4. Materials Flashcards
What is density, p
Density is the mass is the mass per unit volume of an object
p=m/V
where V= volume (m^3)
What is upthrust, U?
The upward force an object has when it’s submerged in a fluid or gas
So acts against weight
As pressure increases with depth, the pressure at bottom of object is greater than at the top, creating a net upward force.
The size of this upthrust force is described by Archimedes Principle
What’s Archimedes’ Principle?
The upthrust force equal to the weight that the fluid displaces
F(U) = p(fluid)vg
E.g the water would weigh 70N if the box weren’t there, so the upthrust is 70N
Don’t need to derive how it works
How do we calculate upthrust?
As U=weight of fluid displaced
U=mg , p=m/v so m=pv so…
U=p(fluid)vg
How does upthrust actually work?
In a fluid, pressure. hits the object from all angles
- But the force at bottom >top
- results in a force upwards
How does floating work?
In order for an equilibria, the weight of the object, only under water, must equal the upthrust
So the volume displaced will vary on how much it weighs
U=pvg
so if density of water= 1000
U=1000 x v x 9.81
What is laminar flow?
Laminar flow is where the particles in a fluid move by smooth paths
- with no/little mixary
Tends to occur at lower speeds
What is turbulent flow?
Turbulent flow is where particles mix between layers and form separate currents
- ‘chaotic’ movement
Tends to be at faster speeds
What is Viscous drag force, F?
Viscous drag force is the force acting against the movement of an object in a fluid
- if an object was falling, there would be a drag against it
- its like air resistance in fluids
- so goes in opposite direction of flow
So for falling objects:
W=U+F at terminal velocity
They are equal as its not accelerating, it’s at a constant velocity
For rising objects:
U=W+F
What is Stokes Law?
States that if the viscous drag force, F is experienced by objects that are:
- small
- spherical
- moving slowly
- with laminar flow:
F=6πηrv
where η(eta) is the viscosity of the fluid, pascal seconds (Pas) or (Nsm^-2)
where r=radius of sphere
where v=velocity of object
What is viscosity, η dependant on?
Viscosity, η is temperature dependant
They also depend on pressure
How does viscosity, η change in most fluids?
If temp increases, η of liquid decreases
This is because the particles are free moving warmer
so the object moves through it easier
How does viscosity, η change in most gases?
If temp increases, η of gas increases
This is because it gets more ‘sticky’ so it’s harder to move
How would you find the viscosity, η for a fluid when a small spherical ball is slowly falling through the liquid?
W=U+F
p(object)vg=p(liquid)vg + 6πηrv
Then rearrange for η
What is Hooke’s Law?
States that the force needed to extend a spring is proportional to the extension of the spring
Force applied(N)=spring/ stiffness constant (Nm^-1) x extension(m)
F=k△x
where △x=extension(m)
What assumption is made when calculating the energy stored in a material under tensile stress?
That Hooke’s law applies
So the extension is directly proportional to the force
Material extended linearly
When does a material obey Hooke’s Law?
A material only obeys Hooke’s law if it’s not past it’s limit of proportionality, P
So it has to only be a small force
The point limit of proportionality, P is the first point on the graphs
If 2 springs are in parallel vs a force, how much do they stretch?
The stretching force is shared between them
Hence the extension for the given force is half what it would be for a single spring
So the stiffness is double what it would be, k+k
What is the Elastic limit (E)?
Anything after E, the material will be permanently deformed
The second point on the graphs
What happens to the boat if you throw an anchor in the water?
The weight will increase,
So as upthrust = weight in equilibrium
Weight will rise, so more of the ship will be taken out of the water to decrease the weight back and go back into equilibrium with the upthrust
What is stress, σ?
Stress, σ means how much force per unit a material is having put on it
σ=F/A
where A=area(m^2)
σ (Nm^-2 or Pa)
What is strain, ε?
Strain, ε means how much a material extends per unit length
Result of tensile force, so this is the same as tensile strain
ε=△x/x
where x=length(m)
so strain is just a proportion, so has no unit
What are pascals, Pa?
Pascals is the unit of force per m^2
So =Nm^-2
So it’s pressure
What is a tensile force?
Tensile forces pull an object to extend it, causing strain
The higher the tensile force = the more stress put on the material
What is a compression force?
Compression force pushes and compresses an object (squash it)
What is the yield point?
Beyond the yield point, the material has a sudden increased tension
As it’s atomic structure is significantly re-organised
- like a ‘slip’
The third point on the graphs
What is the Ultimate tensile stress?
The max stress the material can take
- The highest point on the graph
The fourth point on the graphs
What are the orders of the 5 points on the stress strain graph?
- limit of proportionality
- elastic limit
- yield point
- ultimate tensile stress
- breaking point
What’s the breaking point?
The point where the material breaks in half
The fifth (last) point on the graphs
What is the Young Modulus, E?
The Young Modulus, E tells us how stiff a material is
It’s the stress/strain
So E=σ/ε
E=Fx/A△x
In (Nm^-2 or Pa)
The higher YM, The more stiff the material is
What is a stress - strain graph?
Stress (y axis)
Strain (x axis)
Compares how much a material is strained with a set amount of stress on it
Same thing as an force - extension diagram
Gradient = YM
- As YM=σ/ε
- only for the part that follows Hooke’s Law
How do we find the elastic strain energy/ work done, E(el)?
We know work done=fd
- But Hooke’s Law tells us how the force is constantly changing with deforming metals
So its the avg force x extension
Which works out to be E(el)=1/2 x F△x
So this is the area under the graph is △E(el)
Since Hooke’s Law is F=k△x
△E(el)=1/2 x k(△x)^2 as well
What is a Force - extension graph?
Force - y axis
Extension - x axis
Tells us the force needed to extend gets more and more past the limit of proportionality
How can you tell which material is the strongest?
‘Strongest’ means which one can deal with the most stress without breaking
So the highest ultimate tensile stress = strongest
How can you tell which material is the stiffest?
The highest gradient = most stiff
As it can take more stress without being strained much
How can you tell which material is the most ductile?
The highest strain, the most ductile
As it can take the most extension without breaking
What is a brittle material?
A material which can’t take much strain (extension)
So opposite of ductile
Breaks with little plastic deformation
What is elastic deformation?
Strain before the elastic limit
So the material isn’t permanently damaged
What is plastic deformation?
Strain before the elastic limit
So the material is permanently damaged
What is the work done when loading and unloading a material
There will be energy lost when unloading it but gone past elastic limit
The energy lost/ work is the loading are - unloading area under graph
What’s compressive stress vs tensile stress?
Compressive
- When volume is decreased by squeezing/ compressing object
Tensile
- Where object is stretched/ pulled/ extended
