M3 Springs and Materials

Question 1

What is Hooke’s law?

Answer 1

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

Question 2

what is stiffness constant/ spring constant measured in

Answer 2

Nm^-1

Question 3

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

Answer 3

small constant means less stiff spring

large constant means stiff spring (more force needed)

Question 4

What is gravitational field strength on earth?

Answer 4

9.81 ms^-2

Question 5

what do you have to remember about the y intercept

Answer 5

it is when x = 0

Question 6

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

Answer 6

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

so E = 0.5Fx

Question 7

define stress and what’s its unit

Answer 7

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

Question 8

define strain and whats its unit

Answer 8

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

Question 9

what’s the young modulus

Answer 9

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

Question 10

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

Answer 10

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

Question 11

what does the gradient equal on a stress-strain graph

Answer 11

young modulus

Question 12

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

Answer 12

1 / gradient

Question 13

what does the area under a stress-strain graph equal

Answer 13

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

Question 14

what are the stages on a general stress-strain graph

Answer 14

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

Question 15

give examples of ductile materials

draw its stress-strain graph

Answer 15

copper, aluminium, steel

same as the general graph (look it up)

Question 16

give examples of brittle materials

draw its stress-strain graph

Answer 16

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

Question 17

give examples of polymeric materials

Answer 17

rubber and polythene

Question 18

draw a stress-strain graph for rubber

Answer 18

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

Question 19

draw a stress-strain graph for polythene

Answer 19

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

Question 20

what are the two general types of deformation in springs

Answer 20

tensile and compressive

Question 21

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

Answer 21

1 / k = 1 / k1 + 1 / k2 + 1 / k3 …….

Question 22

when springs are in parallel what is the combined force constant

Answer 22

k = k1 + k2 + k3 ………..

Question 23

what is the limit of proportionality

Answer 23

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

Question 24

what is the elastic limit

Answer 24

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

Question 25

what is elastic deformation

what is plastic deformation

Answer 25

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

Question 26

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

Answer 26

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

Question 27

what is ultimate tensile stress

what happens after this point

Answer 27

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

afterwards it breaks and the stress is known as breaking stress

Question 28

what’s the yield point

Answer 28

when the material stretches without any extra load

Question 29

define the strength of a material

Answer 29

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

Question 30

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

Answer 30

stiff and strong material would have a steep gradient

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

Question 31

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

Answer 31

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