13 - materials (young modulus)

Question 1

springs and elasticity

Answer 1

• hookes law = Force is directly proportional to extension (F=kx, k is stiffness of spring)
• gradient of an F/x graph will be constant while the spring obeys hookes law
• gradient = k, spring constant (stiffness)
• only DIRECTLY proportional when straight line passes through origin, otherwise just a straight line means regularly proportional
• limit of proportionality is the point when line stops being straight, hookes law is no longer obeyed

Question 2

Elastic potential energy

Answer 2

• energy stored in a body due to deformation
• equivalent to the work done in compressing a material
• equal to average force*extension, or 1/2Kx^2
• work done = area under the F/x graph
• elastic strain energy = 1/2Fx

Question 3

young modulus

Answer 3

• ratio of stress to strain (stress/strain)
• stress = force/cross sectional area = force per unit area (Pa)
• strain = change in length/original length = extension per unit length (no unit)
• young modulus = stress/strain = (F/A)/(l+x/l) = (Fl)/(Al+x)
• unit is still Pa as strain has no unit

Question 4

points in a stress/strain graph

Answer 4

-elastic limit = the point where Hooke’s law lo longer applies (when it goes from straight to curved)
- yield point = when a material gives in under its Ultimate Tensile Stress (when the line peaks)
-breaking point = point where it breaks (when the line
stops)
- elastic deformation occurs while the line is still straight, plastic is when it will not
-UTS = strength
- Area under graph = toughness
- gradient = stiffness

Question 5

polymeric graphs

Answer 5

• non linear shape (s-shaped)
• odd shape is due to the relationships of IMF between polymer strands
• more steep sections = stretching bonds between atoms
• less steep sections = straightening strands of polymer

Question 6

Energy density/Hysteresis

Answer 6

• energy density = work done/volume = 1/2 young modulus
• also the area between the line and the strain (x) axis on a graph
• when loading and unloading a force on a polymer, some energy is lost as internal energy
• this leads to a difference in the two lines when shown on a stress/strain graph
• the area between the two lines is equal to the applied force converted into internal energy i.e heat