P11 materials

• the density of a substance is defined as its mass per unit volume
• the equation for density is: $\rho =$$\frac{m}{v}$

  $\rho$ is density in $kgm^{-3}$

  $m$ is mass in $kg$

  $v$ is volume in $m^3$
• hooke’s law states that the force needed to stretch a spring is directly proportional to the extension of the spring from its natural length
• the equation for hooke’s law is: $F =$$k\Delta L$

  $F$ is force in N

  $k$ is spring constant in Nm

  $\Delta L$is extension in m
• the elastic limit of a spring is the point where if a spring is stretched beyond it, the spring does not regain its original length when the force applied is removed
• the limit of proportionality of a spring is the point where it stops obeying hooke’s law
• for two springs in parallel, the overall spring constant is equal to the spring constant of one spring plus the spring constant of the other spring
• for two springs in series, the overall spring constant is equal to 1 divided by the reciprocal of the spring constant of one spring plus the reciprocal of the spring constant of the other spring
• the energy stored in a stretched spring is elastic potential energy
• when a spring is released, the elastic potential energy is converted into kinetic energy
• the work done to stretch a spring is $\frac{1}{2} F\Delta L$, this work done is stored as elastic potential energy
• the equation for elastic potential energy stored in a stretched spring is: $E_p =$$\frac{1}{2}k\Delta L^2$
• force-extension graphs describe the behaviour of a specific object
• on a force-extension graph, a spring following hooke’s law would appear as a straight line, until its limit of proportionality when the line would begin to curve to the right
• the elasticity of a solid material is its ability to regain its shape after it has been deformed or distorted, and the forces that deformed it have been released
• deformation that stretches an object is tensile
• deformation that compresses an object is compressive
• tensile stress is defined as force applied per unit cross-sectional area
• the equation for tensile stress is $\sigma =$$\frac{F}{A}$

  $\sigma$is tensile stress in $Pa$

  $F$is force in $N$

  $A$is area in $m^2$
• tensile strain is caused by tensile stress, it is extension over original unit length
• the equation for tensile strain is $E =$$\frac{\Delta L}{L}$

  $E$is tensile strain in no units

  $\Delta L$is extension in m

  $L$is original length in m
• from zero to the limit of proportionality of a material, tensile stress will be proportional to tensile strain
• young modulus is a constant value, different for each material, which describes the stiffness of the material, it is represented by E
• the equations for young modulus are: $E =$$\frac{tensile\:stress}{tensile\:strain}$ and $E =$$\frac {FL}{A\Delta L}$
• stress-strain graphs describe the behaviour of a material
• the highest point of the line on a stress-strain graph is the ultimate tensile stress, this is the maximum stress the material can possibly withstand
• the end of the line on a stress-strain graph is the breaking point, this is the point where the material breaks apart
• the gradient of the straight part of the line on a stress-strain graph is the young modulus
• the point where the line stops being straight on a stress-strain graph is the limit of proportionality, this is where the material stops obeying hooke’s law
• the strength of a material is its ultimate tensile stress
• a brittle material snaps without noticeable yield, this would appear on a stress-strain graph as a straight line which ends before curving much at all
• a ductile material can be drawn into a wire, this would appear on a stress-strain graph as a line which is relatively long horizontally
• force-extension graphs can show two main behaviours: plasticity and brittleness
• plasticity on a force-extension graph is when the material experiences large amount of extension as force is increased, even beyond the elastic limit
• brittleness on a force-extension graph is when the material extends very little and is likely to fracture at low extension
• loading is adding force to a material, unloading is taking force away from a material
• once a material is stretched beyond its elastic limit, a force-extension graph showing loading and unloading will not return to the origin, but the loading and unloading lines will be parallel

  this means the material has a permanent extension
• the area between a loading and unloading line is the work done to permanently deform the material
• when a stretch is elastic, all the work done is stored as elastic strain energy
• when a stretch is plastic, work is done to move atoms apart, so work done is dissipated as heat