E = Youngs modulus (N/m?)
6 = Deection (m)
F = Force (N)
M = Moment (Nm)
l. = Length (m)
b = Width (m)
t = Depth (n1)
6 = End slope (a)
l = See Table 8.2 (m4)
y = Distance frOm neutral axis cfw_m
R =
MSE 330/BE 330 Soft Materials
Problem Set #3 Solutions
1.
I.
vt =
2 a2 g
9
a. A grain of sand: a = 50 mm,
vt =
=22001000=1200
2 a2 g
m
=6.5103
9
s
b. A polymer particle: a = 0.5 mm,
v t =2.7108
v t =
MSE 330/BE 330 Soft Materials
Problem Set #1 Solution
1. (10 points total)
a. (1 point each)
Dimethyl ether (CH3OCH3)
Hydrofluoric acid (HF)
H
Cellulose (C6H1005)n
F
b. (2 points each, where doted lin
MSE330/BE330: Soft Materials
Problem Set #4
Assigned: Thursday, November 16th, 2017
Due: Thursday, November 30th, 2017
1. Consider the following monomers: styrene, methyl methacrylate, and lysine.
Sty
BE/MSE330: Soft Materials
Problem Set #2
Assigned: 14 September 2017
Due: Thursday, 21 September 2017
1. This figure shows the phase diagram for mixtures of poly(styrene) and poly(methyl methacrylate)
6.
7. a) difference in behavior is due to the difference of the glass transition temperature of the two balls.
Even though they are of the same material and similar crosslinking, the addition of oil o
MSE 330/BE 330 Soft Materials
Problem Set #1
Due: In Class Tuesday, 12th September 2017
1.
In class, we have drawn the chemical structure of water (H2O) showing hydrogen bond formation. Answer the
fol
MSE 330/BE 330 Soft Materials
Problem Set #3
Due: In Class Tuesday, October 24th, 2017
1.
Jones 4.1 (Sedimentation & Brownian Motion)
2. Consider the motion of a fish (L 10 cm ; v 102 cm/s) and a bact
MSE 393 HW #1
Due 1/26/17 in class
Use the CES database for the elements and/or for engineering materials to create the
following plots. Then, based on your general knowledge of Materials Science, com
MSE 393 HW #2
Due 1/30/17 in class
1. Determine the location and the value of the maximum stress (for the onset of yielding or
fracture) for the 1st, 4th, 5th and 6th examples in Table B.4 (attached),
Homework #2
1. a) Durhamium is an FCC metal and Zhouium is BCC. Their atomic radii are equal, but
their molar masses are significantly different (105 and 180 g/mol, respectively). Calculate
the ratio
Homework #8
1. You are a researcher attempting to investigate the
nanoscale electrical properties of Carpickium with an
Atomic Force Microscope (AFM). A cantilever with a
nanoscale tip on the end (~25
Homework #9
1. Popeium is a metal used extensively to make tetrahedral nanoparticles, since nuclei of
solid Popeium tend to form regular tetrahedron when liquid Popeium is crystallized. For a
regular
Homework #6
1. Consider a body-centered tetragonal single crystal
material with unit cell orientation and dimensions
shown.
a. What is the most likely family of slip
0.8
directions for BCT? Determine
Homework #7
1. A block of Francium is loaded with a tensile stress. During testing, a hole with its
longest dimension perpendicular to the direction of loading was noticed.
a) What shape of hole gives
Homework #10
1. a) Using tables 12.2 and 12.3 from the textbook, predict the crystal structure of potassium
chloride and calculate its density. Compare your result to the actual value of 1.98 g/cm3.
b
Homework #5
1. Explain qualitatively why the stress vs. strain curve is linear when the applied stress is
low. (Hint: consider the energy vs. separation curve of two atoms.)
2. Europium has a Young's
Homework #4
1. In materials science, it is often advantageous to
perform experiments in vacuum to remove the
effects of contamination. A high-vacuum scanning
electron microscope (SEM) continually pump
Homework #1
1. Consider two ions:
a) Draw the U (r ) vs. r curve for the two interacting oppositely charged ions. Label
the equilibrium bond length, if any.
b) At small values of r, what force dominat
Homework #3
1. a) Recent calculations by the Srolovitz group suggest that the metal Philadelphium,
which has FCC structure, will exhibit zero electrical conductivity (the opposite
phenomenon to superc
Notations
1 if i = j
Kronecker delta: ij =
Permutation tensor:
0 if i j
0 if i = j or i = k or j = k
+1 if ijk is an even permutation of 1,2,3
1 if ijk is an odd permutation of 1,2,3
ijk
For example:
Legendre equation and Legendre polynomials
The Legendre equation, which arises in problems with spherical symmetry, e. g. when solving
the Schrdinger equation for atoms where x = cos , is
2
(1 x )
d2
Integral with a variable in the limits 0 and 2 of a function of
2
trigonometric functions cos and sin:
f (cos,sin) d .
0
Instead of integrating over the real variable we use the following transformati
Sturm-Liouville Theory Linear differential operators
We introduce the following second order differential operator L acting on a function y(x)
L y(x) = p 0 (x)
d 2 y(x)
dx
2
+ p1 (x)
dy(x)
+ p 2 (x)y(
ORDINARY DIFFERENTIAL EQUATIONS AND FOURIER
TRANSFORM
Direct application of the Fourier transform
General linear differential equation is
Dy(x ) = f(x)
where D is a linear differential operator. This
DIFFUSION
Basics
First Ficks law in isotropic medium: The flux of diffusing species is F = D grad(c) , where D is
the diffusion coefficient and c the concentration of diffusing species that is general
LAPLACE TRANSFORM AND DIFFERENTIAL EQUATIONS
cfw_
f(x)exp( px)dx
Laplace transform of a function f(x) is: g(p) = L f(x) =
0
It is defined only for x > 0 and p is either real or complex with the real
Partial differential equations
In this section we shall deal with second order partial differential equations where the function to be
determined depends on several variables x, y, z etc. (or marked d
FOURIER TRANSFORM
Exponential Fourier transform
We can expand any function f(x) into the Fourier series on an interval x (L, +L) , which
means expansion into sinusoidal plane waves of the type exp(inx