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Synopsis for an Introductory Physics Course with Peter Eyland

*Introduction*

The goal of Physics is to find and express the underlying patterns that help us understand nature.

the methods of Physics revolve around:

observation and measurement,

explanation by reasoning from specific instances to general patterns,

prediction by reasoning from general patterns to specific instances, and

verification by testing predictions with observation and measurement.

*Measurement*

Measurements are expressed in S.I. units using decimal prefixes.

Symbols and equations are shorthand ways of expressing concepts

In the Laboratory the following instruments are used:

mass balances, Vernier calipers, Micrometers, stopwatches and measuring cylinders.

Random errors occur because of measurement technique, reaction time variations, variations in the system conditions between measurements
(temperature, pressure etc), or simply variations in object dimensions.

Systematic errors always push the measurement higher or lower.
They occur when the scale on the instrument has changed with temperature, or some physical element within the measuring instrument (e.g. a spring) has changed due to age or humidity etc.

When adding or subtracting quantities you add the absolute errors.

When multipying or dividing quantities you add the relative errors.

When graphing with error bars: the best-fit line gives the mean slope and the error in the slope
comes from (usually) the largest difference from the worst-fit lines.

*Waves*

Waves move energy through a medium without moving the whole medium.

Longitudinal waves transfer energy by pushing neighbours in the same direction that the energy moves.

Transverse waves transfer energy by pulling neighbours sideways to the direction that the energy moves.

The amplitude is half the measurement between a minimum to a maximum.

The wavelength is the distance between successive maxima.

The period is the time between successive maxima.

The frequency is the number of maxima that pass per second.

The phase tells us how far through a cycle something is.

Reflection occurs when a surface throws back the heat, light, sound etc that falls on it.

Refraction is the change of direction that occurs when the medium changes.

Diffraction occurs when a wavefront bends near a gap or an edge in the same medium.

Interference occurs when waves pass through each other at a point in space and the result at that point is the sum of the wave heights.

Polarisation occurs for transverse waves when the vibration directions are not randomly oriented.

Sound is produced from a sudden local compression of a gas, liquid or solid.

Infrasonic waves have frequencies < 20Hz: ultrasonic waves have frequencies > 20kHz.

An ultrasonic transducer is a device that changes its physical size when an electric potential is applied to it.

The acoustic impedance (density x speed) measures the "hardness" of a medium.

At an interface there is reflection, transmission and absorption.

The size of the reflected wave depends on the difference in acoustic impedance.

Ultrasound can be used in diagnosis and therapy.

The pulse-echo technique has many applications e.g. in fishing, oil exploration and non-destructive measurement.

Thermoacoustics: heat transfer by using sound.

Optoacoustics: the interaction between light and sound.

Resonance occurs when the frequency of a forcing vibration is the same as the natural frequency of a system and there is a big increase in the amplitude of the vibrations.

A standing wave is a resonant condition with nodes and antinodes where the energy stays in place.

The distance between adjacent nodes is always a half a wavelength.

*Sound*

The lowest standing wave frequency is called the fundamental or first harmonic or first partial.

Harmonic frequencies are multiples of the fundamental, and the second harmonic is the first overtone etc.

The harmonic content determines the timbre of a sound.

The actual harmonics that do form are called partials.

Strings are symmetrical and may form all the harmonics (depending on how they are played).

Open pipes are symmetrical and may form all the harmonics.

Closed pipes (with constant diameter) are not symmetrical and cut out the even harmonics.

Pressure nodes occur just outside the open ends of a pipe.

The ear has an automatic gain control but it is relatively slow.

The overall amplification from ear canal to cochlea is about 100x.

The cochlea sends an auditory sensation to the brain with a frequency spectrum.

Sound Intensity is Power per unit Area and measured in W.m^{-2}.

Sound Intensity Level is a logarithmic scale of Intensity and is measured in deciBels.

The Fletcher-Munson curves show lines which are an averaged perception of equal loudness (in phons).

Frequency is measured in Hertz and the perceived frequency (or Pitch) is measured in Mels.

*Light*

Light travels in straight lines.

Newtons "corpuscular" theory explained reflection and refraction.

Snell's law defines refractive index:

Huygen's construction: each point on a wavefront emits wavelets and the next wavefront is the envelope that forms after one period.

Huygen also explained reflection and refraction and said that light slowed down in higher refractive media.

The *relative refractive index* is

The *absolute refractive index* is given by

The speed of light in a vacuum is always constant at 3 x 10^{8} m.s^{-1}.

In terms of absolute refractive indices, Snell's law is:

Young's two slit experiment confirmed a wave nature for light.

When the phase difference between waves arriving from each slit is zero or a multiple of 2π,
the waves reinforce and produce a maximum in the light's intensity (brightness).

Bright fringes appear up the screen, at distances from the centre given by:
where m = 0,1,2,3 ….

Mirages are caused by refraction (or reflection) and optical illusions are a product of human perception.

When light changes from a higher refractive index medium to a lower refractive index it bends away from the normal.

At the critical angle the refracted ray is at 90^{0}, i.e. parallel to the surface.

and

*Lenses and Optical Instruments*

The lens equations use the convention: real is positive

(where minus means inverted).

Cameras focus the image of a near or distant scene onto photgraphic film (or CCD array).

A small aperture gives good depth of field and a large aperture gives good illumination.

The f-number is the focal length divided by the aperture: smaller f-numbers mean brighter images.

A single spherical lens has chromatic and spherical aberration.

The Galilean telescope has a concave lens for the eye-piece and a convex lens for the objective.

The Keplerian telescope has two convex lenses and an inverted image.

The final image in either telescope is at infinity and the focal planes coincide.

Binoculars are twin telescopes with prisms to reduce their length.

The Newtonian telescope has a paraboloidal primary mirror and a plane mirror to reflect off to the side.

Microscopes usually have three positive lenses and the final image is at 250mm.

Electron microscopes can image individual atoms.

*Pressure*

Pressure (the intensity of force) is force/area and measured in Pascal.

Pressure at a depth in a liquid:

Pascal's principle states that a change in pressure is transmitted throughout a liquid without loss.

A vacuum is space that is emptied of matter, but it is not "nothing" because it has properties.

Standard Air Pressure =1 Atmosphere =760mm Hg =760torr =101.3kPa

Normal eye pressure 12->23 mm Hg (1.6->3.0 kPa).

Interpleural pressure 5->10 mm Hg below atmospheric (0.7->1.3 kPa).

Pressure in the digestive tract is above atmospheric.

Pressure in the knee joint can be greater than 10 Atmospheres (> 1 MPa).

At 30 cm H_{2}O (3 kPa) the micturation reflex occurs.

On the high pressure side of the heart, the normal range is 120/80 mm Hg (16/11 kPa).

On the low pressure side of the heart, the normal range is 25/10 mm Hg (3.3/1.3 kPa).

A Mercury manometer is a "U tube" with Mercury; the difference in height gives the pressure above atmospheric.

The Bourdon gauge is an oval tube bent into a circular arc or helix.
Pressure in the tube will tend to straighten it and it can give an "absolute" pressure.

The "sphymomanometer" is a specialised Mercury manometer which measures systolic and diastolic blood pressure.

*Archimedes*

Archimedes lived from 287 to 212 BCE in Syracuse, Sicily, and constructed levers, pulleys, screws, catapults etc.

Archimedes' principle says that the apparent loss in weight of a body partially or totally immersed in a fluid
is equal to the weight of fluid displaced.

*Vectors and scalars*

The Cartesian co-ordinate system has an origin and perpendicular axes.

A point is space is specified by co-ordinates along each axis.

The distance between two points depends on the actual path you take.

The displacement has the length and direction of the minimum straight-line between the two points.

Polar coordinates have a straight-line length in a specified direction.

Vectors can be added by arrowed lines in scale diagrams. The arrowed lines may be positioned sequentially or simultaneously.

Vector subtraction is done by adding the negative.

Vector components are vectors at right angles which add to give the original vector.

Vectors may be added without scale diagrams by using components.

*Moments*

The moment about the turning point is defined as the magnitude of the force, times, the perpendicular distance from the turning point to the line of action of the force.
Mass measures the amount of matter that a body has, and weight is the gravitational force on a mass.
Equilibrium means balanced forces, and centre of gravity is the point where all the gravitational force can be considered to act through.

*Friction*

Maximum static friction is given by: F_{s} = μ_{s}N

Kinetic frictional force is reasonably constant and smaller than maximum static friction.

*Equilibrium*

There are two conditions to be met for a body to be in equilibrium.

• it does not accelerate (force rule)

• it does not rotate (moment rule)

The size of a couple equals the size of one of the forces times the perpendicular distance between them.

*Kinematics*

The velocity of a system is its speed in a given direction.

*Dynamics*

The momentum of a system is the product of its mass and velocity.

*Newton's laws of motion:*

1. Bodies remain in a state of rest, or of constant speed in a straight line, unless compelled to change by a push or a pull.

2. The size of the force on a system is measured by how quickly its momentum changes.

3. To every action there is an equal and opposite action, i.e. an equal reaction.

Internal forces are one part of a system acting on another part of the system, they do not cause motion, they keep a system together.

The force which causes the motion of a system is the resultant external force.

• The instantaneous force is the slope of the blue tangent to the force/time graph at that instant:

• The effect of force through time is the red area
under the graph and written as
.

• The effect of force through time is to change the momentum:

In the absence of external forces on a system the momentum of the system is conserved.

*Work and Energy*

The work done by a force,
in Joule

A conservative force does no net work in going through a closed path.

The kinetic energy, T =
in Joule.

The change in potential energy of a system = the work done against the system force = the negative of the work done by the system force

Gravitational potential energy = mgh.

The effect of force through distance, (the work done by the force), changes kinetic energy.

The effect of force through time, (the impulse of the force), changes momentum.

In the absence of dissipative forces mechanical energy (i.e. KE and PE) is conserved.

Power is the rate at which energy is delivered, or the rate at which work is done.
in Watt

The output power from an engine is given by:

The drag force on a car at typical speeds:

The efficiency of a machine measures the percentage of useful power out to the total power in.

Energy resources are: Oil,gas and coal - Nuclear - Solar - Hydroelectric - Wind - Wave - Tidal - Geothermal.

*"The greatest challenge facing humanity in the next twenty years is to preserve our fundamental life support systems
in the face of increasingly inequitable and unsustainable production and consumption patterns."*

*Gas Laws*

Boyle's law: For a given gas at a fixed temperature, the product of pressure and volume is a constant.

Charles' law: For a given gas at constant pressure, the ratio of volume to absolute temperature is constant.

The unit of Absolute temperature is called the Kelvin (K) and is the same size as the Celsius scale.
The Absolute temperature scale has a zero at -273^{0}C.

Gay-Lussac's law: For a given gas at constant volume, the ratio of pressure to Absolute temperature is constant.

Combined Gas equation:

Avogadro's number (*N _{A}*) for 1 g mol of molecules is: 6.023 × 10

Universal Gas law: (where

*Kinetic Theory*

The microscopic view of matter has particles that can't be seen, heard, touched etc.

The high speed movement of these particles through the void between them produces macroscopic ("observable") effects.

The kinetic theory equation:
,
shows that macroscopic pressure is the average result of a many microscopic particles colliding with the walls.

The kinetic theory equation combined with the Universal Gas equation:
,
shows that Absolute Temperature is proportional to average kinetic energy per molecule.

The Internal Energy of a gas is the total kinetic energy of its particles:

The atomic mass unit is 1/N_{A} grams = 1.67 x 10 ^{-27} kg

The Maxwell-Boltzmann distribution gives the distribution of molecular velocities.

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