M3 Springs and Materials Flashcards
What is Hooke’s law?
F=kx
the extension of a spring is directly proportional to the force, provided the elastic limit is not exceeded
k is the stiffness or force constant
what is stiffness constant/ spring constant measured in
Nm^-1
what does it mean if the stiffness constant is small vs when it’s large
small constant means less stiff spring
large constant means stiff spring (more force needed)
What is gravitational field strength on earth?
9.81 ms^-2
what do you have to remember about the y intercept
it is when x = 0
what does the area under a force-extension graph equal and whats the equation to work it out
work done in stretching the spring
Fx / 2 because 1/2 b X h which is 1/2Fx
so E = 0.5Fx
define stress and what’s its unit
the force acting on unit cross-sectional area of the wire
unit - Pa (pascal)
Stress = force / area
define strain and whats its unit
the fractional change in length of the wire
NO UNITS
Strain = extension / original length
what’s the young modulus
measure of the stiffness of a solid material. … It defines the relationship between stress and strain in a material.
what does it mean if a material has a large value of E
will resist elastic deformation (it is stiff) so a large stress is needed to produce a small amount of strain
what does the gradient equal on a stress-strain graph
young modulus
what would you do if the graph was a strain-stress graph to find the young modulus?
1 / gradient
what does the area under a stress-strain graph equal
1/2 X stress X strain = 1/2 X F/A X x/L = Fx / 2AL Al = volume so area = energy stored per unit volume of the material
what are the stages on a general stress-strain graph
1) limit of proportionality (up to this point Hooke’s law applies)
2) elastic limit - up to this point, material still behaves elastically (after now behaves plastically)
3) yield point - material suddenly starts to stretch without any extra load
4) UTS (ultimate tensile stress) - maximum stress a material can withstand before breaking
give examples of ductile materials
draw its stress-strain graph
copper, aluminium, steel
same as the general graph (look it up)
give examples of brittle materials
draw its stress-strain graph
a straight line
has elastic behaviour until its breaking point without any plastic deformation
the smaller the gradient on the line the lower the UTS
give examples of polymeric materials
rubber and polythene
draw a stress-strain graph for rubber
doesn’t obey hooke’s law so a s shape
loads and then doesn’t break so returns ot its original shape
look graph up
draw a stress-strain graph for polythene
straight line cause obeys hooke’s law but then curves and straight horizontal line
once you unload polythene once it has been permanently deformed it will not return to its original shape/size eg plastic bag handles
what are the two general types of deformation in springs
tensile and compressive
when springs are in series, what is the total force constant
1 / k = 1 / k1 + 1 / k2 + 1 / k3 …….
when springs are in parallel what is the combined force constant
k = k1 + k2 + k3 ………..
what is the limit of proportionality
the point beyond which the force is no longer proportional to extension
aka Hooke’s law limit
after this point the graph begins to curve
what is the elastic limit
if you increase the force past the elastic limit, the material will be permanently stretched
what is elastic deformation
what is plastic deformation
elastic - the material returns to its original shape once forces are removed
plastic - the material doesn’t return to its original shape when forces are removed
link Hooke’s law and the equation for work done in a force-extension graph
from the graph E = half b X h
E = 0.5Fx
hooke’s law is F = kx
so when you sub in F into 0.5Fx
E = 0.5kx^2
what is ultimate tensile stress
what happens after this point
the maximum stress that the material can withstand before it will break
afterwards it breaks and the stress is known as breaking stress
what’s the yield point
when the material stretches without any extra load
define the strength of a material
a measure of the material’s ability to withstand stress without breaking
stronger the material, the higher the UTS
on a stress-strain graph, what gradient would a stiff and strong material have compared to a weak and less stiff material
stiff and strong material would have a steep gradient
and the less stiff and weak material will have a shallow gradient
describe an experiment you can do to determine the breaking stress of a thin metal wire
Procedure • labelled diagram • incremental increase in load / mass until wire breaks • method of attaching wire at fixed end • method of attaching load at other end • use of safety screen / goggles to protect eyes • method of securing retort stand Measurements • measurement of load / mass • measurement of diameter • use micrometer to measure diameter • averages diameter • repeats experiment Analysis • equation to determine force, e.g. mg • equation to determine cross-sectional area or A = πr2 • (breaking) stress = (max) force / cross-sectional area or 𝜎 = 𝐹/𝐴
