Chapter 6 - materials Flashcards
what do tensile forces produce and what do compressive forces produce
tensile forces produce extension (tensile deformation) and compressive forces produce compression (compressive deformation)
at what point on a force-extension graph does elastic deformation occur
the linear section
outline a practical used to investigate Hooke’s law
hang a spring from a fixed point and measure its length
hang known masses on the spring and calculate their weight, measure the extension of the spring when acted upon by these weights
plot a force-extension graph
be more specific than this in an exam in terms of wording e.g. using two set markers and measuring the distance between them using vernier callipers
what can be done following loading to investigate plastic deformation
the weights added can then be removed one at a time and another line is plotted on the graph, the difference in the x intercepts of the loading line and the unloading line is the plastic deformation
state Hooke’s law
“for forces less than the elastic limit of the spring, the extension of the spring is directly proportional to the force applied”
equation for Hooke’s law
F = kx
what represents the work done on a force-extension graph
the area under the graph
equations for work done/elastic potential energy
E = 1/2 x force x extension E = 1/2 x kx^2
how can knowing the work done help calculate the possible kinetic energy if a spring is released
set them equal
from this velocity can be calculated
why might a loading and unloading curve of a force-extension graph be different
the material has undergone plastic deformation
how does a metal wire react to having forces applied/removed to/from it
it follows Hooke’s law up until its elastic limit when it undergoes plastic deformation
the unloading line will be parallel but different
how do rubber bands react to loading/unloading
rubber bands do not follow Hooke’s law, they are elastic (to a point) so will return to their original shape but their loading and unloading curves are different.
they follow a hysteresis loop, more work is done loading than unloading
what is the name of the shape of the force-extension graph for rubber and how is most of the energy lost
a hysteresis loop and through heat
how does polythene react to loading and unloading
polythene does not obey Hooke’s law and easily undergoes plastic deformation
two things occur under tensile forces, what are they
tensile stress and tensile strain
calculating tensile stress (lowercase sigma)
tensile stress (lowercase sigma) = force/cross-sectional area
calculating tensile strain
strain (epsilon) = extension (x) / original length
what does a stress-strain graph look like for a ductile material
increases linearly until limit of proportionality, then hits elastic limit then curves round forming an n shape where you have yield limits, then increases under necking to hit UTS then breaks
what does a stress-strain graph look like for a brittle material
a straight line then nothing, the steeper the line the more brittle the material
what is the young modulus and how is it calculated
it can be thought of as a measure of ‘brittleness’
young modulus = stress/strain
how can you calculate the young modulus from a stress-strain graph
the gradient of the linear part
what is a strong material
one with a high ultimate tensile strength UTS
what is the yield point of a material
the point at which the material starts to extend rapidly as stress increases
what is plastic deformation
a permanent change in shape which remains after the load is removed
what is the ultimate tensile stress of a material
the maximum force (stress) a material can withstand before it breaks
what is a typical magnitude for young modulus
10^9 —> 10^12
what are some things which you should always mention when describing the properties of materials
- brittle or polymeric or rubber
- undergoes plastic/elastic deformation
- obeys or doesn’t obey Hooke’s law
what can we say about the breaking points of two objects of the same material
they are likely to both break at the same stress
this does not mean the same force
outline a practical which can be done to find the young modulus of a material
- fix a wire at one end and where it runs over a pulley at the other end
- measure diameter (at different points) and original length of the wire from the clamp to the marked point
- add masses (of a known mass) and measure extension (difference in distance from clamp to marked point) until the wire snaps
- plot a force- extension graph or stress-strain graph
- the young modulus = gradient / (a/l) or just gradient if stress-strain
what is something to remember when calculating forces for F = kx and then F = ma to calculate acceleration when something is hanging vertically
- if a mass is causing the extension you will have to consider NET force so
F(net) = kx - mg or something similar
what is the best way to lay out questions involving the young modulus and f = kx questions
write at the top all the quantities you know with their symbols so you don’t get confused
what two things to always mention if talking about how graphs show Hooke’s law
- straight line/linear
- passes through origin (if force-extension graph)
why might a rubber material be good when you don’t want elastic collisions e.g. tyres
- Rubber has a hysteresis loop shape for its force-extension graph
- hence energy is lost through heat when it is repeatedly loaded and unloaded
- hence collisions won’t be elastic
what is an important thing to watch for in strain measurements
- strain should be as a fraction/decimal not percentage but it is sometimes given as a percentage
what are some safety precautions and reliability points to make when doing the young modulus practical
Safety:
- wear goggles/ stand behind a screen when doing it in case the wire snaps
reliability:
- take 3 measurements of diameter and find an average
- put a small initial load on the wire to ‘take up slack’
- use long wire (to give larger extension values)
