Materials Flashcards
Density
A measure of how closely packed particles are in a material
Defined as the mass per unit volume of a material
Density equation
p=m/v
Kgm-³
Whatever you do to the unit…
You do to the conversion factor
Pico
-12
Fempto
-15
Measure mass
Balance
Measure mass of liquid
Measure mass of container empty and full With balance Subtract to get mass of liquid Read off volume on beaker Density calculation
Measuring irregular solid density
Measure mass with balance
Read off volume on beaker with and without object fully submerged in the water
Difference in volume is volume of solid
Density calculation
If an objects density is less than the density of a fluid then
It will float
Hooke’s law
The extension produced by a force in a wire or spring is directly proportional to the force applied
Up to the limit of proportionality
Express Hookes law mathematically
F=kx
Limit of proportionality
Point up to which Hookes law is obeyed in which force is directly proportional to extension
Point beyond which f and x stop being proportional
Elastic limit
Not the same as the limit of proportionality
Occurs after limit of proportionality
Point beyond which a stretched spring won’t return to its original length
When doesn’t a spring return to its original length
Beyond the elastic limit
Gradient of force extension graph
Spring constant
Stiffness
Before limit of proportionality
What is the spring constant
Measure of resistance to stretching
Stiffness
Extension of springs in parallel
Spring constant
Stretch by half
Meaning spring constant has doubled
Springs in parallel
Extension
Spring constant
Stretch twice as far
So spring constant halves
Combined spring constant equation for series
1/ktotal = 1/k1 + 1/k2
Combined spring constant for springs in parallel
Ktotal = K1 + K2
Area under the graph of force extension
Work done on the spring
Since W=Fs and s=extension
Explain the area under a force extension graph
Weight of masses stretches spring and does work on it
Increasing its elastic potential energy
So area gives elastic potential energy/strain energy stored stretching it to that point
In region before limit of proportionality area is a triangle
So can be calculated by doing 1/2 Fx
Three equations to work out strain energy
E=1/2kx²
E=1/2F²/k
E=1/Fx
Plastic deformation
Point in which an unloaded spring no longer returns to its original length when unloaded
How do you work out the permenant extension
Draw a line from top of graph parallel to gradient of the region of proportionality
Where it crosses x axis
What is the difference in energy for the area loading and unloading
Energy used to permentantly deform the spring
Elastic behaviour
Sample that has been deformed by a force returns to its original shape when the force is removed
Elastic limit
Maximum force applied up to which a material can be stretched and return to its original shape
Plastic behaviour
When the deforming force is removed and the material does not return to its original shape
Ductile
Can be easily and permenantly stretched
Drawn out into wires
Brittle
Cannot be permenantly stretched Will break soon after the elastic limit Tend to be very strong under compression But weak under tension Concrete Mortar Brick Stone
Fracture
Point at which the material breaks due to the force applied
Small plastic region
Brittle
Large plastic region
Ductile
Higher fracture point
Stronger material
Steeper gradient
Stiffer material
Special case rubber
Isn’t really a Hookean region or limit of proportionality
Gradient still represents spring constant
But spring constant is constantly changing
Difference in energy/area for rubber
Energy retained by the rubber as heat
How does the graph of rubber show it doesn’t obey Hookes law
No linear section to the graph
Where force is proportional to the extension
What does spring constant depend on
Material
Dimensions
A material will stretch … if longer
More
A material will stretch … if its thicker
Less
Why is youngs modulus better than spring constant
Isn’t affected by materials dimensions
Stress accounts for thickness
Strain accounts for length
Youngs modulus
Tensile stress/Tense strain
Tensile stress
F/A
Tensile strain
Change in length over original length
Ratio
Youngs modulus terms
YM=Fl/A◇L
Units for stress/YM
Nm-²
Pa
Assumption with YM
Assume the cross sectional area is constant
In reality the decrease in area is very small
So say negligible
Breaking stress
Stress at the fracture point
Breaking strain
Strain at the fracture point
Area under a stress strain graph
Area=Stress x Strain
Area=F/A x ◇L/L (W=F◇L)
A=W/AL
So the work done per unit volume
Can the energy equations be used for youngs modulus
Yes
Breaking strain equation
Max extension/Origional length
Breaking stress
Maximum force/Area
True or false
A graph of stress against strain is always linear up to the elastic limit
False
Limit of proportionality
True or false
If a material is stretched up to its elastic limit it will return to its original shape when released
True
Hasn’t passed its elastic region which just means F and X aren’t proportional