Elasticity
What are the units of stress?
Pascals (Pa)
What are the units of frequency?
Hertz (1/s)
What are the units of the friction coefficient?
It's dimensionless (A ratio)
What are the units if viscosity?
Pascal seconds (Pa*s)
What are the units of energy?
Watts (W)
How is Young's Modulus defined?
E = stress / strain
What is the formula for intrinsic frequency of a simple harmonic oscillator?
w = (m/k)^1/2
How is the friction coefficient defined?
miu = Normal Force / Lateral Force
What are the terms in Newton's Law of Viscosity, and what are their units?
τ = μ * (du/dy)
τ = Shear stress, Pa
μ = Viscosity of the fluid, Pa*s
du/dy = Shear rate, s-1
What are the terms in Fourier's Law of Thermal Conduction, and what are their units?
q = -k * dT/dl
q = local heat flux, W/ m²
k = material conductivity, W/m·K
dT/dl = Temperature gradient, K/m
What are the possible elastic behaviors of materials in the crust?
1. Elastic
2. Plastic
What's the difference between a subcritical, critical and over- damped harmonic oscillator? How does a plot of amplitude vs time would look for each?
Subcritical = Normal friction reduction
Critical =Door stopper
Over = Line
What is Amonton's first and second law of friction?
1st Law: μ = N / F
μ = Friction Coefficient
N = Normal Force, N
F = Lateral Force, N
2nd Law: Friction does not depend on the area of contact between the object and the surface
What is the definition of a Newtonian fluid? Of a Non-Newtonian fluid? Give examples.
Describe and explain the Pe, Ra and Nu dimensionless numbers and their significance to convection modeling.
Péclet number (Pe) is a dimensionless number that represents the ratio of the convection rate over the diffusion rate in a convection-diffusion transport system.
Rayleigh number (Ra) is a dimensionless number that represents the ratio of buoyancy and thermal diffusivity. The difference between solid surface temperature and free stream temperature can be used as the characteristic temperature difference. It is associated with buoyancy-driven fluid flow and can be regarded as a measure of the driving forces of natural convection.
Nusselt number (Nu) is the dimensionless that measures the heat transfer coefficient between convection and advection and appears when you are dealing with convection. It provides a measure of the convection heat transfer at the surface.
Write the equation that generalizes the problem: If you have a spring with a spring constant (k) and length (l). You attach it from the top to a stable support and append a mass (m) to its bottom end. The local gravitational acceleration is (g). It stretches a certain distance (x). You want to increase this distance a (C) amount of times. How much extra mass should you append to the bottom end the spring?
F = -kx
CF = -Ckx
Cmg = -Ckx
What are the the three numerical approximations used when modelling harmonic oscillators? What does each one include or introduce?
1. Simple harmonic oscillator
2. Damped harmonic oscillator
3. Driven harmonic oscillator
Write the equation that generalizes the problem: You are given the static friction coefficient (μs) between a box and a surface, the mass (m) of the box, the local gravitational acceleration (g). How much force is required to begin movement on the box?
f = μN
f = μ * m * g
F > μ * m * g
What is the driving force of mantle convection?
The driving force of mantle convection is primarily attributed to the heat generated by the decay of radioactive isotopes in the Earth's interior, which leads to the formation of thermal gradients and temperature differences within the mantle. As hot material rises and cooler material sinks, the resulting convective flow drives the motion of tectonic plates on the Earth's surface. Other factors, such as the lateral pull of sinking plates, the buoyancy of subducting plates and the release of latent heat during phase changes in the mantle, can also contribute to mantle convection.
What is the approximate Nusselt (Nu) number for a small Rayleigh number (Ra ~ 1000) in aconvective setting?
It is approximately 1.
Write the equation that solves the general problem for: You have the Young’s Modulus (E) of the material, a measured cross-sectional area (A) and a length (l) of wire. How much force (F) should you apply to stretch the wire from its original length to a determined extra percent (p%) length?
𝐹=𝐸∗𝐴∗Δ𝑙/𝑙
Write the equation the generalizes the problem: What is the period (T) for a Harmonic Oscillator built by attaching a mass (m) to the bottom end of a vertical spring with a spring constant (k) ?
𝑇=2𝜋√(𝑚*𝑘)
Write the equation that generalizes the problem: You are given the kinetic friction coefficient (μ) between the slider and the surface, the mass (m) of the slider, the local the local gravitational acceleration (g), the spring constant (k) of the spring attached to a side of the slider and the velocity (v) of the string elongating the spring. What is the time gap between box translations
𝑡=𝜇∗𝑚∗𝑔/(𝑘∗𝑣)
Write the equation that generalizes the problem: What is the equation and the terms that describe the terminal velocity (vt) acting on a sphere of radius (r), density (σ) and mass (m) that is falling at a constant speed (v) through a liquid of density (ρ) and viscosity (η)?
vt = 2r2Δρg / 9η
Remember the equation to estimate the temperature at depth (beneath the surface), assuming linearity:
T = mz + b
Where m is the geothermal gradient so that m = ΔT/z
Given the geothermal gradient ΔT/z = 18.4°C/km and a known point at depth A where T = 12.0°C and z = 400m, estimate the temperature at the seafloor (z=0).
T = mz + b
b = T - mz
b = 12°C - 18.4°C/km * 0.4km
T = 4.64°C