materials Flashcards
what does hooke’s law apply to, and when?
MATERIALS
hooke’s law applies to all materials, but only up to a point (the limit of proportionality)
what is Hooke’s law?
MATERIALS
Hooke’s law states that “the extension of a stretched wire (x) is proportional to the load or force (F)”
what happens if a weight is attached to a metal wire, where the top of the wire is supported (like tied around the clamp of a stand)?
MATERIALS
⋅ if a metal wire is supported at the top and then a weight is attached to the bottom of the wire, the wire stretches
⋅ the weight pulls down with a force F, so the wire will exert an equal force back on the support
what forces are required for a material to deform?
MATERIALS
a material will only deform (stretch, bend, twist, etc) if there is a pair of opposing forces acting on it (newton’s third law of motion)
what can hooke’s law be written as in equation form?
MATERIALS
hooke’s law can be written as: F = kx
where
k = spring constant
what does the spring constant depend on and what does it also measure?
MATERIALS
⋅ k depends on the object being stretched
⋅ k is also a measure of the stiffness of an object
what are the units for a spring constant?
MATERIALS
the units for k are: N m^-1
what does stretching a material create across the material?
MATERIALS
stretching a material creates tension across the material
where does the tension created in a stretched material act, and what is this an example of?
MATERIALS
⋅ forces of tension act along the same line as the forces stretching the material but in the opposite direction at each end of the material
⋅ they ‘pull’ on the object at either end of the material [pulling it together]
⋅ this is an example of newton’s third law of motion
does hooke’s law also apply to springs and why?
MATERIALS
⋅ YES
⋅ the extension of a spring is proportional to the force applied to it, so hooke’s law applies
what happens when you apply a pair of opposite forces to a metal spring?
MATERIALS
⋅ like any other material/object, a metal spring also changes in length when you apply a pair of opposite forces to it
what does it mean if the forces applied on a metal spring is compressive?
MATERIALS
⋅ if the forces applied on a metal spring is compressive, the spring is being squashed
⋅ and therefore the extension of the spring is negative
does hooke’s law work for compressive forces as well as tensile forces?
MATERIALS
⋅ yes, hooke’s law works just as well for compressive forces as tensile forces
⋅ for a spring, the spring constant (k) has the same value whether the forces are tensile or compressive (however this is not true for all materials)
do all materials obey hooke’s law?
MATERIALS
⋅ yes
⋅ hooke’s law doesn’t just apply to metal springs and wires, all other materials obey it up to a point (up to limit of proportionality)
when does hooke’s law stop working and what does this mean?
MATERIALS
⋅ hooke’s law stops working when the load attached to the object is great enough
⋅ this means that there is a limit to the force you can apply for hooke’s law to stay true (the limit of proportionality)
what does this graph show?
MATERIALS
⋅ the graph shows the force against the extension for [stretching] a typical wire or spring
⋅ the graph up to the point P shows that the hooke’s law is being obeyed - bc there is a linear relationship between the force and the extension (so the relationship is proportional)
⋅ when the force becomes great enough, the graph starts to curve (between points P and E)
-> metals generally obey hooke’s law up to the limit of proportionality (P)
⋅ the point marked E on the graph is called the elastic limit
-> if you exceed the elastic limit, the material will be permanently stretched (after the elastic limit, the material has plastically deformed)
-> up to the point E, the material elastically deforms - so if you remove all the forces, the material will return to its original length
⋅ beyond the elastic limit, the material will stretch further for a given force
how does rubber obey hooke’s law?
MATERIALS
some materials, like rubber, only obey hooke’s law for really small extensions
up to what point does a material show elastic deformation and what does it show after this point?
MATERIALS
a material will show elastic deformation up to its elastic limit, and plastic deformation beyond it
what types of stretches can a material undergo?
MATERIALS
materials can stretch elastically or plastically
what is elastic deformation?
MATERIALS
if a deformation is elastic, a material will return to its original shape once the forces applied are removed
what happens when a material is elastically deformed?
MATERIALS
when a material is put under tension:
1) when a material is put under tension, the atoms of the material are pulled apart from one another
2) atoms can move slightly relative to their equlibrium/resting positions, without changing their actual position in the material
3) once the load is removed, atoms return to their equilibrium distance apart
what is plastic deformation?
MATERIALS
if a material plastically deforms, the material is permanently stretched and won’t return to its original shape when the forces are removed
what happens to atoms during plastic deformation? (simple)
MATERIALS
1) some atoms in the material move position relative to one another
2) when the load is removed, the atoms don’t return to their original positions
what is an elastic material and what is a plastic material?
MATERIALS
⋅ an ‘elastic material’ is a material that deforms elastically
⋅ a ‘plastic material’ is a material that deforms plastically
how do you investigate the extensions of an object by stretching an object?(practical)
MATERIALS
method:
1) set up experiment as shown in diagram - support object being tested at top (eg. by clamp) and measure its original length with ruler
2) add masses on at time to bottom of object
3) after each weight is added, measure new length of object, then CALCULATE EXTENSION: extension = new length - original length
4) plot graph of FORCE (weight, which = mass x g) against EXTENSION for results
analysing the data:
⋅ where line of best fit is STRAIGHT, object obeys hooke’s law + gradient = k (as F = kx, like y = mx)
⋅ if you’ve loaded object beyond its limit of proportionality, graph will start to curve
how much a material stretches for an applied force depends on what? and what does this mean?
MATERIALS
⋅ how much a material stretches for a particular applied force depends on its dimensions
⋅ so the spring constant (k) won’t be constant for all samples of a particular material
if spring constant changes from one sample of material to another, what should you use to compare materials instead?
MATERIALS
if you want to compare one material to another, you need to compare their stresses and strains instead
what is strain caused by, in the simplest of terms?
MATERIALS
stress causes strain
what does it mean if forces stretch a material and if other forces squash a material?
MATERIALS
⋅ as said before, a material subjected to a pair of opposite forces might deform, i.e. change shape
⋅ if forces stretch a material, they are tensile forces
⋅ if forces squash materials, they are compressive forces
what is stress defined as and what are its units?
MATERIALS
⋅ stress is defined as the tension (force applied) divided by the cross-sectional area of the material
⋅ the units for stress are: N m^-2 or Pascals, Pa
what equation defines stress?
MATERIALS
⋅ stress = force applied / cross-sectional area
⋅ σ = F/A
what is strain defined as and does it have units?
MATERIALS
⋅ strain is defined as extension (i.e. change in length) divided by the original length of material
⋅ no, strain has no units as it is a ratio (of lengths)
what equation defines strain?
MATERIALS
⋅ strain = extension / original length
⋅ ε = x/L
when using the equations for stress and strain, does it matter if the forces are tensile or compressive?
MATERIALS
⋅ it doesn’t matter whether the forces producing the stress and strain are tensile or compressive, the same equations still apply
⋅ the only difference is that you tend to think of the tensile forces as positive and the compressive forces as negative (so compressive forces would cause negative extension)
what do you call the stress at which a material breaks?
MATERIALS
the stress that is big enough to cause a material to break is called the fracture stress
what happens to the stress on a material as the tensile force applied to the material increases?
MATERIALS
as the tensile force applied to a material increases, the stress on the material increases
describe what happens at points UTS and B on this stress-strain graph for a hypothetical material
MATERIALS
⋅ UTS on the graph shows the ultimate tensile strength of the material
⋅ point B shows the fracture stress (stress at which a material fractures):
1) as the stress increases, the atoms start to be pulled apart from one another, causing atomic planes to slip over one another
2) eventually the stress becomes so great that atomic planes can no longer slip over each other and you’re pulling on the actual bonds between atoms, causing the atoms to separate completely
3) when the atoms separate completely, the material fractures (breaks)
what is the ultimate tensile strength (UTS) of a material?
MATERIALS
the ultimate tensile strength (UTS) the maximum stress that a material can withstand before breaking (/fracturing)
where is elastic strain energy stored when a material is stretched?
MATERIALS
elastic strain energy is stored in the material that is being stretched
what is done when a material is stretched or compressed?
MATERIALS
when a material is stretched or compressed, work is done in deforming the material (bc energy is transferred to material)
what is given by the area under a force-extension graph up to the elastic limit?
MATERIALS
1) on a graph of force against extension, the work done [/energy transferred to a material when it is stretched or compressed] is given by the area under the graph
2) before the elastic limit, all work done in stretching or compressing the material is stored as energy in the material
3) this stored energy is called elastic strain energy
what makes it easy to calculate the strain energy stored inside a stretched / compressed material?
MATERIALS
⋅ the strain energy stored inside a material can be calculated quite easily if the material is obeying hooke’s law
what is the work done on stretching an elastic material equal to?
MATERIALS
the work done on an elastic material in stretching it is equal to the energy stored in the material as elastic strain energy
how do you calculate the work done on an elastic material when stretching / compressing it, and what do you need to consider?
MATERIALS
⋅ usually, work done = force x displacement
⋅ however, the force exerted on the material isn’t constant - it rises from zero to a force F
⋅ to calculate the work done, you use the average force between zero and F - which is 0.5F
⋅ therefore, work done = 0.5 x force x displacement
⋅ therefore, work done = 0.5Fx
[as the elastic strain energy transferred to a material when stretching/compressing it is equal to the work done on a material when stretching/compressing it,] what is another equation for elastic strain energy?
MATERIALS
⋅ elastic strain energy = 0.5 x force x displacement
⋅ E = 0.5Fx
(like work done = 0.5Fx)
what does the equation for elastic strain energy look like on a graph?
MATERIALS
⋅ E = 0.5Fx
⋅ this is the triangular area under a force-extension graph for a material (so the elastic energy stored by the material until the limit of proportionality)
given that hooke’s law is being obeyed, what equation can you get if you combine ‘F = kx’ and ‘E = 0.5Fx?’
MATERIALS
⋅ bc hooke’s law is being obeyed, the F in ‘F = kx’ can be replaced with ‘E = 0.5Fx’ (rearranged to give F first though befire plugging it in)
⋅ this gives E:
E = 0.5k(x^2)
what happens, in terms of work done, if a material is stretched beyond its elastic limit?
MATERIALS
⋅ if a material is stretched beyond its elastic limit, some work is done in separating the atoms
⋅ this energy (work done) will NOT be stored as elastic strain energy by the material, and so isn’t released when the force is removed
what is the equation for the young modulus?
MATERIALS
⋅ young modulus = stress / strain
⋅ E = σ/ε
what is the young modulus and what are its units?
MATERIALS
⋅ the young modulus of a material is a measure of the stiffness of a material
⋅ the units for the young modulus are: N m^2 or pascals, Pa
(young modulus has the same units as stress since strain has no units [bc strain is a ratio])
what is the relationship between stress and strain up until the limit of proportionality and what does this mean?
MATERIALS
⋅ up to the point called the limit of proportionality, stress and strain are proportional to each other
⋅ so before this limit, for a particular material, stress/strain = constant
⋅ this constant is called the young modulus, E
what happens when you apply a load to stretch a material, what does the material experience?
MATERIALS
when you apply a load in order to stretch a material, the material experiences stress and strain
what do engineers use E (young modulus) for?
MATERIALS
engineers can use E to make sure their materials can withstand sufficient forces
how do you find the young modulus of a material/wire? (method)
MATERIALS
1) set up apparatus as shown below:
2) find cross-sectional area of wire using micrometer
⋅ do this by measuring diameter of wire at three different points along wire + find average diameter
⋅ then use area of circle = πr^2
3) clamp wire to bench (as shown in diagram) so you can hang weights off one end of it
⋅ start with smallest weight necessary to straighten wire (DON’T include this weight in your final calculations)
4) measure distance between fixed end of wire + marker - this is your unstretched length
then if you increase weight, wire stretches + marker moves
5) increase weight in steps (eg, in 1 N intervals), measuring extension each time
⋅ extension = marker’s position - unstretched length
⋅ use balance to accurately find weight you add at each step
6) use your results from this experiment to calculate stress + strain on wire, + plot stress-strain graph
7) gradient of stress-strain graph gives young modulus, E
what are some safety precautions you should take when investigating the E of a wire? (for practical)
MATERIALS
you should:
⋅ conduct the experiment standing up so you can get out of the way quickly if the weights fall
⋅ wear goggles to protect eyes if wire snaps
what should you consider about the wire when setting up the equipment for investigating the E of a wire? (for practical)
MATERIALS
⋅ when setting up the equipment, the test wire used should be thin, and as long as possible
⋅ bc the longer and the thinner the wire, the more it extends for the same force, reducing the uncertainty in your measurements [for the extension, x]
what two things does a stress-strain graph give?
MATERIALS
⋅ the gradient of a stress-strain graph gives the young modulus (E) of a material
⋅ the area under the graph gives the elastic strain energy (or elastic strain energy stored) per unit volume of material (i.e. energy stored per 1 m^3 of wire)
what are features of brittle materials?
⋅ brittle materials break suddenly without deforming plastically
⋅ if you apply a force to a brittle material, it won’t deform plastically, but will suddenly snap when the force reaches a certain size
⋅ brittle materials can also be quite weak if they have cracks in them
⋅ you can break pieces off of a ceramic without the whole thing breaking
⋅ ceramics fracture/shatter via crack propagation
what are ductile materials?
MATERIALS
⋅ ductile materials can be drawn into wires without losing their strength
⋅ you can change the shape of ductile materials by drawing them into wires or other shapes - the important thing is that they keep their strength when deformed like this
why is copper being ductile a good thing?
MATERIALS
⋅ copper is ductile, and with its high electrical conductivity, this means that it’s ideal for electrical wires
what are strong materials?
MATERIALS
⋅ strong materials can withstand high stresses without deforming or breaking
what is strength a measure of ?
MATERIALS
⋅ strength is a measure of how much a material can resist being deformed by a force without breaking
⋅ this can be resisting a pulling force (so has tensile strength) or a squeezing force (so has compressive strength)
what must the steel beams that are used to create bridges be?
MATERIALS
steel beams used to create structures like bridges are very strong - they withstand the forces caused by lots of vehicles going over them without bending or breaking
what are hard materials?
MATERIALS
⋅ bc of their structure, hard materials are very resistant to cutting, indentation (becoming dented) and abrasion (scratching)
⋅ (this is bc their structure makes it very difficult to dislodge atoms from the surface of hard material)
how hard do cutting tools need to be?
MATERIALS
cutting tools need to be harder than the stuff they’re cutting
what are cutting tools often made from?
MATERIALS
cutting tools are often made from hardened steel
what are stiff materials?
MATERIALS
stiff materials have high resistance to bending and stretching
what is the relationship between the young modulus and the stiffness of a material?
MATERIALS
⋅ the stiffness of a material is measured by the young modulus (E)
⋅ so E of material ∝ stiffness of material
⋅ so the higher the E, the stiffer the material
why does the outer casing of safety helmets and safety boots need to be very stiff?
MATERIALS
the outer protective casing of safety helmets and safety boots need to be very stiff so that they keep their shape and don’t crush onto your body when something impacts on them
what are tough materials?
MATERIALS
tough materials are really difficult to break bc they can absorb a lot of energy before they break
what is toughness a measure of?
MATERIALS
⋅ toughness is a measure of how much energy a material can absorb before it breaks
what type of material is known to be tough?
some polymers, such as polythene (material that plastic bags are made from)
why must the hull of a kayak be tough?
MATERIALS
the hull of a kayak must be made from a tough material so it won’t break on rocks (so it can absorb energy from the collision and not break)
what does the stress-strain graph look like for a ductile material?
MATERIALS
⋅ the stress-strain graphs for ductile materials curve
do the stress-strain graphs for different materials change and why?
MATERIALS
⋅ yes, they do change
⋅ bc different solids have different properties, their stress-strain graphs look different too
what do the different points on this stress-strain graph for ductile material mean?
MATERIALS
Y - point Y is the yield stress
⋅ here the material suddenly starts to stretch without any extra load or with a reduced load
E - point E is the elastic limit
⋅ at this point, the material starts to behave plastically
⋅ from point E onwards, the material would no longer return to its original shape once the stress is removed
P - point P is the limit of proportionality
⋅ after point P, the graph is no longer a straight line but instead starts to bend
⋅ at this point, the material stops obeying hooke’s law, but would still return to its original shape if the stress was removed (so behaves elastically up to point P)
⋅ before point P, the graph is a straight line through the origin
⋅ this shows that, before point P, the material is obeying hooke’s law
do brittle materials behave plastically and why?
MATERIALS
⋅ brittle materials don’t tend to behave plastically
⋅ they fracture before they reach the elastic limit
what are the properties of metals?
MATERIALS
1) the atoms in a metal are usually arranged in a crystalline lattice, where metal atoms are arranged in a regular repeating pattern
⋅ the structure of metals can also be polycrystalline
2) metals are good conductors bc:
⋅ outer electrons of metal atoms don’t need much energy to escape their atoms in this crystalline structure
⋅ electrons then form a ‘sea’ of free electrons, leaving behind a lattice of ions
⋅ these free electrons make metals good conductors of heat and electricity
3) metals are stiff bc:
⋅ electrostatic attraction between ion lattice + free electrons forms metallic bonds
⋅ metallic bonds are very strong
4) metals are tough bc:
⋅ the strongly bonded lattice structure of metals makes metals tough
5) metals are ductile bc:
⋅ ions within the lattice can move when you apply a force to the metal - making it ductile
what happens when you apply a force to a metal? (atomic spacing)
MATERIALS
1) when a force is applied to a metal, the interatomic spacing between ions increases
2) this increase in interatomic spacing is uniform during elastic deformation
3) once the stress is high enough to cause plastic deformation, planes of atoms within the metal slip over each other (+ form new bonds [holding planes in place])
4) if there is a dislocation in the metal, the stress needed to cause slipping is lower than the stress needed to cause slipping in a perfect metal
what is alloying, and what is its effect?
MATERIALS
⋅ alloying is where the atoms of a second metal can be placed inside dislocations of metal (impurities) to pin them down
⋅ this increases the stress needed to cause slipping
⋅ alloying makes metals harder and less ductile
what is a crystalline structure?
⋅ where the atoms in the structure of a metal have a regular, repeating pattern
⋅ such as atoms all lining up in the same direction (/having the same orientation)
what is a polycrystalline structure?
where the structure of the material has many regions (or grains) of crystalline structure - but the structure is not completely crystalline
what happens when you apply force (dislocations moving + concentrating on edge of grain)
what are the properties of ceramics?
MATERIALS
1) ceramics like pottery, brick and glass are made by melting certain materials and then letting them cool
2) arrangements of the atoms in a ceramic can be crystalline or polycrystalline (as shown below)
⋅ the atoms in each grain of crystalline structure line up in the same direction
3) some ceramics like glass are amorphous
⋅ amorphous: there’s no overall pattern; atoms are arranged at random
⋅ the quicker a molten ceramic is cooled, the more likely it is to be amorphous
4) ceramics rarely deform plastically before they fracture bc:
⋅ the random atomic bonding in [amorphous] ceramics means there are no slip planes in ceramic lattices
⋅ bc of random atomic bonding, ceramics also don’t have mobile dislocations (dislocations that can move) - meaning that ceramics rarely deform plastically before they fracture
5) ceramics are stiff and brittle bc:
⋅ the atoms in ceramics are ionically or covalently bonded in a giant rigid structure
⋅ the strong [covalent] bonds between atoms make ceramics very stiff
⋅ while the rigid structure means that ceramics are very brittle
6) ceramics break via crack propagation bc:
⋅ ceramics being brittle means that cracks spread through them when they fracture
⋅cracks spread bc the applied force acts on a small area (the tip of the crack) so the stress is high
what are polymers?
MATERIALS
polymers are molecular chains made up of single repeating units (called monomers) joined together
what are the properties of polymers?
MATERIALS
1) polymers are very strong bc:
⋅ the monomers in a polymer chain are covalently bonded together, and so are very hard to separate
⋅ this makes even the thinnest polymer materials very strong
2) polymers are very flexible bc:
⋅ polymer chains are often entangled, and can be unravelled by rotating about their bonds when you pull them
⋅ unravelling polymers by rotating about their bonds is what makes polymer materials flexible
⋅ the more easily the monomers can rotate, the more the chains will untangle and the more flexible the polymer will be
3) polymers can be very rigid bc:
⋅ the strength and the number of bonds between the polymer chains also affect the polymer’s flexibility
⋅ the stronger the cross-linking bonds and/or the more cross-linking bonds in the polymer material, the more rigid the material
what are the two types of polymers?
MATERIALS
the two types of polymers are natural polymers (eg, rubber) and man-made polymers (eg, polythene)
how did rayleigh estimate the size of the atom? (describe rayleigh’s oil drop experiment)
MATERIALS
1) the radius of a drop of oil was measured and its volume calculated
2) the drop of oil was then released into a tub of distilled water
3) rayleigh assumed the oil drop would spread as much as it could, so the thickness of the oil patch would be the size of one molecule of oil
4) by knowing the volume of oil dropped and the radius of the oil patch, you could equate the equation for the volume of a sphere (approximately the shape of the oil drop) and the equation for the volume of a cylinder (approximately the shape of the oil patch) together to find h (the thickness of the oil patch), finding the size of one atom
what are better ways to measure the size of the atom and atomic spacing than rayleigh’s experiment?
MATERIALS
⋅ x-ray crystallography
⋅ scanning tunnelling microscope (STM)
⋅ scanning electron microscope (SEM)
⋅ transmission electron microscope (TEM)
⋅ atomic force microscope (AFM)
how does x-ray crystallography work?
MATERIALS
⋅ in x-ray crystallography, x-rays are fired at a sample
⋅ the x-rays’ diffraction patterns are then used to investigate atomic spacing and the atomic structure of the sample
how does a scanning tunelling microscope work and what is a benefit of their high resolution?
MATERIALS
1) a scanning tunnelling microscope (STM) has a very fine tip to which voltage is applied to
2) electrons from the sample’s surface tunnel from the surface to the tip and cause a current to flow
3) the tip is moved across the surface of the sample, and the height of the tip is adjusted to keep the current constant, meaning any small bumps or dips in the surface can be detected
⋅ an STM has such a fine resolution that individual atoms can be resolved and their size and spacing measured
how do SEMs and AFMs measure atomic sizes?
MATERIALS
⋅ SEMs and AFMs don’t let you ‘see’ the material’s surface directly, but they can be used to build an atom-by-atom image of the surface on a computer screen
⋅ by knowing the magnification of the image on the computer screen and the size of the ‘blobs’ representing each atom, the sizes of atoms can be calculated
what diameter do modern techniques give for an atom?
MATERIALS
⋅ modern techniques give the diameter of an atom as 0.1-0.5 nm, depending on the atom being measured
⋅ this is much more accurate than the values rayleigh estimated from his experiment
what gave the biggest percentage uncertainty in the size of an atom in rayleigh’s oil drop experiment
⋅ the biggest percentage uncertainty was given by trying to measure the very small radius of the oil drop precisely, while using equipment that has a very low resolution
⋅ the radius is cubed in the equation for the volume of a sphere, so the percentage uncertainty contributed by radius would end up being very large
