3 185 Problem Set 7 Adjusted
Fluid Dynamics
Due Friday November 14 2003
1. Power-law non-Newtonian uid behavior (20)
A polymer melt is forced through a at channel of thickness between two xed horizontal plates
by a pressure dierence P (inlet pressure minu
Solution 8.1
Hookes law for an isotropic linear elastic deformation is given by
i=3
0n = 2Mij + Mn 2 (iii (1)
7,21
where 61-]- = 0 if i 7é j and 61-]- = 1 if i = j. This equation is the component
form of the matrix equation in the Lecture Notes. The above
2.003 Engineering Dynamics
Problem Set 9-Solution
Problem 1
Find the equation of motion for the system shown with respect to:
a) Zero spring force position. Draw the appropriate free body diagram.
b) Static equilibrium position. Draw the appropriate free
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
6.013 Electromagnetics and Applications
Problem Set 12 (six problems)
Suggested Reading:
Text:
Sections: 12.3-12.4, 13.1-13.2.1, 13.2.3-13.2.4, 13.3, 9.4
Probl
1. Settling of magnesia particles in water (17)
Small and relatively uniform magnesium oxide particles can be made by precipitation from a supersat-
urated aqueous solution. Here we will study how quickly they sink through stagnant solution so they
can be
Solutions to Problem Set 12
12.1 (a) c = sin-1(k2/k1) = sin-1(c1/c2) = sin-1(2/1)0.5 = 80.9 degrees
(b) x = (kz2-ko2)0.5 where kz/ko = sin 850. It follows that -1 = 0.60 o
(c) D = ~4o. Note that decay is rapid relative to D, so we might guess D = ~0.6(x/2
Erratum
0 Usually 1M?) denotes the solution of the S.S.E7 and \II(?7t) that of the T.D.S.E.
Thus7 equation (2) should be corrected:
V2¢(?) + WWW?) = EM?) (1)
Same correction for (a5):
\II(J;,t) = Aedkxm) + BeKkww) is a solution of the timedependent Schrod
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.013 Electromagnetics and Applications
Problem Set #1 SOLUTION
Fall Term 2005
Problem 1.1
b.
T=
s
Q1Q2
Mg
=
where sin = ,
2
2l
cos 4 0 s sin
Q
Q1 = Q2 =
2
2.71/2.710 Optics, Spring 2014, Solution for Quiz 1
MASSACHUSETTS INSTITUTE of TECHNOLOGY
Department of Mechanical Engineering
2.71/ 2.710 OPTICS - - Spring Term, 2014
Solution for Quiz 1
Issued Wed. 03/12/2014
Problem 1.
The given optical system is made