bar magnet further. This clearly violates the law of conservation of energy as kinetic energy and electrical energy is being created. That is why induced emf MUST oppose the change in flux that induced it, otherwise it would violate one of the most fundamental laws of physics!

Example:
dia02

From the diagram, we can see a magnet moving towards a coil. By Faraday’s Law as there is a change in flux and relative motion between a magnet and a conductor, emf is induced. As it is a closed circuit, current is formed. This current will flow to oppose the change in flux that induced it by Lenz’s Law. Thus by using right hand grip rule, the current will flow anticlockwise as viewed from the magnet.

As the current will flow to oppose the change in flux that induced it, the current will induce a north pole at X, to repel the magnet. Using right hand grip rule, our thumbs point north and our fingers indicate the direction of current flow. 

The Photoelectric Effect and it’s use in Solar Cells

Updated website at: http://sciencehsc.com.au 

 

When electromagnetic radiation is shone onto the surface of a metal and if the incident photons are of higher work function than the metal, electrons would be physically ejected. This is due to the photoelectric effect. However more detail is required. A photon of higher energy (thus higher frequency, E=hf) than the work function of the metal will elastically collide transferring completely both momentum and energy to an electron on the surface of the metal. This electron will have enough energy to be physically ejected.

It is essential to note that :

  • The energy (or velocity) of the ejected electrons are dependent on the frequency of the incident photons
  • The quantity of the ejected electrons are dependent on the intensity of the incident photons

The threshold frequency is the minimum frequency of electromagnetic radiation to cause electrons to be ejected. Thus below this frequency, no electrons are emitted from the metal. This threshold frequency depends on the metal involved.

The kinetic energy of the ejected electron can be measured using a variation of Plank’s formula.
Energy=Frequency x Plank’s constantWork function of metal

It is also key to note that although Einstein was the first to correctly explain the photoelectric effect with the help of Plank’s idea of the quantisation of energy, it was Hertz who first observed this effect.

Continue reading

BCS Theory explained

Updated website at: http://sciencehsc.com.au 

 

The BCS theory of superconductivity explains that lattice distortions at below critical temperatures lead to the formation of Cooper pairs. Bardeen, Cooper and Schrieffer modelled this theory to successfully explain Type I superconductors.

Type I superconductors are metals which exhibit superconducting properties at below their critical temperature. All of which are below 30K. Note that the BCS theory cannot explain superconductivity in Type II superconductors (made from ceramics and have much higher critical temperatures) as its structure is more complicated.

Examples of Type I superconductors and their critical temperatures:
Zinc – 0.85K
Mercury – 4.15K
Tin – 7.72

As the Type I superconductor is cooled to below critical temperature, the lattice vibrations are minimised. An electron passing through the structure will attract the positive lattice, thus distorting the structure. This distortion releases a phonon (a packet of vibrational energy) and creates a net positive area. Another electron is attracted to this area, absorbing the phonon providing it sufficient energy to overcome electrostatic repulsion and joins with the initial electron, forming a Cooper pair. The Cooper pair acts as one particle and can move through the lattice unimpeded, thus there is zero electrical resistance.

If you have any questions feel free to ask in the comments.

 

Practicals – reliability, accuracy, validity and errors

Updated website at: http://sciencehsc.com.au 

 

ACCURACY (exactness)

Most measurements contain some uncertainty. Accuracy refers to the exactness of a measurement.
We can measure a small distance with a metre rule or with much greater accuracy using a micrometer.

RELIABILITY (dependability)

Reliability refers to the consistency with which we can confirm a result. Consistency is usually achieved by repetition.

VALIDITY (fairness)

A procedure is valid if it tests what it is supposed to be testing. A procedure is invalid if the method of the experiment is incorrect or partially incorrect.
In a valid experiment all variables are kept constant apart from those being investigated, all systematic errors have been eliminated and random errors have been reduced by taking multiple measurements.
In determining validity, students should consider the degree to which evidence supports the assertion or claim being evaluated. This may be done by making comparisons or conducting further experiments.

first-hand information and data

secondary information and data

Accuracy Instruments should be precise and calibrated. Sources should be reputable?
Reliability All tests should be repeated a significant number of times. Information obtained should be consistent with information from other reputable sources.
Validity Experiments should test the hypothesis that is proposed.The experimental method must be correct?All variables should be identified and controlled. Information should be gathered in an unbiased and professional manner.Findings must relate to the hypothesis or problem.

ERRORS

The two different types of error that can occur in a measurement are:

1. Systematic error – this occurs to the same extent in each measurement. EG when the needle of a voltmeter is not correctly adjusted to zero when no voltage is present.

2. Random/Human error – this occurs in any measurement as a result of the variations in measurement technique. Eg parallax error, limit of reading.

Determining ‘g’ – Pendulum Practical

Updated website at: http://sciencehsc.com.au 

Using a Pendulum to determine G

 

Aim:

To calculate and the rate of acceleration due to gravity by investigating the gravitational effects on the oscillatory motion of an average pendulum.

Background:

When a pendulum swings with a small angle, the mass on the end performs a good approximation of the back-&forth motion (simple harmonic motion) the period of the pendulum is the time taken to complete one single back and forth motion.  This depends on just two variables length of the string and the rate of acceleration due to gravity. The mass has a very minute or no affect at all. The formula to find a period is:

               Where  T- is period (s)  i.e. time for 1 oscillation

lis length (m) of the pendulum

 g-is acceleration (m/s2 )due to gravity

Apparatus:

  • Retort Stand
  • Clamp
  • Boss Head
  • String 1- meter
  • Mass Carrier
  • Mass 50g
  • Metre Rule
  • Stopwatch
  • Large Protractor

Screen Shot 2013-04-15 at 8.55.49 AM

Method:

  1. Set up the apparatus as shown in the diagram above.
  2. Collect a mass carrier and tie it strongly to a string.
  3. Pick up the mass carries by the string and have another member of the group carefully measure 1 of the string starting from the base of the mass carrier.
  4. Record the length of the pendulum. Attach the string to the clamp really tightly and ensure that you still have 1 meter from the top to the bottom of the string.
  5. Ensure that the vicinity is free of any obstructions to the swinging pendulum.
  6. If necessary place a g-clamp or excess weight on the retort stand to stop the retort stand from absorbing the motion energy of the pendulum by vibrating.
  7. Reset all stop watches and gently move the pendulum from equilibrium to a measured distance of 15º or less using a large protractor. Ensure the angle of deviation from the vertical is measured properly and is kept the same throughout all trials.
  8. Carefully release of the mass from the deviated angle and allow it to swing for 2-3 swings and lose some of the vibrations that may have been transferred.
  9. Activating the stopwatch as the string oscillation commences a new period.
  10. Continue timing the pendulum until it has moved through 10 complete oscillations (periods) and record the times.
  11. Repeat steps 3 through 9 a total of 5 more times. However before each new set shorten the string by 10 cm of its length. Ensure that the deviation angle is controlled for constancy through all trials.
  12. Use the equation g = 4π2l/T2 and determine g for each result and finally perform necessary calculation to determine the average.
  13. Represent the results graphically by plotting a graph for period squared vs. length. Draw the line of best fit.
  14. Use the gradient of the line and sub into equation g = 2 1/m
  15. Write a conclusion for the experiment and outline which final result is valid and why this is so.

 

Conclusion: Gravitational acceleration was found to be __________ form the result calculations and ________ form graphical solution. These values were ____% off the accepted value of 9.8m/s^2. the independent variable in this investigation was the length of the string and, therefore, the length of the pendulum this is only if the dimensions of the mass carrier are kept constant which in this case were. The reason for starting the experiment from 1 m with 0.1 m in between was to increase the accuracy of measurements and in turn minimise error. Using shorter lengths was not a good idea because shorter pendulums have shorter periods. Since measurements of period were taken with a stopwatch by a timekeeper, the shorter the periods would have been more difficult for the timekeeper to make accurate judgments o when to start and stop. Using the longest strings is very practicable and means that this source of error was reduced in this investigation.

∙ the second dependent variable in this investigation was period of oscillation. For a pendulum in simple harmonic motion (shm) with a small deviation angle, period of oscillation depends only upon the pendulum length and the acceleration due to gravity. The reason for timing 10 oscillations, rather than just one, was to eliminate the errors in judgment associated with panic and mad scrambles during short time frames. Prolonging the oscillations meant that the timekeeper was able to better anticipate the point of closure and, hence, take a more accurate reading of time. A possible source of error in this procedure, however, lies in the division of each recorded time by 10. This was done on the assumption that period of oscillation remains constant for 10 full oscillations, when, in reality, it would decrease over time (since the pendulum would lose momentum through interactions with forces retarding its motion, including air resistance).

 

Evaluation of the validity of conclusions and sources of error

∙ The value for gravitational acceleration calculated in this experiment differed slightly from the theoretical value of 9.80ms-2 published in each of the below texts. One possible reason for this deviation lies in the levels of accuracy of the measuring instruments used. The limits of reading of the instruments, and of the rule and stopwatch, in particular, were a limitation in this investigation, and a barrier to achieving results of utmost exactness and, hence, a conclusion of utmost reliability. Substitution of measuring apparatus of higher levels of accuracy would have improved the validity of the conclusion through minimising absolute errors in both collected and calculated data.

∙ Gravitational acceleration was both a calculated, and a controlled variable in this investigation. The formula above works on the assumption that acceleration due to gravity is a constant. However, it is known that gravitation acceleration changes with such factors as altitude, crustal density and position on the Earth’s surface. For this reason, no change in string length was made without adjusting the boss head and clamp so as to keep the distance between the mass carrier and the ground constant for all trials. Also, the retort stand was always kept in the same position on the lab bench to preserve reliability.

∙Another reason for the discrepancy between the true and experimental values for gravitational acceleration could have been the failure of the investigation to adequately account for the error ranges of measuring instruments in both calculations and the graphical representation. To eliminate this error source, these ranges could have been factored into calculations involving T, T2 and l, giving more exact values of g and bringing greater validity to drawn conclusions. Also, instead of simply taking the average of the 6 values of g as the definitive value, an allowance for error could have been made by determining the greatest residual from the arithmetic mean and expressing the final value as a range, rather than a definite figure. This would have had the added advantage of showing clearly the level of accuracy of the investigation and, hence, giving a truer indication of the reliability of the conclusion.

∙ A possible source of error, and a possible cause for the difference between the value of g calculated in this experiment and the theoretical value, lies in the variations in gravitational acceleration that relate to geographical position. Depending on the thickness and density of the Earth’s crust, proximity to the Earth’s poles and the magnitude of centrifuge forces at any one point on the Earth’s surface, the value for g calculated in this experiment could have deviated by as much as 0.032ms-2 due to factors beyond direct control.

∙ Also contributing to the stated discrepancy could have been inherent faults in the apparatus used, including weak and/or worn components of the boss head, clamp, mass carrier and/or retort stand, as well as frailty of the string, or even a weakening of an otherwise strong string through repeated use. Solutions to this source of error include replacing the string with a fresh length before each new trial and carefully examining and replacing other apparatus where, and when, necessary.

∙ Another reason the validity of conclusions may have suffered could have been the intervention of humans in both the data collection, and the data analysis process. Both systematic, and accidental errors, including those related to parallax, arising from human involvement would have had a negative impact on the reliability of gathered data, the accurate analysis of that data, and the validity of the drawn conclusion. Replacing humans with artificial intelligence in the form of robots and/or computers in the areas of data collection and analysis (for example, having the line graph produced on Microsoft Excel instead of by hand) would have rectified this error source and improved the reliability of the investigation as a whole.

∙ Each time the pendulum is brought from equilibrium back to its extreme of motion before release, it is critical that no, or, at the very least, little tension is lost from the string. By supplying flexion to the string, the mass carrier is given additional potential energy on top of the weight force already being exerted. This means that, on release, the pendulum will have additional and unwanted forces acting on it, resulting in further reaction forces, impulses through the string and the disturbance of harmony in the shm system. This could lead to inaccurate results and an unreliable conclusion.

Robert Goddard – Father of modern rocketry

Updated website at: http://sciencehsc.com.au 

 

In HSC Physics one of the dot points is about a contributor to rocket science. Here is a completed research task (as you may be asked to complete one) of Robert Goddard.

Robert Goddard

Robert Goddard, being born in 1882 in America, is informally known as the father of modern rocketry due to his work on liquid fuels for his rockets. Several years after his death, the US government for $1million, showing how the opinion of society had changed due to scientific discoveries and achievements, bought Goddard’s patents.

Rockets in a Vacuum

In a vacuum, there is no air but rather an absence of any matter. The most special thing about a vacuum is the way the dispersion forces work. Dispersion forces that hold a lot of substances together now work in reverse as the substance attempts to fill the space in which it is occupied (which is boundless). As such there have been serious concerns in the past about whether or not a rocket could travel in a vacuum.

To understand this, an understanding of how a rocket works must be achieved. A rocket works through the Law of Conservation of Momentum (momentum initial=momentum final), and Newton’s 2nd and 3rd laws of motion ( F=ma and every action has an equal and opposite reaction). By this it is meant that a rocket is a reaction engine, what it does, has an affect that in turn powers the rocket. Through combining the equations we get F=(mv-mu)/t (force = change in momentum / time)

The matter is caused by a combustion reaction that releases chemical potential energy and converts this to kinetic energy, moving it out of the engine of the rocket at a high velocity . Despite this matter weighing very little, the velocity that it comes out at means that it has a relatively high momentum, compared to being stationary. This in turn through the law of Conservation of Momentum means that the rocket is moved in the opposite direction to the direction that the matter is thrown out of . Then although the rocket has a reaction force acting upon it, the effect of this force is divided by the time over which it is felt. In some modern rockets the thrust can be greater than 3.3×107 N; however Newton’s 2nd law of motion means that the acceleration of the rocket is the force divided by the mass, significantly lowering the acceleration .

So the contribution from Goddard towards this aspect of rocketry was not the theory, but rather the testing of the theory. He did this through the use of a ballistic pendulum with a rocket and a rocket at first, measuring the height the rocket with rock reached on the pendulum. Years later he tested the theory again through the use of a calibrated spring and firing the rocket into it, calculating the thrust and proving that there needed to be no air to push against for a rocket to provide thrust. This allowed for the commencement into the development of space exploration technologies without the risk of failure and a massive waste of resources.

Liquid Rockets

There are a number of advantages to the use of liquid fuel rockets over solid fuel rockets. These include:

  •  Liquid rockets able to be stopped once started
  • Able to be pumped through pipes
  • Variable thrust
  • Boosters are more re-useable than solid rocket boosters

However there are disadvantages to liquid fuelled rockets:

  • Fragile (they contain many complex parts)
  • The liquid oxygen must be kept liquid (-183’C)
  • Less thrust per size than solid fuelled rockets

Liquid rockets, however, still use combustion reactions. Combustion reactions release heat and kinetic energy when the chemical potential energy is released from the compounds. The rocket immediately uses the kinetic energy, however the sound and heat energy needs to be transferred to another device to convert them into kinetic energy.
Attachments to Rockets

While proving that rockets could work without the presence of air to push against, he also measured the efficiency of which rockets use the chemical energy released by the combustion of various materials. By firing a rocket whilst submersed in water, he found that only about 2% of the amount of energy available in the chemicals being used was actually being used in the thrust of the rocket. This was calculated through the rise in the water temperature, and calculated using the specific heat capacity of water. To solve problem with the waste of energy, Goddard looked at ways of converting this ‘wasted’ energy into the thrust of the rocket. As most of this energy was lost as heat, Gustav De Laval who had designed a steam turbine that could reach speeds of faster than the speed of sound relative to the surface of the earth, had already solved the solution to the loss of heat for Goddard [H1]. This device transferred the heat energy into the turbine, and then converted the heat energy to kinetic energy through using steam [H7]. The use of this steam turbine increased the theoretical efficiency of Goddard’s rockets to roughly 60%, greater than other steam powered turbines due to the temperature at which a rocket operates. This increased the amount of matter being propelled backwards thus increasing the thrust of the rocket, as discussed earlier.

He developed pumps suitable for the rocket fuels, cooling rocket motors and other such contraptions designed to carry man to outer space. Goddard’s prototype rockets reached an altitude of 1.6x103m (1.6km). These inventions have allowed for the commencing research into space exploration and as such have had a significant impact on the space community.

Guided Rockets

Another area that Goddard looked deeply into was that of guided rockets. In this area he used gyroscopes to control the motion of the rocket while it was in flight, steering the rocket with small vanes in the sides of the rocket. This allowed the motion of the rocket to be predicted and a suitable landing point constructed. Gyroscopes work using the law of conservation of momentum, and stay unchanged relative to a set point. This means that if a gyroscope was used and spun around in circles, the centre of the gyroscope would still be unchanged (not spinning) relative to the starting point, even if the rest of the object was.