3.4- Mechanics and Materials

definition of a moment

force × perpendicular distance from the point to the line of action of the force

definition of a couple

a pair of equal and opposite coplanar forces

moment of a couple

force × perpendicular distance between the lines of action of the forces

what is Hooke’s Law

F=ke (up to the limit of proportionality!)

what is the limit of proportionality (P)

the point when Hooke’s law is no longer obeyed

what is the elastic limit (E), and what are its units

if any more force (in N) is applied than this, the material will deform plastically

what is the opposite of elastic deformation and what does this mean

plastic deformation, which is when the material is permanently deformed (ie won’t return to its original shape)

what is plastic behaviour

material has lots of extension as the force is increased, especially beyond the elastic limit

what is brittle behaviour

it will extend very little as force increases, likely fracture at a low extension

where does the energy go in an elastic stretch

elastic potential energy/ elastic strain energy

where does the energy go in a plastic stretch

dissipated as heat

how to calculate elastic strain energy without the formula

area under force-extension graph

how are cars designed for safety

* crumple zone- work done plastically deforming bonnet of car reduces car’s kinetic energy
* seat belts- stretch to convert passengers’ kinetic energy to elastic potential energy

what does Young’s modulus measure

stiffness of a material

how to calculate Young’s modulus (words and symbols)

stress/strain or E=σ/ε

how to calculate tensile stress (σ) and units

force/cross-sectional area in Pa or Nm⁻²

how to calculate tensile strain (ε) and units

change in length/initial length (no units)

what is the breaking point and what does it look like on a stress-strain graph

the value of stress at which the material will break apart (can vary for a material according to conditions such as temperature)- the point when the graph ends

what is the yield point and what does it look like on a stress-strain graph

when you get an increase in strain/extension without an increase in stress/force- the graph has a gradient ≤0

what is the UTS and what does it look like on a stress-strain graph

ultimate tensile stress, the highest stress the material can take without breaking- the highest point on the graph

what are the missing labels

* green- elastic
* red- plastic
* pink- limit of proportionality
* purple- elastic limit
* yellow- yield point
* blue- ultimate tensile stress (UTS) + necking begins
* brown- breaking point