Peter's Physics Pages
Synopsis for Physics for Civil Engineering
Electric Charge, Current and Potential Difference
There are two kinds of electric charge, positive and negative
Electric charge is measured in Coulomb
The smallest naturally occuring charge is 160 zC
Electric current is the flow of electric charge & measured in Ampere
Electric Potential Difference is the work done/charge & measured in Volt
Microscopic picture gives
Conductors and Insulators
A Conductor is a device, Conductance, G, and Conductivity, σ, are defined by:
A Resistor is a device, Resistance, R, and Resistivity, ρ, are defined by:
Conductors allow the free passage of charge through them
Insulators (Dielectrics) don't allow the free passage of charge though them
Semiconductors are intermediate between conductors and insulators
Temperature coefficient of resistivity:
Heating effect of current:
Circuit elements are devices that produce currents or have potential differences formed across them.
An electric circuit has a number of circuit elements connected to form a closed loop or system of loops
An Electromotive force (e.m.f.) is any energy source that induces an electric current
Resistors are connected in series when the same current flows through them and they are connected + to -
For resistors in series:
Resistors are connected in parallel when they have the same potential difference across them and they are connected like to like
For resistors in parallel:
For two resistors in parallel:
The waste heat of an electric cell is accounted for by thinking of it as heat dissipated from an internal resistance
When the external load equals the internal resistance then maximum power is transferred from the source
For simple circuits, currents and potential differences can be found by series and parallel substitutions.
Kirchhoff's rules are needed for networks, i.e.
Rule 1: The total current that flows into a junction must equal the total current that flows out of the junction
Rule 2: Around a closed loop, the sum of the e.m.f.'s equals the potential drops across the resistors.
(i) label the salient points of the circuit
(ii) apply rule 1: go to a junction and guess the currents
(iii) make the currents consistent at all the junctions
(iv) put the polarities on the resistors
(v) apply rule 2: to a number of loops (one loop for each unknown current )
(vi) solve the equations for the unknown currents
Definition of capacitance:
Parallel plate capacitance:
The dielectric strength is the resistance to breakdown, i.e. the maximum allowed potential difference per distance between the plates.
For capacitors in series:
For capacitors in parallel:
Energy stored in a capacitor:
Solids hold their shape; fluids take the shape of their container;
plastics can be moulded; plasmas are ionised gases.
Lagrange's technique solves for the position and velocity of all fluid particles as functions of time
Euler's technique specifies the density and velocity at each point in space
Four parameters: Steady/Turbulent, Compressible/Incompressible, Viscous/Nonviscous, Rotational/Irrotational.
In steady flow the velocity at a point doesn't change in time, the trajectory of every particle follows the same path called a streamline.
Equation of continuity:
A static fluid has zero velocity everywhere, so
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.
Laminar flow occurs when a fluid can be pictured as split into thin layers which slide smoothly over each other.
Laminar flow can be in planes or cylinders
Newton's law of Viscosity:
Viscosity is important in materials with secondary bonding between tightly bound molecular units.
The bonds between atoms weaken with increasing temperature.
Time provides opportunities for bond breaking.
Viscous Drag force for a car at typical speeds
Terminal speed for a sphere falling under gravity:
Reynold's number: , above 3000 gives turbulent flow.
Surface Energy and Surface Tension
Surface energy is the work per unit area done by the force that creates the new surface.
Roughly, surface energy varies inversely with the tendency to brittle failure.
The surface energy decreases with increasing temperature.
Contaminants on the surface reduce the net inward force and decrease surface energy.
The surface energy of solids can be measured by fracture and indentation techniques.
The surface tension in liquids can be measured by using wire frames.
The angle of contact is the angle through the liquid to the solid.
Capillary action can support a column of liquid to a height (or depth) given by: .
The size of bubbles is a balance between excess pressure and surface tension.
For a single spherical surface:
Microscopic Picture of Solids
Negative Potential Energy indicates a bound state.
Force is the negative of the potential gradient
The Lenard-Jones Potential Energy Function
Equilibrium Separation (or bond length):
is the distance to the bottom of the potential well, and
is found by setting the force equal to zero.
The Maximum Binding Energy:
equals the minimum potential energy,
is found by substituting equilibrium separation into interatomic potential,
depends on the size of the attractive potential (A), and
is greater with shorter equilibrium separations.
One electron volt (eV) is the energy acquired (or lost) by an electron in crossing through 1V (1eV = 1.6 x 10-19 J = 160 zJ)
The Periodic Table gives an indication of how electrons will be shared.
Ionic bonds tend to form between elements at the edges.
Covalent bonds tend to form between elements in the middle.
Metallic bonds have overlapping potentials releasing some electrons to form a "glue".
Secondary bonds are the result of electric dipole interaction.
Hydrogen bonds form with permament dipoles.
Van der Waals bonds form with fluctuating dipoles.
Van der Waals
charge stacking requirements
no charge stacking requirements
no charge stacking requirements
Ionic crystals tend to be brittle because of the charge restriction.
Covalent crystals tend to be brittle because of the directional restriction.
Metals tend to be plastic because there are no directional or charge restrictions.
Crystals, Amorphous solids, and Polymers
Crystals have a geometrical arrangement of atoms, which is repeated indefinately.
The bond type and atom size determine the crystal structure.
Some crystal structures are fcc, bcc, hcp and diamond.
Amorphous solids do not have long range atomic order because the sub-units are disordered.
Polymers have long Carbon chains which are held together by a combination of weak and strong bonds.
Defects in solids
Microscopic defects can occur in crystals, amorphous solids and polymers.
In crystals there are:
Point defects (Vacancies, Interstitials, Impurities),
Line defects (Edge and Screw Dislocations),
Planar defects (Grain boundaries, Microcracks) and
Volume defects (Voids).
Microcracks and Voids occur in Amorphous materials.
Polymers can have partly crystalline regions so can have all of these defects.
An elastic solid will return to its original size and shape when the deforming force is removed.
Normal Stress is Normal Force/Area,
Shear Stress is Tangential Force/Area, and
Bulk Stress is the Pressure.
Normal Strain is (Extension in force direction)/(original Length force direction),
Shear Strain is (Extension in force direction)/(Length at right angles to force direction), and
Bulk Stress is the (Change in Volume)/(Unstressed Volume).
An elastic modulus shows how much strain results from the stress.
Young's Modulus is (Normal Stress)/(Normal Strain),
Shear Modulus is (Shear Stress)/(Shear Strain), and
Bulk Modulus is (Pressure)/(Bulk Strain).
The restoring force between atoms can be represented as springs if the applied force is small.
The interatomic spring constant equals Young's modulus times the equilibrium spacing.
Why materials are weak
The weakness of brittle solids is due to microcracks.
The weakness of plastic solids is due to dislocations.
Simple Harmonic Motion
Damped Simple Harmonic Motion:
Forced Simple Harmonic Motion:
Vibrations in structures come from two main sources, internal or external.
Vibrations can be reduced by damping materials and design.
Waves move energy through a medium without moving the whole medium.
In longitudinal waves the vibration is in the same orientation as the wave movement.
In transverse waves the vibration is at right angles to the wave movement.
Amplitude: A, is half the wave height.
Wavelength: λ, is the distance between successive maxima (or minima).
Frequency: ν, is the number of maxima (or minima) that pass per second and the reciprocal of the Period, T.
Hearing depends on both frequency and intensity.
Frequency is measured physically in Hertz and subjectively in Mels.
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