M3 Springs and Materials Flashcards

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1
Q

What is Hooke’s law?

A

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

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2
Q

what is stiffness constant/ spring constant measured in

A

Nm^-1

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3
Q

what does it mean if the stiffness constant is small vs when it’s large

A

small constant means less stiff spring

large constant means stiff spring (more force needed)

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4
Q

What is gravitational field strength on earth?

A

9.81 ms^-2

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5
Q

what do you have to remember about the y intercept

A

it is when x = 0

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6
Q

what does the area under a force-extension graph equal and whats the equation to work it out

A

work done in stretching the spring
Fx / 2 because 1/2 b X h which is 1/2Fx

so E = 0.5Fx

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7
Q

define stress and what’s its unit

A

the force acting on unit cross-sectional area of the wire
unit - Pa (pascal)
Stress = force / area

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8
Q

define strain and whats its unit

A

the fractional change in length of the wire
NO UNITS
Strain = extension / original length

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9
Q

what’s the young modulus

A

measure of the stiffness of a solid material. … It defines the relationship between stress and strain in a material.

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10
Q

what does it mean if a material has a large value of E

A

will resist elastic deformation (it is stiff) so a large stress is needed to produce a small amount of strain

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11
Q

what does the gradient equal on a stress-strain graph

A

young modulus

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12
Q

what would you do if the graph was a strain-stress graph to find the young modulus?

A

1 / gradient

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13
Q

what does the area under a stress-strain graph equal

A
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
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14
Q

what are the stages on a general stress-strain graph

A

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

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15
Q

give examples of ductile materials

draw its stress-strain graph

A

copper, aluminium, steel

same as the general graph (look it up)

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16
Q

give examples of brittle materials

draw its stress-strain graph

A

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

17
Q

give examples of polymeric materials

A

rubber and polythene

18
Q

draw a stress-strain graph for rubber

A

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

19
Q

draw a stress-strain graph for polythene

A

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

20
Q

what are the two general types of deformation in springs

A

tensile and compressive

21
Q

when springs are in series, what is the total force constant

A

1 / k = 1 / k1 + 1 / k2 + 1 / k3 …….

22
Q

when springs are in parallel what is the combined force constant

A

k = k1 + k2 + k3 ………..

23
Q

what is the limit of proportionality

A

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

24
Q

what is the elastic limit

A

if you increase the force past the elastic limit, the material will be permanently stretched

25
Q

what is elastic deformation

what is plastic deformation

A

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

26
Q

link Hooke’s law and the equation for work done in a force-extension graph

A

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

27
Q

what is ultimate tensile stress

what happens after this point

A

the maximum stress that the material can withstand before it will break

afterwards it breaks and the stress is known as breaking stress

28
Q

what’s the yield point

A

when the material stretches without any extra load

29
Q

define the strength of a material

A

a measure of the material’s ability to withstand stress without breaking
stronger the material, the higher the UTS

30
Q

on a stress-strain graph, what gradient would a stiff and strong material have compared to a weak and less stiff material

A

stiff and strong material would have a steep gradient

and the less stiff and weak material will have a shallow gradient

31
Q

describe an experiment you can do to determine the breaking stress of a thin metal wire

A
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