PHYSICS! -PART 2-
Thick and thin liquid feel and flow differently because they have different densities and vicosities. Solids also have densities, but measuring their viscosity would be absolutely fucking pointless, and if you tried, I'd call you a brain-dead moron.
DENSITY is the mass per unit volume of the material - Kilograms per metres cubed. Kgm^-3
p = m / V -> V = m / p
VISCOSITY is a measure of a fluid's resistance to flow. It's denoted by neeta, which is a curly, upside-down mu thing, but I can't get Greek letters so we'll call it 'n'
Upthrust in a fluid (this is both liquids and gases!) - Archimedes knew all about this. EUREKA and that shite.
The upthrust force on an object wholly or partially immersed in a fluid is equal in size to the weight of the fluid displaced.
Upthrust force = volume of fluid x density of object x gravity
U = Vp(OF SOLID)g
An object will float if the upthrust is greater than or equal to the weight of the object.
'Falling ball' method for viscosity
The ball falls because the weight is bigger than the upthrust, its speed increases. The drag increased until the drag and upthrust balance the weight (net force is zero) - it stops accelerating, this is terminal velocity.
STOKES LAW
r= radius of sphere, n = viscosity, v = velocity.
Viscous drag Fdrag = 6(pi)rnv
Volume of sphere V = 4/3 (pi) r^3
Upthrust on ball U = 4/3 (pi) r^3p(OF FLUID)g
Weight of ball mg = 4/3 (pi) r^3p(OF SOLID)g
Viscous drag force is measured in Nm^-2, it depends on the viscosity of the fluid and the volume and mass of the ball.
AT TERMINAL VELOCITY
6 (pi) rnv = 4/3 (pi) r^3g (p SOLID - p FLUID)
v = (2 / 9) ((gr^2 (p OF SOLID - p FLUID)) / n)
Terminal velocity is directly proportional to the square of the radius of the ball. Viscosity can be found from the gradient of a v / r^2 graph
FLOW OF FLUIDS
Stokes law lets you calculate drag force and is accurately valid for slow and meduim flow rates. This is for LAMINAR FLOW, where layers of fluids at different velocities flow smoothly past one another without mixing.
THEY ARE STREAMLINED
Faster flow rates create TURBULENT FLOW, causing eddies and whorls to mix the layers and increase drag
Think about when a train or a lorry goes past, and then you get a great massive gust of wind going in all directions and messes up your hair - that's turbulent flow. Turbulence transfers kinetic energy from the motion of the fluid as a whole into the kinetic energy of spinning pockets of fluid. This eventually becomes the kinetic energy of the random motion of individual atoms and molecules - creating HEAT etc.
Forces and things
A 5N force acting on an area of 0.01m^2 creates a pressure of 500Nm^-2, but the same force on an area of 0.001m^2 gives a pressure of 5000Nm^-2
Forces cause deformation - a change in size such as compression or extension. Unequal deformation in different parts of an object cause a change of shape.
PROPERTIES OF MATERIALS:
Elastic - Will spring back to original shape when force is removed
Plastic - Remains deformed when force is removed
Ductile - Can be pulled out by a tensile force into a longer thinner sape
Malleable - Can be deformed by compression
Strong - Requires a large force to break
Stiff - Does not easily change shape when force is applied
Hard - Dents or scratches another material
Brittle - Easily cracked - will not deform, is just broken
Tough - Deforms plastically and requires a large force to produce small deformation.
HOOKE'S LAW - F = kx for some materials
F is force, x is extension
When Hooke's law is obeyed, the F/x graph is a straight line through the origin, but when the graph begins to curve, the material's structure is changing - in many cases this is PLASTICALLY.
H is the limit of proportionality - beyond this, Hooke's law is no longer obeyed
P is the elastic limit. Beyond this, some deformation is permenant.
A is the yeild point. Beyond this, stretching continues for the same or even a reduced load force.
In simple materials, H and P may be the same point, but some polymer materials like rubber have H very close to zero, and may not have a yeild point at all.
A greater maximum graph height means a larger force is required.
Breaking force = max F value of graph.
A STIFFER sample has a steeper graph. The gradient of an F / x graph is stiffness. F = Kx, where K is the stiffness. Stiffness is measured in Nm^-1
The area under a F / x graph is equal to the total work done. If the material obeys Hooke's law, the area is just 0.5 x Kx^2 = o.5 x Fx
MATERIAL PROPERTIES
STRESS (denoted by a small sigma) is the force acting per unit of cross-sectional area.
sigma = F / A (in Nm^-2 or Pascals (Pa))
STRAIN (detoned by a small epsilon) is the ratio of extension and original length - the change in length over the total original length. IT HAS NO UNIT. REMEMBER THAT EXTENSION CAN BE COMPRESSION in this case - a can crushed from 12cm to 2cm has a change in length of 10cm!
epsilon = x / L
Breaking stress is a fair measurement of the strength of a material, whereas breaking force only measures the strength of the object.
YOUNG MODULUS
The Young modulus (E) of a material is given by the inital gradient of a stress / strain graph. Unlike the stiffness of a particular sample, E is independant of size and shape. It is a property of a material. It is the gradient during the ELASTIC part fo the graph.
When Hooke's law is obeyed and stress is directly proportional to strain, the ratio will equal the Young Modulus.
AND ONE LAST THING
PREFIXES!
Pico p = 10^-12
Nano n = 10^-9
Micro (mu) = 10^-6
Milli m = 10^-3
Kilo k = 10^3
Mega M = 10^6
Giga G = 10^9
Tera = 10^12
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... My mind hurts.
A cruel, cruel lover is Physics, I TELL YOU NOW. -runs off to print this-
I wish I'd done some practice papers instead, sortof. PAH.