2.71 Optics
Final Exam Solutions
Spring 09
1. Consider the following system.
(a) If we position an on-axis point source at the center of the object plane (front
focal plane of L1), a collimated ray bundle will emerge to the right of L1 and
its diameter is
2.003 Engineering Dynamics
Problem Set 4
Problem 1:
1. Determine the velocity of point A on the outer rim of the spool at the instant shown when
the cable is pulled to the right with a velocity of v. Assume r<R and that the spool rolls without
slipping.
C
2.003 Engineering Dynamics
Problem Set 3Problems with concept questions and answers
Problem 1:
a) A satellite is circling the earth. It spins at a constant angular rate
0.05(rads/s)k . Two
sensitive science instruments, indicated by P in the figure, are s
2.003 Engineering Dynamics
Problem Set 11
Problem 1: Torsional Oscillator
Two disks of radius r1 and r2 and
mass m1 and m2 are mounted in
series with steel shafts. The shaft
between the base and m1 has
length L1 and the shaft from m1 to
m2 has length L2.
1. (25 ) For the telescope conguration shown below, where lenses L1 and L2 have
focal lengths f1 , f2 , respectively, the object plane and two stops S1 and S2 of
halfsizes a1 , a2 , respectively, are at the locations shown,
object
plane
L1
L2
S1
S2
a1
f1
Sample Exam 1 - Solutions
Problem 1
a.
i.
ii.
b.
Eg
Nc Nv exp
2kT
For Si: ni = 1010 cm3 , Eg = 1.12eV
Therefore: Nc Nv = 1010 exp(1.12/2 0.0258)
= 2.167 1019 cm3
ni =
For Ge: ni = 2.167 1019 exp (0.67/2 0.0258)
= 6.1 1013 cm3
1
This is 6000 times larger
Homework V solution
Problem 1.
1. The reaction rate equations for the three reactions are as follow:
k b ,1 = k f ,1 / K C1
k b,2 = k f , 2 / K C 2
Rr ,1 = k f ,1 [CO ][H 2 ] k b ,1 [CH 3 OH ]
2
Rr , 2 = k f , 2 [CO ][H 2 O ] k b , 2 [CO2 ][H 2 ]
Rr ,3 =
MASSACHESUTS ISNTITUTE OF TECHNOLOGY
FUNDAMNETALS OF ADVANCED ENEFRGY CONVERSION
SPRING 04
HOMEWORK V
DUE DATE, March 29, 2004
Problem #1
In this problem, you will practice working with finite rate reaction equations in the
context of synthetic fuel produ
3.032 Problem Set 5 Solutions
Fall 2007
Due: Start ofLecture,Monday10.29.07
(NOTETHATTHISDATEISLATERTHANINYOURSYLLABUSDUETONEWDUEDATEOFLAB2.)
1.Wehavediscussedthatlinearviscoelastic(LVE)deformationofpolymerscanresultinenergy
dissipation(i.e.,anelasticorno
MASSACHESUTS ISNTITUTE OF TECHNOLOGY
FUNDAMNETALS OF ADVANCED ENEFRGY CONVERSION
SPRING 04
HOMEWORK IV
DUE DATE, March 10, 2004
1. For an overall reaction of
H2O <=> H+ + OH(a) Use the Table 4.1 in the Lecture Note Electrochemical Energy Conversion and
St
3.15 Electrical, Optical, and Magnetic Materials and Devices
Caroline A. Ross
Fall Term, 2005
Exam 1 (4 pages)
Closed book exam. Formulae and data are on the last 2.5 pages of the exam.
This takes 80 min and there are 80 points total. Be brief in your ans
Homework IV Solution
1. For an overall reaction of
H2O <=> H+ + OH(a) Use the Table 4.1 in the Lecture Note Electrochemical Energy Conversion and
Storage to define two half cell reactions for the above reaction and calculate the
electrochemical potential