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Terminology

Hardness - The relative resistance of a metal or other material to denting, scratching or bending.

Tough - Able to widthstand great strain without tearing or breaking.

Strength - The limit states of compressive stress, tensile stress and shear stress.

Elastic - Capable of returning to an initial form or state after deformation. The elasticity of a solid is inversely proportional to te strength of the material.

Plastic - Capable of undergoing continuous deformation without rupture or relaxation. (Opposite of elastic).

Ductile - Being capable of sustaining large plastic deformationswithout fracture. A ductile material is any material that fails under shear stress.

Malleable - Being capable of deformation, especially by hammering or rolling.

Brittle - A material which is subject to fracture when put under stress or strain.

Creep - A failure mode of metals and some other materials when under stress in hot conditions. Rather than failing suddenlt with a fracture, the material permanently strains over a long period of time until it finally fails.

What makes a useful material?

A useful material has to widthstand forces:

• Tension and compression [along the axis, perpendicular to the material]
• Bending
• Shear [parallel to the surface]

Stress (Pa or N/m²)= force (N) / area (m²)

This can also be MN/m² or Mpa etc. [See Wikipedia]

Hooke's Law

Hooke found that materials stretch when you apply a force. Up to the point where you stress it too much, it goes back to it's origional shape. This is an elastic material (with elastic energy). After is has been overstretched too much, it breaks. [Wikipedia has more information.]

Strain = Extension (m) / Original Length (m)

Young's Modulus (Pa or N/m²) = Stress (Pa or N/m²) / Strain

Snell's Law

The angle of incidence and angle of refraction [measured using the normal], are given a constant refractive index by the formula:

μ = Sin i / sin r = speed of light in air (or vacuum) / speed of light in material = 1 / Sin C

Where i is the angle of incidence, and r is the angle of refraction, and C is the critical angle. This constant is given as Mu, μ. [Wikipedia has more information]

The sin i / sin r formula only works when the light is travelling from air into the material. If you are given a question where the light is going from the material to air, you need to invert the direction of the light (for calculation purposes only). So the angles of incidence and refraction have swapped. So if the light is going from air into a material, the formula is sin r / sin i.

Factors Affecting Resistance

• Resistivity - is an intrinsic property of a particular material. It depends on many factors e.g. density, structure, position of shells etc.
• Cross-Sectional Area - the smaller the cross-sectional area of a material, the less room there is for electrons to flow. They are therefore more likley to collide with each other and other particles
• Length - the longer the piece of material you have, the more total particles there are which the electrons have to pass. There is therefore a higher chance of collison
• Temperature - the higher the temperature, the more energy particles have, hence they vibrate more. The more they vibrate, the harder it is to pass them without colliding.

At a constant temperature:

• Resistance is proportional to length
• Resistance is proportional to 1 / cross-sectional area
• Resistance is proportional to Resistivity

From these facts, this formula can be derived:

Resistance (Ohms) = Resistivity (Ohm-metre) X Length (m) / Cross-sectional Area (m²)

R = ρl / A

Drift Velocity

Drift velocity is the average velocity of the electrons moving whena current is flowing. The electrons want to move in a straight line but will collide with atoms and other electrons. The result is that some electrons are moving in every direction. The average velocity will be from negative to positive and this is the drift velocity.