04 Materials Flashcards
What is density?
Density = mass / volume
What is Archimedes’ principle?
Upthrust = weight of fluid displaced
What is a fluid?
A substance that can flow
What is density?
A measure of the mass per unit volume of a substance
What is upthrust?
An upwards force on an object caused by the object displacing fluid
What is a hydrometer?
An instrument used to determine the density of a fluid
When is viscous drag exerted?
When an object is in laminar flow
What does viscous drag depend on?
Viscosity of fluid, speed of body, surface area
What is mass?
The amount of matter in an object
What is viscous drag?
A resistive force acting on an object traveling through a fluid
What is Stokes’ law?
F = 6πrηv
What are the units of the coefficient of viscosity
η? Nm^-2s or Pas
What does Stokes’ law apply to?
Small spherical objects traveling at slow speeds with laminar flow
What are the steps in proving the viscosity equation?
- Sum of forces W = U + F
- W = m(s)g, U = m(f)g, F = 6πrηv
- m = ρV
- V = 4/3πr³
- Cancel like terms in each expression
- Rearrange for η
What are some uses for Stokes’ law?
Alcohol testing, food, sports, car design, medicine, cosmetics
How do you measure the volume of irregular objects?
Measure how much water it displaces
What is upthrust?
Weight of fluid displaced
What are the properties of laminar flow?
Streamlines, no mixing of layers
What are the properties of turbulent flow?
Dissipation of energy, eddy currents, mixing of layers
What forces act when a material is stretched?
The stretching force, interatomic forces
What is Hooke’s law?
The force is directly proportional to the extension (and compression)
F = kx
What is the gradient of a force-extension graph?
The stiffness (spring constant) (nm^-1)
What is the limit of proportionality on a force-extension graph?
Where the gradient stops being constant
What is the yield point on a force-extension graph?
Where the gradient levels out (no longer proportional)
What is the elastic limit on a force-extension graph?
Between the limit of proportionality and yield point
What is the breaking point on a force-extension graph?
when there is a fracture
What is elastic deformation?
Material returns to its original shape once the deforming force has been removed
What is plastic deformation?
Material does not return to its original shape once the deforming force has been removed
What is the yield point?
Where there is a large increase in extension for a small increase in force
What does the steeper the gradient of a force-extension graph mean?
The stiffer the object
What is elastic potential energy?
The work done to stretch a spring
How do you calculate elastic potential energy from a force-extension graph?
Area underneath the graph (up to the limit of proportionality)
What is the formula for elastic potential energy?
Elastic potential energy = 1/2Fx
What are the properties of materials?
Stiff/flexible,
elastic/plastic,
ductile/malleable,
tough/brittle
What is flexible?
Small force for large extension
What is ductile?
Can be drawn into wires, materials that can be stretched or bent without breaking under stress
What is malleable?
Can be hammered into shape
What is tough?
The ability to absorb energy and plastically deform without fracture
What is brittle?
materials that are easily broken, cracked, or snapped when subjected to stress. Brittle materials have little or no plastic deformation
How does area affect how much a wire stretches?
Thin wires stretch more
, thick wires stretch less
What is tensile stress?
Tensile stress = force/area
What is the unit of stress?
Pascal
What is the difference between stress and pressure?
Stress only happens to solids, pressure applies to a surface stress occurs throughout the solid
What is ultimate tensile stress?
The maximum stress reached before fracture
What is tensile strain?
Tensile strain = extension / original length
What is the unit of strain?
No unit (it’s a ratio/fraction)
What is Young’s modulus?
Young’s modulus = stress/strain
What is Young’s modulus? definition
A property of a material that measures how difficult it is to change the shape of a material
What is the unit of Young’s modulus?
Pascals
How do you find Young’s modulus in an experiment?
- Measure the diameter of the wire
2.measure the original length of the wire
3.attach the wire to the desk and thread it over a pulley with hanging masses on the end
4.put a sticky label on the wire at the end of the meter ruler
5.add the masses to the hanger and record the distance movement of the sticky marker - workout area through pi x r^2
- workout stress for each value through force / area
- workout strain through the extention /original length
- plot stress x strain
- gradient is young
What is the area under a stress-strain graph?
The energy stored per unit volume
What is hard?
Resistant to indentation or surface is resistant to plastic deformation
What is stiff?
Large force for small extension
What is high tensile strength?
Undergo a large stress/force before breaking
What is a linear relationship?
Increase in x is constant for fixed increases in y
What happens when a wire passes its limit of proportionality?
There is a large increase in extension for a small increase in mass.
It will no longer return to its original shape as it has been plastically deformed.
How can you make the extension measurement more accurate?
Use a pointer on the wire/masses to make it easier to read,
read at eye level to avoid parallax, use a set square to ensure the ruler’s vertical,
wait for extension to finish,
add masses gently
What is laminar flow?
Where the layers of flow are parallel and do not mix/cross, no abrupt change in speed or direction of flow.
What is turbulent flow?
Where the layers of flow mix forming eddy currents and causing energy to be dissipated. Random changes in speed or direction.
What is F in Stokes’ law?
Viscous drag
What happens when spring constants are in parallel?
Kt = K1 + K2
What happens when spring constants are in series?
1/Kt = 1/K1 + 1/K2
What is the viscosity equation?
(2gr²(ρs - ρf))/9v = viscocity
How do you find the drag on an object?
Drag = ± upthrust ± weight (measure radius + mass of object & use known densities)
What is the area under a stress-strain graph?
Toughness (energy it can absorb before it snaps)
What is the difference between compressive strain and tensile strain?
Compression decreases in length, tensile increases in length
Accuracy
how close you are to the true value
sensitivity
how small a division a piece of equipment can measure to
precision
how similar repeated values are
whats the relationship between upthrust and weight when the object is floating with no movement
Upthrust of fluid = weight of object
pfvfg=povog
pfvf=movo
whats the relationship between upthrust and weight when the object is floating on the surface but is partiall submerged
density of fluid > density of object
Uf =Wo
if the object is fully submerged
volume is the same therefore the densities of the submerged object and material around is the same.
pf=po
free body diagram of falling
^ Force due to drag
I
I Upthrust+Drag=weight
O
I ^
I I upthrust
I
v Weight
free body diagram of rising
^ upthrust
I
I
I Upthrust=Drag+weight
O
I I Drag
I v
v Weight
