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IB Physics/Physics and Physical Measurement

Return to IB Physics

1.1.1
Fundamental units are, in general, those which can't be expressed in terms of others (there are exceptions). The seven base units are: Mass(kg), length(m), time(s), electric current(amp) (this is defined in terms of force between wires, but is fundamental in terms of electric circuits), temperature(Kelvin), amount of substance (moles) and intensity of light (candela). The newton is a derived unit, because it is defined as the force required to accelerate 1kg at 1 ms-2. Other derived units include Power (work / time), Pressure (force per unit area), density (mass per unit volume).

1.1.2
Kilogram: A measure of mass, defined by a platinum-iridium cylinder kept in Sevres, France (Though I really can't imagine the IB exam asking that)

Meter: Unit of distance, defined as the distance travelled by light in 1/csec, where c = the speed of light (about 3 x 108 m/sec).

Second: Unit of time, based on the time taken for a caesium atom to vibrate about 9.1 x 109 times.

1.2.1
Vector quantities have both a magnitude and a direction. Scalar quantities have only a magnitude. Vector quantities are those such as displacement, velocity and acceleration. Scalar quantities are mass, distance, speed, work and energy (those last two are important apparently).

"Scalar" magnitude only, can be described by single number and a unit e.g. speed (meter per second) temperature (K), time (sec), mass (kg), density (kg.m-3)

"Vector" magnitude and direction, can be described by two numbers or derived units e.g. velocity (meters per sec), force (N), acceleration (m.sec-2)

1.2.2
Vectors can be represented as lines, where the length is the magnitude and the direction is the direction on the paper.

Graphical representation of vector:

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Length represents magnitude

Arrow represents direction

Vectors can be added by using a scale diagram. The first vector is drawn, then the second from the end of the first, and so on. The resultant vector goes from the beginning of the first to the end of the last (in that direction, not the other way).

1.2.3
Multiplying or dividing a vector by a scalar only affects the magnitude, not the direction. This works just like normal multiplication / division.

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1.2.4
Place the vector as a diagonal of a rectangle. This allows the vertical and horizontal components to be calculated via Pythagoras' theorem and basic trigonometry.

The sum of all the vertical components = the vertical component of the resultant vector and so for the horizontal.

1.3.1
Graphs should be drawn with the dependent variable on the vertical axis (unless the slope is supposed to be a particular unit over another, in which case use that). Usually only the dependent variable uncertainties are relevant, which means you only need vertical uncertainty bars. Make sure to label both axes and title the graph. Draw a line of best fit, which is usually a straight line, but it is not always necessary. Some points may have to be discarded if they do not fit with the rest of the data.

1.3.2
The units of the constant defining the slope of the graph (also called the gradient) will be $$ \frac{the\ units\ of\ the\ vertical\ axis}{the\ units\ of\ the\ horizontal\ axis} $$. The range of possible slopes can be found by taking a maximum line of 'best' fit and a minimum line of 'best' fit using the uncertainty bars.

The intercepts' relevance varies from graph to graph. In general, the intercept is the value of one component when the other is zero, i.e. on a temp (x) vs pressure (y) graph for an ideal gas, the (x) intercept will be at -273.15 degrees Celsius, representing absolute zero.

1.3.3
By playing around with powers (including negative powers) you can get a linear graph, from which it is much simpler to determine the relationship. When you have a straight line which goes through the origin, the unit on the vertical axis is directly proportional to that on the horizontal axis.

1.3.4
Any straight line graph can be put in the form y = mx + c, where m is the slope and c is the y intercept. Note: if c is not zero, then x and y are not directly proportional.

1.3.5
sin(x), or any other repeating functions have the following characteristics:

Amplitude: The difference between the highest, positive y value and the X-axis.

Wavelength: The distance from the top of the crest of a wave to the top of the next crest (or equivalently, the distance between successive identical parts of a wave).

Period: The time required for one cycle. For example, the time for a pendulum to make one back and forth swing.

Frequency: Usually relevant in graphs against time, where frequency is the number of cycles per second. frequency = velocity/wavelength.

1.3.6
Draw bar graphs: Choose the appropriate intervals (they should all be of the same width, not too large or small to mask trends) and then find trends.

Millikan's oil drop: The bars all differ by the same amount (the charge of an electron). The frequency of values may increase or decrease with larger, or smaller values.

1.4.1
Uncertainties: are due to lack of precision in measuring equipment.

Errors: are actual inaccuracies i.e. equipment being mis-used, or mis-measurements.

Uncertainties can come from the fact that a ruler is only marked down to 1 mm. Errors can occur if you misread 15 on the ruler as 14. Uncertainties cause uncertainty bars, errors usually result in the particular piece of data being discarded.

Uncertainties can use different rules. For analogue devices, like ruler, the uncertainty of that device would be half of the smallest increment. For digital devices, the uncertainty of that device would be ± 1 of the smallest increment (or last significant figure).

1.4.2
Random uncertainties result from the randomness of measuring equipment...sometimes The jaws of a micrometer will close one way, sometimes another. They're random, and you can't do anything about them. Systematic errors are those built into the equipment.

1.4.3
Record uncertainty along with data. The minimum uncertainty is half the limit of the reading. i.e. if the measurement is 3.64g, then the uncertainty is ± 0.005g.

1.4.4
Random uncertainties are found by measuring the greatest difference from the arithmetic mean of the values. This decreases, at first rapidly and then more slowly as more data is collected. By using graphs we can obtain a line of best fit which fits within all the uncertainties.

1.4.5
When adding or subtracting, the uncertainty is the sum of the absolute uncertainties for each term. When multiplying or dividing, the uncertainty is the sum of the relative uncertainties (ie uncertainty/value). This can result in large uncertainties being created by performing operations on data with small uncertainties.

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IB Physics/Thermal Physics

=3.1 Thermal concepts=

3.1.1 State that temperature determines the direction of thermal energy transfer between two objects.
Thermal energy is transferred down, from a high temperature to a low temperature.

3.1.2 State the relation between the Kelvin and Celsius scales of temperature
T(K) = t/(°C) +273

To convert temperature in degree Celsius to temperature in Kelvin add 273.15. To convert temperature in Kelvin to temperature in  degree Celsius subtract 273.15.

3.1.3 State that the internal energy of a substance is the total potential energy and random kinetic energy of the molecules of the substance
$$ Internal Energy = Kinetic  Energy + Potential  Energy $$

3.1.5 and 3.1.6 Define the mole and molar mass. Define the Avogadro constant.
=3.2 Thermal properties of matter=

3.2.5 Explain in terms of molecular behaviour why temperature does not change during a phase change.
A phase change is associated with an increase or decrease in the potential energy of a molecule, not the kinetic energy. Hence, there is no temperature change during a phase change.

3.2.6 Distinguish between evaporation and boiling
Evaporation takes place at the surface of the liquid, whilst boiling takes place throughout the liquid.

3.2.7 Define specific latent heat
Specific latent heat is the amount of energy per unit mass absorbed or released during a change of phase.

$$ L=Q/m $$

Whereby,

L= Specific latent heat in Jkg^-1

Q= Energy in J

m= mass in kg

3.2.9 Define pressure
Pressure is the force exerted per unit area. It is measured in pascals.

$$ P=F/A $$

3.2.10 State the assumptions of the kinetic model of an ideal gas.
Assumptions:
 * Newton's laws apply to molecular behavior
 * No intermolecular forces exist
 * The molecules are points
 * The collisions are elastic
 * No time was spent on these collisions

3.2.11 State that temperature is a measure of the average random kinetic energy of the molecules of an ideal gas.
Temperature is a measure of the average random kinetic energy of the molecules of an ideal gas

3.2.12 Explain the macroscopic behaviour of an ideal gas in terms of a molecular model.
=Old Syllabus=

Maxwell-Boltzmann Distribution Curve

The speed (or energy) distribution curve for a gas usually has speed on the x-axis, and number of molecules on y. The curve goes from the origin up to a peak, and then down exponentially as if the x-axis were an asymptote. Higher temperatures are 'flatter' with a lower peak, but a slower decrease beyond it.

10.2.1
Evaporation is the process by which individual molecules escape from a liquid. This occurs with any liquid, and, unless the liquid is in an enclosed system, eventually all the liquid will evaporate.

As the liquid evaporates, it's temperature is reduced. The cooling effect results from the fact that it is the fast moving molecules which escape, leaving behind the slow ones. This means that the average speed of the molecules is reduced, and thus the temperature of the liquid is reduced. This is the principle behind evaporative cooling.

10.2.2
The coefficient of linear expansion has the symbol a, and defines how much the length of an object (say a wire) changes for a give change in temperature. It is used in the equation ΔL = a x L0 x ΔT, where L0 is the initial length, and ΔL is the change.

It is (apparently) important to understand that L0 should appear in this equation. The expansion is a result of molecules moving faster, and thus further apart as they vibrate. As a result, the more molecules there are, the greater the expansion of a given change in them will be, because the space between all the molecules expands.

10.2.3
Thermal expansion of a solid results from increased amplitude of vibrations of the component particles. As the temperature is increased (i.e. heat is added) the particles gain more energy, which becomes Ek (though not translational), resulting in bigger vibrations. Due to this, there is greater space between the molecules, and so the overall solid becomes larger.

10.2.4
The linear expansion equation can be applied in any direction (in most substances), and so it is possible to use it to find expansion in both area and volume. To find the area, just find the expansion in two perpendicular directions, then find the change in area as a result of the two changes. For volume, find the expansion in three perpendicular directions, and find the change in volume.

10.2.5
Making use of thermal expansion
 * Bimetallic strips (where two different strips, with different values of a are bonded in the middle), when heated or cooled, bend over (because the metal on one side is expanding/contracting faster than the other). This can be used to complete or break circuits, and is often used in thermostats (i.e. things which turn a heater on if the temperature falls below, or off it is above a certain temperature).
 * When a ring of metal expands, both the outside edge and the hole in the middle expand (which might not be obvious, but is true). Thus, the 'hole' can be expanded to make a ring fit over something, which then locks tight when it cools. This technique is used in fitting bands around wagon wheels (which is done really often these days).
 * Volume expansion of liquids is the basis for both mercury and alcohol thermometers. As the temperature increases, the volume of the mercury increases, pushing it up the tube.

Overcoming problems with thermal expansion
 * Bridges are constructed of concrete blocks which will expand into one another and shatter if the temperature is increased. To combat this, gaps are left between the blocks, for them to expand into. This is why there are gaps in bridges, and results in that 'thunk, thunk' sound as you drive over them. The same goes for railway tracks.
 * Steam pipes must be allowed to expand, because they have large variations in temp (i.e., when there is vs isn't steam in them). To allow for this, the pipes are connected to 'corner' junctions. These are sort of an L shape, so the vertical pipe can expand up or down in the junctions, and the horizontal one left and right without distorting the shape of the pipe (it also creates a series of short sections where expansion occurs, rather than one long one, which would be harder to deal with).

10.3.1
Thermodynamics is used to describe the relationships between thermodynamic variables in different parts of thermodynamics systems. The primary example of thermodynamic variables are heat, work and entropy but there are many more, such as pressure, volume, surface tension, magnetizability and (molar) concentration. All these changes are studied in the context of the transfer of heat, work and entropy both in and out of systems. Classical thermodynamics is concerned entirely with states of equilibrium, so no quantity with the dimensions of time occur in its equations. Only the direction of time may occur (before, after). 64.134.223.225 (discuss) 02:08, 26 August 2014 (UTC)

10.3.2
Heat and work are both forms of energy, and thus, heating an object or performing work on it causes a transfer of energy. A performing work on B, increases B's internal energy, while decreasing A's and so on.

10.3.3
A system in thermodynamics is something which has a certain amount of internal energy.

Take a block of metal could, for example. Heat can be put into or taken out of it. The concept of work being done on or by it is a bit fuzzy, but possible to imagine.

A fixed mass of gas could also be a system. Heat can go in or out, and if you compress it, you are doing work (and thus increasing the internal energy), If the gas does work (i.e. is allowed to expand but pushing a piston back or something) then its internal energy decreases.

A thermodynamic process is any process in which heat is taken out of, or put into a system, or where work is done on or by it.

10.3.4
If a gas is quickly compressed, then it's temperature is increased. Work has been done by compressing the gas, which has been converted into internal energy. If the gas is then allowed to cool, heat equal to the amount of energy supplied by the work will be released into the surroundings.

The reverse happens if the gas is allowed to expand. Temperature (and internal energy) is decreased, and the system then absorbs heat from the surroundings. To state it another way, work (to expand) is done by the system, resulting in a loss of internal energy, but heat will then be absorbed back in if the system is left do so.

Work is converted to heat (in the first case) and heat is converted to work in the second.

10.3.5
Isothermal : Isothermal processes are those in which there is no change in internal energy ( or temperature ). An example of such a process could be expanding or compressing a gas very slowly, so as work is done on or by the system, heat is absorbed from/released to the surroundings. Thus the temperature remains constant, even though work is being done, and heat is being transferred. In an isothermal process, the work done and the heat transferred out must occur in opposing directions at the same rate.

Adiabatic : Adiabatic processes are those in which ΔQ is zero (i.e. no heat leaves or enters the system). The most common example of this is compressing or expanding a gas very quickly, so there is no time for heat to be transferred. In such a process, internal energy (i.e. temp) changes as work is done.

Isochoric : Isochoric processes are those in which ΔV is zero (i.e the change in volume is zero). In such a process, the work done by the system is zero. An example would be to place a closed tin can containing only air into a fire. To a first approximation, the can will not expand, and the only change will be that the gas gains internal energy, as evidenced by its increase in temperature and pressure. Mathematically, ΔQ = ΔU.

Isobaric : Isobaric processes are those in which the pressure remains constant. A simple example would be heating a pot of water with the lid removed, so that the surface of the water would be subjected to a constant pressure (atmospheric).

10.3.6
Illustrating these thermodynamic processes on P-V diagrams (pressure vs. volume) is another thing which would be much nicer with diagrams.

When work is done on/by a gas, or when heat is transferred into/out of it, both volume and pressure will normally change. Lines of equal temperature on a P vs. V graph curves, have asymptotes to both the x axis and the y axis. Higher temperature curves are further away from the origin.

An Isothermal process will exactly follow one of these temperature curves, since internal energy is constant.

With an adiabatic process, as work is being done on the system, temperature will increase, and so the point on the graph will move 'up' to a higher temp curve. If work is being done by the system, then the point will move 'down' to a lower temperature curve.

Other than that, the resulting curve on a P vs V graph will usually be determine by the nature of the process. Sometimes only Pressure will change (more gas could be added, or temperature could change) and sometimes only volume will change, (temperature could decrease as the volume is reduced, keeping the pressure constant.).

Also worth noting (though I don't know if it's necessary) is that the area under the curve is equal to work done by the system (which gets confusing in the next section).

10.3.7
ΔU = ΔQ + ΔW

This equation relates changes in heat and work to changes in internal energy. The actual signs are a bit of a tricky issue, but can be remembered if we know that a positive ΔU value will result in an increased temperature. Based on this, we then know that temperature will be increased by adding heat to the system, so ΔQ is positive when heat is added to the system.

Similarly, if work is done on the system, temperature will be increased, so ΔW is positive for work done on the system. From this, obviously, ΔQ is negative when heat is released to the surroundings, and ΔW is negative when work is done by the system.

This equation can be applied by substituting in two values, and finding the third. The equation can be simplified in isothermal processes since we know ΔU is zero, and in adiabatic processes since we know ΔQ is zero.

10.3.8
A thermodynamic cycle is where a series of thermodynamic processes eventually put the system back into its initial state, from which the process can be repeated. This idea is used by heat engines, which use a repeated series of thermodynamic processes to produce mechanical energy from heat energy. There are two main types of heat engines (internal and external combustion) which are described below.

External combustion engines : These are the old sort of engines which are used in steam trains. Heat is used to boil water, which turns to steam, increasing the pressure in the pipes above. This increased pressure forces a piston down (the piston being connected to whatever is appropriate for what the engine is doing). Once it is forced all the way down, a valve is released, and the steam is allowed to escape into another set of pipes which eventually return it to the boiler (via a condenser). This reduces the pressure, and the piston is pushed back up, either by other pistons in a cam shaft, or by springs. When it reaches the top again, more steam is allowed in, forcing the piston down again. It is also possible to use a turbine where the steam is used to spin a turbine, resulting in rotational motion (this is often used in power generation). I think that's all we really need to know, internal combustion is the more important one here.

Internal combustion engines : These are the type commonly used in cars today, where the petrol is actually ignited in the cylinder. They are known as 4 stroke, because the process occurs in two cycles (two up strokes, and two down strokes). The piston begins at the top of the cylinder, moving down. The intake valve is opened, and so a mixture of fuel and oxygen is sucked into the cylinder. When the piston reaches the bottom, the valve is closed, and the piston moves up, compressing the mixture until the piston reaches the top. When the piston is at the top, the spark plug fires, igniting the mixture, producing high downward pressure on the piston. This pressure pushes the piston down (this is where the actual work is done by the engine). When the piston reaches the bottom, the exhaust valve is opened and as the piston moves up the exhaust is pushed out. After reaching the top, the exhaust valve is closed, and the intake valve opened (bringing us back to the start). All this can be expressed on a P-V diagram (anyone want to draw it?). There will be a diagram in most physics text books in the meantime.

10.3.9
Entropy (symbol S) is a measure of the disorder in a system. There's a big complicated explanation relating to probability, meta-states and information theory, but I don't think it's necessary. Basically, entropy always increases. It can be decreased in a system, but it will increase in the surroundings of that system as a result. This is the second law of thermodynamics; natural systems tend to move towards a state of greater disorder. In energy terms, increased disorder is energy being more evenly distributed. If there is a point of high energy, and a point of low energy, it is possible to use this difference to do work, entropy tends to decrease this difference. To put it another way, energy tends to spread out evenly rather than concentrating at one point.

10.3.10
Natural systems tend to move towards a state of more disorder (second law of thermodynamics). What this means is that you can't build an engine which will convert 100% of the energy put into it into work (i.e. no engine can be 100% efficient). The first law, for example, suggests that a block of wood sitting on the table could convert some of it's heat energy into work and jump off the table, but the second law says it isn't going to happen (not that it couldn't, just that it's really, really unlikely).

Also, since it doesn't fit in anywhere else, but is in the data book, the equation ΔS = ΔQ/ΔT allows the change in entropy to be found (where Q = heat, and T = temperature). This is actually a calculus equation, but for small changes in T, it's a good enough approximation to use average temperature.

10.3.11
Refrigerators : The basic idea is to do work to over come entropy, producing an area of lower temperature inside, and higher outside. This process occurs with a set of pipes running along the outer wall, and the inner wall of the system. Low pressure (and so cold) gas runs through the inner pipes, which absorbs heat from the inside of the refrigerator. This gas is then pressurised using a condenser (a piston) and pumped through the outside pipes. Because this gas has had work done on it, heat escapes from it to the outside of the refrigerator. The gas is then slowly allowed through a valve connected to the low pressure pipes to be recirculated. In this way, heat is transferred from the inside to the outside, even though the temperature inside is already lower. This may seem to violate the second law, but the overall entropy of the universe is actually being increased, because energy is required to make it happen (to drive the condenser). The efficiency of such a system is defined by the equation Efficiency = QH-QL / QL, where efficiency is the efficiency of the refrigerator (1 is perfect, or 100% efficient), QL is the low (inside) temperature, and QH is the high (outside temperature).

Heat Pump : A heat pump is a special form of a heater, usually installed together with air conditioning capabilities in an HVAC system when the expected climatic variations make it more economical than to intall and use a direct heater. Rather than rely on pure generation of heat, a heat pump moves heat (more accurately: thermal energy) from one place to another. A heat pump works by doing work to move heat from the cold outside to the hotter inside. It is just the reverse of the refrigerator described above. The efficiency of such a pump will be Efficiency = QH-QL / QH, working as above.

Note that in each case, this equation is like the one in the data book, but the denominator will have to be chosen based on what the particular process is supposed to achieve.

10.3.12
If we feel like getting all philosophical about things, entropy can be thought of as what defines 'forward' and 'backward' for time. As time progresses, entropy increases and so it lets us think about time as going forward when entropy is increasing. As above, heat pumps and refrigerators are capable of lowering entropy in a system, but increase it for the whole system + environment. When ice (or something else) melts it is absorbing heat, and thus entropy is increasing. The movements from solid to liquid to gas also mark an increase in entropy, as particles are moving more and more randomly.

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title: IB Physics/Thermal Physics


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IB Physics/Oscillations and Waves

4.1.1
"Describe examples of oscillations."

Simple harmonic motion is defined as...

1. When the body is displaced from equilibrium, there must exist a restoring force (a force that wants to put the body back in equilibrium)

2. This restoring force must be proportional to the displacement of the body

Examples of oscillations include :
 * The motion of a mass at the end of a spring after the mass has been displaced away from its equilibrium position;
 * The motion of an aeroplane wing;
 * The motion of a tight guitar string that has been set in motion by plucking it.

"Key IB Definitions."

Wave: Propagation of energy through a material substance. Displacement: The distance of the oscillating object from equilibrium. Amplitude: The maximum distance from equilibrium an oscillating particle reaches. Frequency: The number of complete cycles of an oscillating particle per unit time. Period: The amount of time it takes an oscillating particle to complete one cycle( an oscillation). Phase Difference: The measure of how "in step" different particles are. If they are moving together they are said to be in phase. If not they are said to be out of phase. Refraction: The bending of waves through materials due to a difference of speed (change in velocity). Diffraction: The bending of waves through a small opening and around corners. Waveray: The direction of energy propagation. Wavefront: Series of particles in phase. Wavelength: The distance between two successive wavefronts for travelling waves or The distance the wavefront moves in 1 cycle for travelling waves.

"3 Types of waves."

Transverse Waves: The particle motion in this wave is perpendicular to the direction of energy propagation(transfer). The particles in this wave are oscillating up and down while the energy is propagated perpendicularly. It is important to note that a larger amplitude denotes greater energy. Electromagnetic waves and shallow water waves are both transverse waves.

Longitudinal Waves: The particle motion in this wave is parallel to the direction of energy transfer. It is key to note that the energy and particles move in the same direction. All sound waves are longitudinal waves. *It is important to note that sound waves graphs can look similar to transverse waves but they are always longitudinal*.

Standing Waves: Standing waves are formed when 2 waves travel towards each other(eg. incidental or reflected) with the same speed and similar amplitude as energy can be lost. The wavelength is the same and there is no net energy propagation. Standing waves have particles which remain stationary called nodes. The average speed of each particle is not the same at one cycle. The anti-node will be the fastest as it travels the farthest in one cycle. The distance between adjacent nodes or anti-nodes is half a wavelength. Microwaves are an example of standing wave. In a microwave, standing waves are established which is why a turntable is necessary.

Students must understand the equation: $$f=\frac{1}{T}$$, where f is frequency and T is period.

$$\lambda = \frac{v}{f}$$ where λ is wavelength, v is the wave speed, and f is the frequency. The equation is the equivalent of that given in the data packet, which is:

$$v = f\lambda$$

Wave speed : The speed at which a given point on the wave is traveling through the medium (i.e. how far a particular crest travels in a second).

Crest : Relevant only for transverse waves, this is the point of highest positive displacement (i.e. upwards) from the mean position.

Trough : The point of largest negative displacement (i.e. downwards) from the mean position (in a transverse wave).

Compression : If a compression (longitudinal) wave is drawn like this || | | | | || | | | | || | | | | ||, the compressions are where the bars are close together. Specifically, it is where the particles are most compressed in the wave.

Rarefaction : The opposite of a compression, i.e. where the bars (or particles) are most spread out.

Different graphs of waves.

Displacement vs time : This graph tracks the movement of a particle as a wave moves through it. With displacement on the vertical axis, and time on the horizontal. The particle will move up and down in a sine curve type pattern. The highest point is called a crest. The lowest point is called a trough.

An example of a displacement vs time graph for a wave

This type of graph allows us to find both frequency (which will be the number of crests in 1 sec) and period (which will be the time between crests). Note that the frequency and period have an inverse relationship. We can also find amplitude (the maximum distance that the wave travels) using this graph. This kind of graph tells us nothing about the wave speed or wavelength.

A demonstration of how to find the period and amplitude on a distance vs time graph

Displacement vs position : This is basically a 'snapshot' of the displacement of all the particles going through the medium at a given time. Displacement is on the vertical axis, and position (or ie distance from an arbitrary origin in the material) is on the x. The distance between peaks represents the wavelength. The wave speed can not be calculated directly from this graph, but can be found by combining the information from this and the displacement vs time graph (as described in the next section).

An example of a displacement vs position graph for a wave

4.1.5
v = f × λ (wave speed = frequency × wavelength)

This equation can be used to find the speed of a wave given it's wavelength and frequency. Deriving this is really rather obvious, but described below.

If the unit of frequency is cycles/second and wavelength is meters/cycle, then when the two are multiplied, cycles cancel out, and we're left with meters/second, which is the unit of wave speed, and so the equation follows from the definitions of frequency and wavelength.

Note, the frequency for a given wave is constant (defined by the source) thus, if the wave speed changes (due to changing mediums) then the wavelength also changes, but frequency remains constant.

4.1.6
Electromagnetic waves are transverse waves, travelling at a wave speed of c (the speed of light = 3 × 108 m/s) when in a vacuum (they can travel without a medium unlike all other waves).

There are different wavelengths that transverse waves travel at. The spectrum of different wavelengths have been divided into different sections. They are commonly given the following names (in order of increasing frequency and decreasing wavelength).

 * Radio waves
 * Microwaves
 * Infra-red waves
 * Visible light
 * Ultraviolet waves
 * X-rays
 * Gamma waves

The easy way to remember this that our physics teacher taught us was "Red Monkeys In Vegas Usually X-ray Girls." This goes from lowest frequency to highest.

Going down the original list, frequency decreases and wavelength increases (because since v=λƒ and c remains constant). The amount of 'energy' in the waves decreases down the list, which is why X-rays are dangerous, and radio waves aren't.

Visible light is split into colours from violet to red, violet having the highest frequency and red having the lowest. Visible light ranges from 400nm (1 nano meter is 1 × 10-9 meters) for violet to 700nm for red.

Electromagnetic waves are usually defined by their wavelength in a vacuum (which seems rather silly, since frequency never changes, frequency and is what defines the characteristics (i.e. color)) but who am I to argue.

However weird it may sound, a Microwave oven at Earth does not emit the same wavelength of wave as one in space. There is a difference between the two locations, albeit a small difference. This is because light travels more slowly when it travels through a medium such as air; all electromagnetic radiation is slowed to some extent by the medium it is passing through. That small difference may correspond to millions of light years in determining the distance of stars, so it is, in fact, very important to refer to vacuum values all the time just for setting a common ground for experiments.

Vacuum is chosen as the common reference point because all electromagnetic radiation, no matter what the frequency, travels at the same speed in vacuum. As mentioned, the speed of light is slower when it's traveling through something, and higher-energy radiation is slowed down less. It is only in vacuum that it all travels at the same speed no matter what the frequency or energy is.

4.2.1
During SHM, the pendulum swings from left to right and back the same way. When the pendulum reaches it's highest point or highest amplitude, it is momentarily at rest and has zero kinetic energy. The kinetic energy it previously possessed when it was moving has been converted to potential energy at this high point. When he swings back down, the potential energy is changed back to kinetic energy and this is highest at the equilibrium point. At this point, though, there is zero potential energy. This model also follows the law of conservation of energy. On a pendulum, the period is independent of mass. Period on a pendulum only changes by the length of the string and the force of gravity. By shortening the string, the time decreases and the frequency increases.

Longitudinal waves travel in one dimension, and so when they strike a boundary, they will be reflected back in the same direction, though the will experience a phase change (i.e. when a compression hits the boundary, a rarefaction is emitted back from it, and vice versa.

This also applies to standing waves travelling in a stretched string. If both ends are connected to a boundary, then nodes (points where the string doesn't move up and down) will occur at both ends, and a number of antinodes will occur through the string, separated by nodes.

In an air column, it is possible to have both open and closed boundaries. At an open boundary, and antinode will occur, while at a closed one a node will occur.

4.2.2
Whenever a wave is reflected from a boundary, the angle of reflection will equal the angle of incidence. Thus, if the wave strikes the boundary at 90°, then it will be reflected straight back, but other angles will reflect the waves away from the source.

Note that it is common for waves to travel in a full, or semicircle out from the source rather than in one line, which complicates reflection, because each wave is entering at a different angle.

Also, curved boundary's must be handled. The basic technique here is to draw in a few important lines representing different waves, see where they would reflect to, and then fill in the rest.

When waves in water strike a boundary, the crests will be reflected as troughs, the same goes for sound. Phase changes in light are a little more complex, but we'll come to those later.

4.2.3
Waves can be refracted when they move from one medium to another, and when they have different wave speeds in these two media. It is easiest to consider this as a series of wavefront lines entering a boundary at an angle. The frequency (the time between lines) must remain constant, but the speed slows (so they must become closer together). As they enter at an angle, the wavefront on one side slows down first, which effectively pulls the entire wave around towards that corner. In ray diagrams, light simply enters at one angle to the normal, and leaves the boundary at another (we get to how to find these angles next).

This phenomena can have some weird effects. When looking into a swimming pool, light from objects at the bottom is diverged (refracted away from the normal). this means that when the virtual rays are traced back, a virtual image is formed much closer to the surface than the actual object (apparent vs real depth).

4.2.4
The angles described above can be found with Snell's law.

n1 × sin i = n2 × sin R

n1 is the refractive index of the initial medium (vacuum = 1, air = 1 (or close enough to 1 that it doesn't mater)), and n2 is the index of the medium it's entering. i is the angle of incidence, and R the angle of Refraction, both of which are measured from the normal.

When light goes from a more to a less dense medium, then there comes a point where the angle of refraction will be 90°. The angle of incidence where this occurs is called the critical angle. If the angle of incidence is above the critical angle, then the light is totally internally reflected. Angle of incidence = angle of reflection applies, and the light is reflected from the boundary.

Unusual examples of this include water ripples travelling slower in shallow water, and sound travelling at different speeds through hot and cold air. Most of the time, though, the problems relate to light entering / leaving water or a glass prism.

4.2.5
When two waves are moving in the same medium, the displacements of the particles add together. It is therefore possible for two waves to produce one wave of larger amplitude, or to produce two waves where the total amplitude is zero. Note, the waves and energies are still there, it's just that the two waves are adding to zero.

Questions about this generally involve two waves traveling in opposite directions down a string (they're usually rather easy).

4.2.6
Principle of Superposition: The principle of superposition states that the resulting displacement of the interference between 2 waves is the algebraic sum of the displacement of each wave. Principle of superposition describes the combination of overlapping waves or wave interference.

Supercrest: When a crest overlaps with a crest

Supertrough: When a trough overlaps with a trough

Constructive Interference: If the result of 2 waves interfering is a greater displacement in the medium, constructive interference has occurred (eg. The formation of a supercrest).

Destructive Interference: If the result of 2 waves interfering is a smaller displacement in the medium, destructive interference has occurred (eg. an equal trough and crest interfering).

Resonance: Large amplitude vibration that is the result of a force that is applied at the same frequency as the object's natural frequency.

Natural Frequency: The frequency at which an object wants to vibrate at without external influence. The natural frequency of a human head is 7Hz.

Beats: The constructive or destructive interference of 2 waves. Beats is the change in amplitude in soundwaves. The beats can heard when the sound goes from loud to quiet to loud or when it goes from quiet to loud to quiet.

Beat Frequency: The number of beats per time or the absolute value of the change in frequencies. eg. If frequency 1 is 1012 Hz and frequency 2 is 1024 Hz, the beat frequency is 12 Hz.

Doppler Effect: The apparent change in a wave's frequency and the wavelength due to the relative motion between the source and the observer. If a wave is blue shifted, the electromagnetic waves are getting shorter. If a wave is red shifted, the electromagnetic waves are getting larger. As the source of the sound approaches me, the higher pitch frequency becomes a lower pitch frequency.

4.2.7
Young's double slit experiment is basically where two slits act as point sources, and form a diffraction pattern, thus demonstrating the wave nature of light. When light is shone onto the backs of the slits, they act as point sources which are initially exactly in phase. Light from each of these travels to a screen, striking it and producing light on it.

The issue is, however, that the light from each slit has to travel a different distance to reach the screen. When the difference between these distance is exactly N × wavelength + 1/2 wavelength of the light, the two waves will destructively interfere and produce a dark spot on the screen. When the difference is a multiple of the wavelength, the two waves arrive in phase, and produce a bright spot.

The resulting pattern is a series of bright and dark bands when monochromatic light is used. When white light is used, different colors will construct and destruct at different points, producing a series of spectra which will eventually overlap as we move away from the centre. In both cases, the center point will have a bright spot, of the original light colour.

The equation for this experiment is given in the optics section of the data book. m × λ = a sin Θ, or the order of the band × wavelength = the distance between the centres of the slits × sin of the angle of the bright band.

Since there are a series of bright bands, different values of m can be substituted. m=0 gives the central bright band, then m=1,2,3,4...give the subsequent band angles.

4.2.8
When two waves which have different frequencies interfere, beats will be heard. The beats are points where the amplitude (volume in the usual case of sound) reaches a peak. The frequency of the beats can be calculated by fbeats = |f1-f2|. Meaning the beat frequency will be the difference between the two frequencies.

This can be seen by drawing two sine curves, say sin x and sin 2x, then adding them. Both high and low points will be found, showing the beats (any graphing calculator will show you).

4.2.9
Diffraction of waves.

Water : When there is something blocking waves in the water, say, a log floating in it, immediately behind the log will be calm water, but eventually the waves wrap around it. This is due to diffraction, meaning as the waves go through, the motion of the particles affect those, not just in the direction of propagation, but also to the side, allowing the wave to spread to the side as well as forward. If waves were passed through a thin slit, they would form a semi circle point source, just like light in the double slit thing.

Sound : Just like water, sound can trace around obstacles, and join back up on the other side, or pass through a thin slit and form a sort of point source. This also shows that both longitudinal and transverse waves act in the same way with respect to diffraction.

Light : As was seen in the double slit experiment, light can be diffracted through a thin slit. Because it moves so fast, we tend not to notice light waves bending around corners, but it can.

4.2.10
Polarisation : Light naturally travels as a transverse wave in all planes, i.e. the 'particles' move left and right, up and down, and at every angle between. It is possible to cut out all but, say, the up and down motion. Light to which this has been done is called polarised.

(More info is in the Optics section if you think you need it.)

4.3.1
Standing waves occur when 2 waves travel towards each other (eg. incidental and reflected) with the same speed and similar amplitude (energy can be lost). There is no net energy propagation.

At a closed boundary, a node (particles which remain stationary) will always be formed, and a antinode will occur at an open boundary. This can occur in a stretched string, or in an air column. Standing waves in air columns can also be referred to as resonance in air columns.

In the first case where the column is opened at one end, the closed end will have a node and the open end will have an antinode. In the first harmonic of an open-end column, the distance is one-quarter wavelength. This is easy to remember when considering that the distance between a node and an antinode is one-quarter wavelength. To get the length of an tube open at one end, you continue to add one-quarter wavelength to the existing length.

In the second case where the column is open at both ends, both the open ends will have an antinode at each node. Between the two antinodes, there is a node. The length of the column will be half wavelength. This is easy to remember when considering that the distance between two antinodes is half wavelength. To get the length of a tube open at both ends, you continue to add half wavelength to the existing length.

To calculate the frequency of a tube, the following formulas can be used.

2 Ends Closed

Frequency = (Harmonic Number)(Fundamental Frequency)

1 End Closed

Frequency = (2n-1)(Fundamental Frequency)

n is the harmonic number

2 Ends Open

Length = [(2n-1)(Wavelength)] ÷ (4)

n is the harmonic number

In each case, the fundamental frequency is the wave with the longest wavelength which satisfies this (i.e. the lowest frequency). After this, harmonic frequencies can be found by adding half a cycle into the string/air column. With two closed boundaries, the fundamental wavelength will be 2 × the length, with one open, one closed, 4 × length, and with 2 open, 2 × length.

All objects have a natural frequency at which they will most naturally resonate. When a source produces such waves into this body (or medium) then it will vibrate 'in sympathy' with it. When this occurs, the amplitude of these vibrations will be at a maximum.

With two closed boundaries, the fundamental wavelength will be 2 × the length. with one open boundary and one closed, 4 × length, and with 2 open boundaries, 2 × length.

The first, second and so on harmonics can be found by adding 1/2 of a cycle in to the diagram, so with one open, one closed, we have 3/4 of a cycle in the pipe, so the wavelength is 4/3 × length. This applies to all other types (2 open and 2 closed), and allows the wavelength to be found. We can then calculate the frequency given speed or vice versa, etc.

title: IB Physics/Oscillations and Waves


text:
IB Physics/Electric Currents

5.1.1
There are two types of charge, positive and negative, and they are the opposite of each other. Positive charges are attracted to negative charges and vice versa, but like charges repel.

Conductors are capable of moving charge in the form of electricity, while insulators will not allow charge to flow through them. This means that when drawing an arrow diagram of the charges, the arrows will go to the center of a conductor, but only to the surface of an insulator.

Insulators are capable of storing charge on their surface. Perspex or ebonite rods can become charged by rubbing them against fur, though they acquire opposite charges.

5.1.2
Electric charge will be conserved, always. If one thing gains a positive charge, then something else must have become negative as a result.

5.1.3
Electrostatic induction is what causes uncharged pieces of paper to 'jump' up to a charged rod. By holding a negative charge above it, the negative charges in the paper are repelled (pushed down), while the positive charges are pulled up. This creates an effective opposite charge on the paper (the reverse happens with positive charged rods), which creates a force of attraction, and pulls the paper up.

The same principle can be applied to an electroscope. When a positively charged rod is brought close to the top, positive charges in the electroscope are repelled away from the rod. This creates a positive charge at the bottom in both the gold leaf and the center shaft, and since the like charges repel, the leaf jumps up. If the electroscope is then earthed, negative charges will neutralize the top of the electroscope, giving it a total negative charge, and thus the leaf stays up even once the rod is taken away.

5.1.4
Inductively charge a metal ring attached to an insulated handle. Then use a charge detector (sort of like a compass only in 3D) to see if there's any charge changing its direction. We should find that it doesn't, illustrating that the inside of a hollow charged surface will not have any net charge (and thus field).

5.1.5
Lightning rods: They conduct lightning more easily than a building, so it goes down the rod rather than the building.

Fires in air-planes: If static charges build up during flight, then it could cause sparks as the plane is being fueled, so the plane is earthed first. The same thing goes for oil tankers.

5.2.1
Coulomb's law: $$F = \frac{1}{4 \pi \varepsilon_0}\cdot \frac{Q_1 Q_2}{r^2}$$

The force is proportional to both the charges, and there is an inverse square relationship between force and the distance between them (so the force gets weaker as the distance, or radius, increases). Charge is measured in coulombs, which is a derived unit describing a flow of 1 Ampere per second (and a lot of charge, a since electron's charge is 1.6 x 10-19C). $$\varepsilon_0$$ is the permitivity of the free space, and is equal to 8.85 × 10−12 Farad per metre.

5.2.2
If an electric charge experiences an electric force then it is in an electric field. The equation E = F/q allows the strength of an electric field, in NC-1 (Newtons per Coulomb), to be found based on the force experienced by a given charge.

5.2.3
Electric field lines go from positive to negative (it's like the old days of conventional current, before they knew about electrons). They describe the effect on a hypothetical positive test charge placed anywhere around the object. These are relatively simple, but really need diagrams to explain (any volunteers want to draw them?). One important point is that field lines always strike a surface at 90 degrees, so make sure to get that right. The following features are common on these sorts of diagrams.

Isolated point charge : Lines go towards, or away from the point. Moving further away, the lines are further apart, representing a weaker field.

Two like point charges: The two charges repel each other's field, and so near each point charge, it is like a single point charge, but in the center, there is an area of no charge.

Two opposite point charges : There is a line straight from one charge to another, then the others come out as normal, but are bent towards the other point charge.

Pair of charged plates : I think we only have to deal with oppositely charged plates. The lines run straight down or up as appropriate, but at the end, some curve is introduced to account for the 90 degree thing as mentioned above.

Equipotential lines : These lines run perpendicular to these field lines, and mark areas of equal potential.

5.2.4
Potential difference (V) is defined as the work done by moving a positive charge from one point to another in an electric field without acceleration. The equation ΔV = ΔW/q, allows the potential difference to be calculated.

5.3.1
Electric current is defined as the amount of charge passed divided by time, and its unit is the ampere. It is usually used in relation to electric charge, where electrons are flowing, often through a wire, which also applies through a vacuum (cathode rays) or in relation to positive ions flowing through something.

5.3.2
In a metal electrons are free to move, although the atoms are held in a reasonably strong, though mobile lattice. As electrons flow through a metal, they 'bump' into the metal atoms, explaining resistance, and the fact that metals may heat up when electricity flows through them.

5.3.3
Electromotive force (emf) : The voltage produced by a reaction in a battery is called its emf (it also applies to any electrical current source, i.e. induced by a magnet etc.). Some of the energy produced is wasted inside, and so a battery with an emf of 3 V may only have a potential difference between its terminals of 2.5 V. The electromotive force is usually referred to as just emf in order to not cause confusion since the emf is not an actual force.

5.3.4
Potential difference : The energy dissipated per unit charge (measured in volts). If the potential difference across a battery is 12v, this means that each coulomb of charge will 'spend' 12 joules of energy going around the external circuit.

5.3.5
Resistance is defined based on potential difference and current as R = V/I, so you can sub in any two values and get the third. Resistance is measured in ohms.

5.3.6
Factors affecting resistance:

 * Length : Resistance increases with the length of the conductor.
 * Cross sectional area : Resistance decreases as cross sectional area increases.
 * Type of conducting material : Well, it's just going to vary. Metals tend to be good conductors.
 * Temperature : As the temperature increases, the resistance also increases for ohmic materials. On the increase of temperature, resistance of semi-conductors decrease.

5.4.1
The circuit symbols are in the front of the data book, though I don't see where transistors or logic gates come into things. Still, it's all fairly obvious. Drawing them is basically a matter of practice, not something we can really explain here. Volunteers to draw up some examples?

5.4.2
Non ohmic conductors are those which don't follow ohm's law ( V = IR ) when the temperature is not kept at a constant (and relatively low) degree. An example of a non-ohmic conductor is an ordinary light bulb. As the filament in the bulb is heated up the resistance increases, giving a non-linear relationship between voltage (V) and current (I).

5.4.3
Electrons flow from the negative terminal to the positive, where as conventional current flows from the positive to the negative. They go in opposite directions because conventional current was invented before anyone knew about electrons. Which one you use doesn't really have any major effect on simple circuits.

5.4.4
A resistor is something which turns electric energy into heat when electricity runs through it (due to electrons 'bumping' into metal ions). Internal resistance refers to the resistance inside the source (like the difference between emf and potential diff).

5.4.5
If resistors are in series, then the total resistance is given by
 * $$R_t = R_1 + R_2 + ... + R_n$$

If resistors are in parallel, then the total resistance is given by
 * $$\frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} + ... +\frac{1}{R_n}$$

This then creates a simple series circuit which can be solved with V = IR.

In a series circuit, the current is constant throughout the circuit, but the voltage is shared between the resistors. In parallel, the current is split between each branch (relative to its resistance) and the voltage in each branch is equal to the voltage across the whole parallel branch.

Once each parallel section has been calculated, and then the whole circuit has been done in series, the information can be put back to calculate the current or voltage in each section of the parallel branch.

5.4.6
work = charge x potential difference and charge = current x time.

Thus, subbing the second into the first, we get W = ItV.

Divide by t, and since power equals work/time, we get P = VI

Substitute in V = IR, giving P = I2R.

Alternately, substitute in I=V/R and we get P = V2 / R

These can all be applied as required. Power is measured in watts (or joules per second), work in joules, time in sec, PD in volts, current in amps and charge in coulombs.

5.4.7
Ammeters should be used in series with the part of circuit for which you want to find the current. An ideal ammeter would have an infinitely small resistance, as to not change the circuit.

Voltmeters should be used in parallel, branched over the part you want to find the potential difference between. An ideal voltmeter would have an infinitely large resistance, as to not change the circuit.

5.4.8
Electricity is generally sold in kilowatt-hours, which have a particular price. Different devices draw different amounts of power, generally given as X kilowatts. If the device runs for 1 hour, then it uses X kilowatt-hours. If it runs for 2 hours then it uses 2X and so on.

When current flows through an appliance, heat is produced, some appliances (kettles, heaters) use this fact (I don't know why this is here, but the syllabus points it out).

5.4.9
Fuses are short pieces of low melting point wire. They are placed in a fuse box, and complete the circuit, but if the current rises over a certain point, the heat produced in the fuse (due to it's resistance) melts the fuse, and breaks the circuit. Circuit breakers work on a similar principle, except they act much faster.

Fuses are used to prevent overheating in other areas of the circuit, which could otherwise cause fires, while circuit breakers (aka overload cut-out systems) are designed to prevent electrocution. Earth-leakage detectors are designed to detect current escaping from the circuitry, and so also help prevent electrocution.

5.5.1
Magnetic fields flow in circles through & around a current carrying wire. If you point your RIGHT HAND thumb in the direction the current is going, your fingers curl in the direction of the field rotation. This "RIGHT HAND RULE" is based on "Electron Flow"; negative to positive.

Note that, in diagrams, the symbol X is commonly used for a current going into the page, and a dot for current coming out of the page. The same convention is used for fields going into or out of the page.

5.5.2
The magnetic field around a solenoid (coil of wire) runs through the center and loops around and back to the other end (Diagram anyone ?). The polarity of each end can be recalled by drawing the letter N (for north) and putting arrows on the ends. Thus, if the current is going around anticlockwise looking down from one end, then a north pole will be at that end, otherwise it's a south pole. Field lines go from the north pole to the south.

5.5.3
Moving further away from a current-carrying wire, the equipotential lines get further apart, because the field is getting weaker. When they are close together, the field is stronger.

5.5.4
The magnetic field produced by a solenoid depends on the current running through it (increases with increased current), The number of turns of wire (an increased number of turns gives an increased magnetic field strength). The substance at the core of the field can also have an effect, though it depends on the core's nature.

5.5.5
The force on a current carrying wire in a magnetic field can be found by again using your RIGHT HAND. The palm is force, thumb is current and fingers (at right angles to thumb) are field direction.

5.5.6
When we have two long wires, the fields are just like single wires. This allows us to work out which way the field from each wire is acting on the other, and so the force. If you want to just remember it, when the current is running in the same direction, attraction occurs and when it's opposite, repulsion occurs.

5.5.7
An ampere is defined as the current which produces a force of 2 x 10-7 N of force per meter of wire between two infinitely long wires 1 meter apart.

5.5.8
F = $$IlB$$ or force = length x current x magnetic field strength.

This is used to calculate the strength of the force on a wire of length l (meters) carrying current I (amps) in a field of force B (teslas).

F = qvB or Force = charge (Coulombs) x velocity (m/s) x field strength.

This applies to a single point charge moving through a magnetic field. To work out the direction, we need to remember that we are working with conventional current here, and so for a positive charge, the current will be in the direction it's moving, but a negative one will be backwards. Other than that, the right hand thing from above still applies.

5.5.9
A d.c. (direct current) motor works on the principle that a force will be exerted on a current-carrying wire in a magnetic field. A coil of wire (sort of a square) is placed in a magnetic field, and allowed to rotate on its axis so the coil can rotate in the field. If a current is passed through, the coil will make one quarter turn, but then the force will push it back, because the current is running in the opposite sense.

To overcome this, the ends of the coil are connected to brushes which run around the edge of a commutator, reversing the current every half turn. (A commutator is sort of a ring, where one half is the negative terminal, and the other is positive, so at it turns, the current is reversed). The direction the coil turns can be found in the same way as for a normal wire, remembering that conventional current runs from positive to negative.

5.6.1
First, a definition of magnetic flux. Ø = BA, or magnetic flux = magnetic field strength x area (in m2). Ø is measured in webbers.

When a conductor is moved through a magnetic field, it cuts through a given amount of magnetic flux in a given time. The induced emf in the conductor = -ΔØ/Δt. Thus EMF = -ΔØ/Δt. This equation is in the data book, only they have a curly E (Like this perhaps? ξ I can't remember anymore) for emf. It should also be noted that this assumes that the conductor is perpendicular to the field. Only HL students have to deal with situations where it's not.

The direction of this emf can be found using the left hand thing, if we know that the force will be in the opposite direction to the motion, and the emf is in the same direction as current.

5.6.2
When a conductor is moved through a magnetic field, a current is induced in it so as to produce a force to oppose the motion. This in known as Lenz's law.

For example, if a wire is moving to the left, then a force to the right will be produced. Based on this, and the known field direction, we can find the direction of the current.

5.6.3
When a coil is rotated in a magnetic field (like the motor described above) an emf will be produced. This will be an alternating current, as no commutator will be used. The emf will be at a maximum when the coil is horizontal, and zero when it's vertical (assuming the field goes horizontally), and so the graph will follow a sort of sine curve. The initial direction can be found as above, and it reverses every time the coil turns through vertical.

5.6.4
Transformers operate based on the principle of induced current, by placing two wire coils close together. One has an alternating current running through it, and so this produces an alternating magnetic field. The magnetic field causes a current to be induced in the other coil, again an alternating current. The amount of power (P = VI) remains constant, but the voltage and current change related to the number of turns in each coil. The primary coil is the one with the current running through it, the secondary coil is the one with the induced current. It needs to be noted that this only works because the alternating current causes a continual flux change, and thus induces an alternating current.

5.6.5
The current and voltage can be calculated using the equation

Vp/Vs = np/ns = Is/Ip.

This relates the number of loops (n) in the coils to the voltage and current in both the primary and secondary. A step-up transformer is one which increases the voltage (and so decreases current) while a step-down transformer is one which decreases the voltage, and increases the current. Most transformers are around 99% efficient, and this can be calculated with the following equation.

efficiency = VsIs/VpIp. (or Ps/Pp).

5.6.6
Power is generally transmitted through power lines at high voltage and low current. This is because the power loss is related to current, not voltage in the equation PL = I2R. Since we can't easily reduce the resistance in the wires, reducing the current can reduce the power loss.

Since current = power/voltage, using a big voltage, with a set power, will reduce the current, and so everything works out nicely. If you have to work it out, substitute the power and voltage into the above equation, then substitute the resulting current.

title: IB Physics/Electric Currents


text:
IB Physics/Energy Power and Climate Change

8.1.1: Parameter of power generation
In any system, thermal (heat) energy can be converted into work in a single process (i.e. heating a piston on a stove to make it expand and do work), but to continuously gain work for said energy, a cyclical process needs to take place, with a transfer of energy from the system to bring it back to the beginning again (i.e. cooling the piston once it's reached maximum volume to return it to normal and continue gaining work from the heat energy of the stove).

You need to be able to State this.

8.1.2: Degraded energy
Degraded energy is thermal energy that is released into the surrounding environment after any process. Once released into the surroundings, this heat energy is completely useless for energy production and is considered 'dead' or 'degraded' energy.

You need to be able to Explain this concept.

8.1.3: Sankey diagrams
A Sankey diagram is something that is designed to show energy losses in various stages in a power generation process. On the left hand side of the diagram, all energy to be converted is drawn as a the stem of an arrow. As you move to the right, the arrow will branch off to either side (depends on the individual diagram) so as to represent energy losses as percentages of what you started with (in Joules or equivalent), until you get to the end, which represents the useable energy produced in the process.

An important thing to note is that the thickness of the stem is, and must be, proportional to the percentage of usable energy remaining. For example, if you drew a Sankey diagram on a graph pad, you could make the stem 10 squares wide. Then say that the first energy loss is 10 percent. So, the arrow that branches off of the main stem would be 1 square wide, with the rest of the stem being left at 9 squares (or 90 percent).

You need to be able to Draw and Interpret these diagrams for various systems, including those detailed in sections 8.3 and 8.4.

8.1.4: General generator mechanism
To produce electrical energy from a power plant, coils of wire are rotated in a magnetic field. This is called a dynamo. Note that saying a turbine generates the energy will not earn you any marks. A turbine simply turns the linear kinetic energy (from steam in a steam turbine, for example) into rotational kinetic energy to be used in the dynamo.

You need to be able to Outline this concept. This process is detailed further in Topic 12: Electromagnetic induction but details are NOT expected in this section of the course.

8.2.1: Different energy sources
You should know of the existance of the following energy sources: coal, natural gas, oil, biofuel, nuclear fuel, wind, tidal, solar and wave.

Coal is plant matter that, over many thousands of years, has turned into a sedimentary rock. It has had nearly all of its moisture taken out in its formation. Oil and natural gas are the products of decaying plant matter in a lack of oxygen - they are found in pockets underground, with the gas found just above the oil. Biofuel is a fuel made from sugar canes and the like. Solar, wind, tidal and wave are pretty self-explanitory. Nuclear fuel is usually made up of Uranium-235, mined from under the ground.

For the most part, the Sun is the main precursor in all of our energy sources - fossil fuels are made from long dead plant matter (which was around because of the sun), and wave, solar and wind are all to do with weather (which the sun plays an inportant role in).

You need to be able to Identify these sources.

8.2.2: Non-Renewable versus Renewable
The main difference between the renewable and non-renewable sources is that non-renewable sources (fossil-fuels) release CO2 when used to make energy. Alternaitvely, you can just say that non-renewable sources are burnt.

On that note however, biofuel, which can almost be classified as renewable as it doesn't use the long-decayed matter, does in fact release CO2 when used. BUT, unlike fossil fuels, it can be renewed by planting more of its source product.

You need to be able to Distinguish between the two.

8.2.3: Energy density versus Specific energy
Specific energy is the amount of energy per unit mass of a fuel, given by Jkg-1.

Energy density is the amount of energy per unit volume of a fuel, given by Jm-3.

You need to be able to Define this.

8.2.4: Choice of fuel
As a general rule of thumb, fuels with higher energy density will be chosen over one with a lower energy density. Uranium-235 has the highest energy density, but it is expensive to start and run a nuclear power generator. Among fossil fuels, which are used often, natural gas has the highest density, followed by oil and then coal.

You need to be able to Discuss these concepts.

8.2.5: Relative proportions
The list of energy source by proportional useage goes like this: Oil ≈ 35%, Coal ≈ 25%, Natural Gas ≈ 20%, Renewable sources (all of them) ≈ 15%, Nuclear ≈ 5%.

Note that you only need approximate values for these. The proportions are what really matters.

You need to be able to State this.

8.2.6: Advantages and Disadvantages
You need to be able to discuss the pros and cons of each energy source listed previously.

Advantages
Fossil fuels
 * Found on every continent, so relativly easy to find and use.
 * Easy to gain energy from - no large technological demand relative to other sources.
 * Easy to construct power station in basically any area.

Nuclear Energy
 * Extremely high energy density.
 * Doesn't contribute to the enhanced global warming effect.

Hydropower
 * Very efficient compared to other sources.
 * Low running costs.
 * Renewable.
 * Doesn't contribute to the enhanced global warming effect.

Wave Power
 * Doesn't contribute to the enhanced global warming effect.
 * Very high potential power output.

Tidal power
 * Renewable.
 * Doesn't contribute to the enhanced global warming effect.

Solar energy
 * Widespread source.
 * Doesn't contribute to the enhanced global warming effect.
 * Can work in more remote areas.

Wind Power
 * Doesn't contribute to the enhanced global warming effect.
 * Many possible sites for construction.
 * Can work in more remote areas.

Disadvantages
Fossil fuels
 * Contributes heavily to the enhanced greenhouse effect.
 * Non-renewable - supplies will run out quite fast at current rate of consumption
 * Low energy density

Nuclear Energy
 * High set up and maintanance costs
 * Creates highly radioactive and hard-to-dispose-of waste.
 * Possibility of a reactor meltdown.

Hydropower
 * Requires large dams to be built - high cost.
 * Causes up river flooding and down river drought.
 * Dam can break and release of water can cause significant damage.

Wave Power
 * Hard to build.
 * High maintanance cost due to power of waves.

Tidal power
 * Low energy output.
 * Long construction times - high cost.

Solar energy
 * Very low energy output.
 * Intermittent energy output.
 * Can't work at night.

Wind Power
 * High setup and maintanance costs.
 * Creates noise pollution.

You need to be able to Discuss these points.

8.3.1: Historical and geographical reasons for use
Fossil fuel consumption increased massively during the Industrial Revolution. Previously, coal, oil and gas were being used, so people knew where to go to get them. Power plants were created to mass produce energy from these sources.

Geographically speaking, fossil fuels, especially coal, is found in at least small amounts all over the world. These are some of the easiest sources of fuel to find.

You need to be able to Outline these concepts.

8.3.2: Energy density.
Basically, the questions will most likely ask you to calculate the energy density (measured in J/kg) given efficiency, mass of fuel consumed (M, measured in kg) and power output (P, measured in J). As can be seen, the formula Energy density = P×ε/M will be used.

You need to be able to Discuss this.

8.3.3
The following problems can be caused by digital equipment :

Quantization : This is caused by converting continuous analogue data into individual digital numbers.

Sampling frequency : The digital systems can only 'grab' a piece of data every x sec (let's say 0.01). If the data is changing significantly within this amount of time, then the sampled results will be almost random compared to the actual signal.


text:
IB Physics/Motion in Fields

9.1.1
On an inclined plane, application of Newton's laws is somewhat complicated. Gravity acts downwards, but the plane exerts a force back on the object at an angle. This can be used to build a right angled triangle, since the resultant force down the slope angles to the normal force, and gravity will be the hypotenuse. If there is friction acting, this will be in the opposite direction to the motion down the plane.

9.1.2
Friction is a force which opposes motion, thus if there is no motion, then there will be no force caused by friction. Friction can never make an object move, it can only slow an object down, and eventually stop it.

For two solid surfaces moving over each other, the friction will be affected by the nature (roughness etc) of the two surfaces, however the surface area and velocity of the object do not affect the friction. There are also two types of friction of solid surfaces, static and kinetic friction. Static friction is that which stops objects from beginning to move, and kinetic is that which slows objects down when they are moving.

These two types are defined individually by their constants µs and µk respectively. µs > µk in all cases (fairly obvious if you think about it).

The force of friction caused by each type is also dependent on the normal force the surface is applying, thus Ffr =< µsFn for objects which aren't moving, and Ffr = µsFn for objects which are moving. In the first case, the frictional force only exists if there is a force being applied, thus the less than or equal to sign. Friction will counteract all forces up to this point.

Objects falling through fluid (or indeed, air) also experience friction which opposes the force of gravity. This friction increases with velocity, and so there eventually comes a point where the force of gravity is being counteracted by friction, and the object falls at constant speed. This is known as terminal velocity.

9.2.1
When objects in projectile motion are launched at an angle, the horizontal and vertical components must first be calculated. From the vertical, we should be able to calculate its peak height, and the time taken to reach this height. From there, we can calculate the time required to reach the ground and using all these times, and the horizontal component, the horizontal distance travelled.

9.3.1
Simple harmonic motion is like that of a pendulum, where the object moves away from, and returns to the equilibrium point, and the restoring force is proportional to the extension (i.e. the further from the center the pendulum is, the bigger the force pulling it back). Starting from a fully extended position, displacement follows a cos curve, velocity a -sin curve, and acceleration a -cos curve (we're differentiating with respect to t each time : cos -> -sin -> -cos). As can be seen from this, a displacement vs acceleration graph will be a straight line with a negative slope (cos and -cos).

9.3.2
The period in simple harmonic motion (SHM) is the time required for the displacement to return to its original position (complete one cycle). The frequency is 1/period, thus the number of cycles per second. The amplitude is the maximum displacement from the mean (or central) position. Period is also defined as T = (2 x Pi)/w where w = 2 x π x f

Graphing displacement vs time : This graph ranges from r (the amplitude) to -r, and follows a cos curve (assuming we're starting at the extended position). It will be a maximum at the points of extension and zero when the object passes through the mean position.

Graphing velocity vs time : This graph ranges from rw to -rw (where w = 2 x π x f ). Velocity will be a maximum when the object is an the mean position, and zero when the extension is at a maximum. Thus it will follow a sin curve, with velocity being a maximum and when displacement is zero and vice versa.

9.3.3
The total energy for an object in SHM is constant. When displacement is maximum, all the energy is potential (since it is being held up, compressed or whatever). When the displacement is zero, all the energy is kinetic (because it is moving, and at its lowest point/no compression or extension etc.), thus the two follow parabolic curves where the sum of the two curves is always equal.

9.3.4
As an example, we have SHM for a mass on a spring. When the mass is pulled downwards to an extension of x, and then released, the mass undergoes vertical oscillations which obey SHM.

Since the spring obeys Hooke's law ( F = kx, where k is the spring constant ) we know that the restoring force = kx. Newton's second law. We also have F = ma, so combining the two we get a = kx/m. This fits the SHM formula a = -w2x producing a = -k/m x (if acceleration is in the same direction as x, i.e. away from mean position) Therefore, w2 = k/m and so, T = 2 x π x (√(m/k)) since T = (2 x π)/w (this is as given in the data book).

If the elastic limit of the spring is exceeded, then it will no longer follow Hooke's law, and no longer follow SHM.

9.3.5
Assume a mass is on a pendulum, with string length l, and is displaced by x. This forms an angle of Ø between the mean position of the string, and the displaced position. The force of gravity towards the origin = mg sinØ ( this can be shown with a right angle triangle, mg is the hypotenuse, mg sinØ is the side at a tangent to the curve, because it is a similar triangle to the one made by the mass, the origin and the top of the string ). For small angles Ø, sin Ø = x/l(If we assume once again, that the curve between the origin and the mass is actually a straight line, which is valid for small Ø). Thus, the force towards O = mgx/l. Since F = ma, acceleration towards O = gx/l. Thus acceleration in x direction (away from O) = -gx/l. So as above, w2 = g/l, and so, T = 2 x Pi x (square root of l/g) (once again, this is given in the data book).

9.4.1
Angular displacement : The angle from the centre of a circle (in radians) around which an object has moved. It's symbol is Ø, and it is defined as Ø = s/rwhere s is the length travelled around the circumference, and r is the radius. It is equivalent to displacement in linear motion.

Angular velocity : Uses the symbol w. angular displacement/time (or w = ΔØ/Δt). Its linear equivalent is velocity. This is no longer included in the syllabus.

9.4.2
s = rØ : The length covered on the circumference is the radius x the angle (in radians) covered. This allows the angular displacement to be converted into a length.

v = rw : The velocity of an object on the circumference is the radius times the angular velocity (as defined above, in radians s-1)

9.4.3
That an object rotating in a circle has an acceleration towards the centre can be shown by taking two vectors at tangents to different points on the circle, and subtracting one from the other. The resulting vector will be directed towards the centre of the circle.

If we take two such vectors (of length V) from close together, so the angular displacement of their starting points is small, and draw them from the same origin point, then the vector between their ends is the centripetal acceleration. Using similar triangles, take the angle between the two vectors to be Ø (the same as the angular displacement), and let the vector between them be ΔV. If ac is centripetal acceleration, then it equals ΔV/Δt. From the triangle, Ø = ΔV/V, so ΔV = VØ. Subbing into the acceleration formula, we get ac = VØ/Δt. From above, w = Ø/Δt, thus Ø = wt, and so ac = vw. This can be rearranged by subbing v = rw to get ac = rw2 = V2/r (as in the data book).

9.4.4
For an object to travel in a circular path, constant acceleration is required. F=ma (newton's second law) in circular motion F = |mac| = |m v2/r| = |4 x π2 x mr/T2| = |mrw2|.

9.4.5
Bodies in circular motion include planets orbiting ( gravity provides ac ), buckets being spun around on ropes ( rope provides ac ) and cars going around banked curves ( The 'down the slope' component of the normal force provides ac ). Problems involving these can then be solved by finding ac and then working back through the above equations.

9.4.6
Masses moving in a vertical circle and affected by gravity : At every point in the circle, the force keeping the object moving in a circle (ie towards the center) must be constant, and can be calculated with the equations above. At the top of the circle, the force total keeping the object in a circle is Fc - Fg (since gravity is providing the force, Fc is smaller). At the bottom, Ft = Fc + Fg. At the sides, Ft = Fc (since no component of gravity is acting towards the center).

9.4.7
Centripetal force does not change the kinetic energy of a body because it only affects the direction of the velocity, not the magnitude, and Ek = 1/2mv2 is only conserved with the magnitude.

9.5.1
Newton's law of universal gravitation : F = (Gm1m2) / (R2), where G is the gravitational constant (on earth, 6.67 x 10-11 N m2 kg-2), m1 and m2 are the two masses in question, and R is the distance between the centers of the two masses. This must be applied both as a source of centripetal and gravitational force (in the pulling objects down sense). (This equation is in the data book)

9.5.2
Gravitational field strength is the gravitational force per unit mass at a particular point in the gravitational field. In simple terms, it's the force on one kg of mass, which is 9.8 N on Earth.

9.5.3
Beyond the surface of the mass, the force of gravity decreases in a parabolic curve (because of the R2 term it obeys the inverse square law). Inside the mass is messy to work out, but luckily it isn't required.

9.5.4
Gravitational potential ( with the symbol V ) is defined as the potential energy per unit mass at a point in the field. V approaches 0 as the distance between the masses approaches infinity. V = -Gm/r where m is the mass of the earth (or whatever) and r is the distance from the center of the Earth. (given in the data book)

9.5.5
Escape velocity is the speed at which an object must leave the planet's surface to completely escape its gravitational field. For this, the object must be given enough kinetic energy to go from the surface, where
 * $$V=-G\frac{M}{r}m$$

to where V = 0. Therefore,

 * $$\frac{1}{2}mv^2 - G\frac{M}{r}m = 0$$

Which rearranges to
 * $$v = \sqrt{2G\frac{M}{r}}$$

Note: this one is not in the data book, so you can either memorize it, or remember how to derive it.

9.6.1
The work done on a force displacement graph is the area under the graph. This would normally be found by integrating, but since there's no calculus in this course, in any given question you'll be able to break the area up into triangles and rectangles to find the area.

9.6.2
For a linear spring, the force to extend (or compress) the spring is directly proportional to the displacement. If no force acts on it, the spring will naturally return to its equilibrium position. Unless, of course, the spring is displaced beyond it's elastic, in which case it's broken and probably no longer interesting.

9.6.3
Energy (elastic potential) is stored in a spring by compressing or extending it. When released, the spring will convert this energy into other forms (kinetic, thermal, sound etc.).

9.6.4
Deriving conservation of momentum for two bodies from Newton's laws.

First assume there are two objects, of mass m1 and m2 travelling towards each other at velocities v1 and v2. First we write Newton's second law in the form 'force is the rate of change of momentum'

$$F =\frac{\Delta P}{\Delta t}$$

$$\begin{align} \therefore F\Delta t &= \Delta P \\ &= mv \end{align} $$

This can then be applied to the first mass giving the equation Ft = m1v'1 - m1v1. Using Newton's third law, we know that the force on m2 will be equal and opposite and so the second mass. -Ft = m2v'2 - m2v2.

These two can then be combined to form m1v'1 - m1v1 = -(m2v'2 - m2v2) which rearranges to m1v1 + m2v2 = m1v'1 + m2v'2, which is the law of conservation of momentum for two masses.

9.6.5
In two dimensions, the law of conservation of momentum applies in both senses, so the momentum value must be broken up into its vector components. The total amount of vertical (or north/south or whatever) momentum will be conserved, and will the total amount of horizontal momentum. Therefore, a problem involving this can be treated as two separate one dimensional conservation of momentum problems.

9.7.1
Angular acceleration is the rate of change of angular velocity : α = Δw/Δt. This is no longer included in the syllabus.

Torque is the rotational equivalent of force : T = I x α (moment of inertia x angular acceleration).

Moment of inertia is the rotational equivalent of mass. It is defined as the sum of (mr2) for every point mass in the system where m = mass and r = the distance form the axis of rotation. This allows dumbbell type arrangements to be calculated, but the following shape formulae should also be known
 * A 'hoop' or cylinder rotating around the center of the hoop : I = MR2
 * A solid disk rotating around the center of the disk : I = 1/2MR2
 * A solid sphere rotating about any axis running through the centre : I = 2/5MR2

Angular momentum is the equivalent of linear momentum : L = Iw (angular momentum = moment of inertia x angular velocity).

9.7.2
All of the quantities and equations in rotational motion are equivalent to others in linear motion. The tables below illustrate this equivalence.

All these can be applied as appropriate to problems.

title: IB Physics/Motion in Fields


text:
XForms/Replace Tester

Motivation
You want to build a form that will allow you quickly test replacement regular expressions using XQuery's replace function.

Link to Working Application
Replace Test

Sample Program

XQuery Replace Tester
If you are using eXist, just place this file on the server in the same folder as your XForms test driver.

In the example above I used a test folder on the localhost:

Discussion
This shows that you can quickly built tools to teach yourself complex functions like regular expression handling. You can also use the XQuery match function with returns a true/false if the regular expression matches an input string.

There are two variations of this example that are interesting. The first is where you replace the input form with a large text area for doing global replacements of large blocks of text. The second is where you replace the patten input box with a selection list with common replacement patterns.

title: XForms/Replace Tester


text:
Classroom Management Theorists and Theories/Fred Jones

History of Fred Jones' Work
Fred Jones worked in clinical psychology at UCLA (University of California, Los Angeles) where he received a Ph. D. specializing in work with schools and families. As the head of the Child Experimental Ward while working at the UCLA Medical Center Dr. Jones developed methods of helping children with severe emotional disorders. He then began to cross these methods over to special education and general classroom setting while working at the Medical Center.

Once his work took him to the University of Rochester Dr. Jones developed the non-adversarial management procedure which led to the writing of his first two books; Classroom Discipline and Positive Classroom Instruction. Since then Dr. Jones has been conducting extensive research and constantly working in classrooms to improve his techniques along with touring the country teaching these methods. Dr. Jones’ most recent book, Tools for Teaching, is an update of his previous work including new material that has been learned since his last publication.

Implementation in the Classroom
Jones has developed a non-adversarial method of creating a classroom that moves smoothly. In his three books Jones addressed many levels that the method can be successful on. One book focuses on the classroom as a positive discipline site, another book looks at how the entire campus can benefit from the positive discipline and the third book takes those concepts to the everyday/every minute problems faced by a teacher.

There are two important systems that have come from Jones’ research. The first is Preferred Activity Time (PAT). PAT is a system that can benefit both the students and the teacher. The students are able to spend time having fun while learning after earning the privilege. The teacher has an incentive for the students to work hard and then can enjoy the activity with their students. The second system is simply positive reinforcement. The teacher can set up simple techniques of their choosing to reinforce behavior from a student that will teach that student the acceptable way to behave/act. These techniques can vary from award presentation after set amounts of time, commendations sent home, point accumulation for buying power of rewards, or any reinforcer (anything that anyone will work for) that is applicable to the individual student/group.

Elementary Implementation
As elementary teachers cross all of the content areas there are many different ways they could establish PAT in their classrooms. For many it may be advantageous to vary the activity to use multiple students’ interests. A teacher who values art as part of the curriculum and would do art projects anyway with the students could get two for the price of one. The teacher might start the day with the following announcement: "Students, I would like to direct your attention to the project table over by the window. As you can see, I have laid out art supplies for our preferred activity at the end of the day. As usual, I have set aside twenty minutes for Preferred Activity Time (PAT). "Of course, once you get started on an art project, you always love to have more time. And this time, you can! All the time we save during the day by hustling will be added to PAT. We could have forty minutes for art if we really get things done." This example gives the students the tangible reward right in front of their face all day long to push them to earn the extra time.

Secondary Implementation
In the secondary setting there are many ways that PAT can be utilized. In an example used by Jones a science teacher used PAT as a fun way to review the day’s concepts with the students. Originally the teacher spent ten minutes each day orally summarizing the important facts that the students needed to have gotten out of the lesson. Instead of losing the students' interest everyday he turned the same amount of time into a quiz show style game. At the beginning of the semester the teams were set up and stayed together until the class ended. After a while the students asked to have a few minutes at the beginning for a short group review – a peer tutoring session! From there the students could earn extra game time if transition time dropped, there was less fooling around and clean up at the end of experiments was efficient. This allowed for a daily review that improved the students learning and their retention of the content.

The PAT time does not have to be a daily activity. It could be an activity that the students earn the minutes toward over an entire quarter or semester. An English teacher, Jones notes, has her Advanced Literature class earn minutes throughout the quarter. At the end they have enough points accumulated to watch one of the books they have read on video. Generally it takes two class periods so the students must have earned 120 points (where 1 point = 1 minute) to watch a film as their reward.

There are ways to take the PAT system and apply it to any content area and to any time frame necessary. The previous implementation ideas are just a few ways to implement the concept into a classroom. There are many more activity suggestions along with helpful tips on implementing them on Jones’ website: www.fredjones.com.

Critique of Jones' Theory
Dr. Peggy J. George is a strong believer in Jones’ PAT program. She has noticed that those teachers who have chosen to use his techniques have found them to be highly effective and very complementary to their existing classroom discipline plans. "PAT is one of the techniques that many teachers choose to use because the kids love it and it works," said George. "In his books, Jones explains that PAT is all about teaching students time management and responsibility. He suggests that the teacher gains instructional time by having students be on task during teaching and then gains additional learning time by selecting PAT activities that are educational but fun, or preferred by students. Obviously if the PAT activities are not motivational, students will not be willing to work to earn them."

There might be articles or other theorists who come out and disagree with Dr. Jones’ positive behavior rewards outright but if so, they are difficult to find. What can be found are other theorists whose overall theories are opposite of Jones’. One in particular is Alfie Kohn. Alfie Kohn has a firm belief that motivation to succeed in school and life must be intrinsically based. A successful person must have self-motivation. Those that have extrinsic motivation (rewards, praise, commendations, etc.) are at a risk of losing their intrinsic motivation completely. Additionally teachers that use extrinsic motivation for behavior and work completion are killing the students’ ability to be self-motivated.

Marci's Critique
I feel that Dr. Jones has a concrete basis for me and others to begin the development of a strong philosophy and belief of teaching. Many of the concepts and ideas that Dr. Jones discusses in his books are basic and occur daily in the classroom. The topics covered in Tools for Teaching are especially useful. The book takes Dr. Jones’ positive reinforcement tools and applies them to the mundane chores of a classroom, everything from desk arrangement to teaching the routines. Even someone that did not agree with the way Dr. Jones thinks a class should be taught and directed in the content area could learn from Dr. Jones on a broad basis. I do agree with Dr. Jones’ basic ideas but I feel that there is a limit to the amount that can actually be taken from one theory. There are aspects of many different theorists that I will combine with the knowledge I have gained through Dr. Jones’ positive classroom discipline.

Questions
1. Discuss how using preferred activity time may influence students to behave differently. 2. Develop a preferred activity time (PAT) that would fit into your lessons for this week. How could you organize the time for your class to receive this reward (when, length, structure)?