Integration
Example 2-17
SECTION 2-4
The Moving Elevator
PICTURE The time of flight of the screw is obtained in the solution of Example 2-16. Use
this time to solve Parts (a) and (b).
SOLVE
Cover the column to the right and try these on your own before lo
1
Freefall
Kinematics
Multiple Choice / Short Answer:
1. If a ball is thrown with a velocity of 25 m/s at an angle of 37 above the horizontal, what
is the horizontal component of the velocity?
a) 15 m/s
b) 18 m/s
c) 20 m/s
d) 25 m/s
2. A stone is thrown h
Name: Vinh Vu
Date: Nov. 19, 2015
Friction and Acceleration
Write out a definition for each term below.
Newton's First Law of Motion- If an object is at rest, it stays at rest unless acted upon
by a force. If an object is in motion, it moves in a constan
Vu1
Vinh Vu
Gregory, Lawrence
English P3
15 May 2015
Is the Use of Standardized Testing Improving Education in America?
As a part of a schooling system, students are required to take a certain number of
standardized tests offered by the states or the scho
Name: Vinh Vu
Date: Nov. 19, 2015
Friction and Acceleration
Write out a definition for each term below.
Newton's First Law of Motion- If an object is at rest, it stays at rest unless acted upon
by a force. If an object is in motion, it moves in a constan
Name: Vinh Vu P.2
The Skate Basic Park Intro to Energy Potential and Kinetic PhET Lab
Introduction:
When Tony Hawk wants to launch himself as high as possible off the half-pipe, how
does he achieve this? The skate park is an excellent example of the conse
Name: Vinh
Vu P.2
Momentum and Simple 1D Collisions PhET Lab
Introduction: When objects move, they have momentum. Momentum, p, is
simply the product of an objects mass (kg) and its velocity (m/s). The unit
for momentum, p, is kgm/s. During a collision, an
Student directions Calculus Grapher for Math
Vinh Vu
Period 2
Directions: For each question, use a colored pencil to draw what you think the derivative and integral curves will
look like. Then use a different color to correct your sketches after testing y
Name Vinh Vu
Class Period 2
Calculus Grapher
Type the answers in bold font
1. What is the derivative of position?
The derivative of position is velocity. When priming the position of an object, the
slope/prime of it represents the rate of change or the mo
AP Physics B
Name Vinh Vu
Period 2
PhET Projectile Motion Lab
Google PhET Projectile, it will be the first hit
(if you NEED a URL, its http:/phet.colorado.edu/en/simulation/projectile-motion)
Then click the
button beneath the picture. Take a few
minutes t
Test # 2 Solution
Problem # 1 Admixing Al to Ag creates an Ag1-xAlx alloy (in which Al atoms substitute for Ag atoms) and leads to an increase of the Fermi energy. Using a free electron model and assuming that Al is trivalent while Ag is monovalent calcul
Test # 2 (Thursday, 21 April)
Problem # 1 Admixing Al to Ag creates an Ag1-xAlx alloy (in which Al atoms substitute for Ag atoms) and leads to an increase of the Fermi energy. Using a free electron model and assuming that Al is trivalent while Ag is monov
Test # 1 (due 24 February)
Problem # 1 X-rays with = 1.54 are scattered off a crystal which has the CsCl structure (see Kittel, Chapter 1, Fig.20) with cubic lattice constant a = 2.7 . Find all allowed scattering angles and the associated lattice planes c
Test # 1 Solution
Problem # 1 The CsCl structure is simple cubic with two non-equivalent atoms in a unit cell which have coordinates r1 = 0 and r2 = (a / 2)(x + y + z ) . Denoting the atomic form-factors of the two atoms f1 and f 2 and taking into account
Homework # 9 - Solution
Problem # 1. Compute the concentration of electrons and holes in an intrinsic semiconductor InSb at room temperature (Eg=0.2eV, me = 0.01m and mh = 0.018 m). Determine the position of the Fermi energy. For an intrinsic semiconducto
Homework # 9 (due Thursday, 14 April)
1. Compute the concentration of electrons and holes in an intrinsic semiconductor InSb at room temperature (Eg=0.2eV, me = 0.01m and mh = 0.018 m). Determine the position of the Fermi energy. 2. Indium antimonide has
Homework # 8 - Solution
Problem #1 A two-dimensional metal has one atom of valence one in a simple rectangular primitive cell of a1 = 2 and a2 = 4. (a) Draw the first and the second Brillouin zones. (b) Calculate the radius of the free electron Fermi sphe
Homework # 8 (due Thursday, 7 April)
1. A two-dimensional metal has one atom of valence one in a simple rectangular primitive cell of a1 = 2 and a2 = 4. (a) Draw the first and the second Brillouin zones. (b) Calculate the radius of the free electron Fermi
Homework # 7 - Solution
Problem # 1 Consider the free electron energy bands of an fcc crystal lattice in the reduced zone scheme in which all k's are transformed to lie in the first Brillouin zone. Plot roughly in the [111] direction the energies of all b
Homework # 7 (due Tuesday, 29 March)
1. Consider the free electron energy bands of an fcc crystal lattice in the reduced zone scheme in which all k's are transformed to lie in the first Brillouin zone. Plot roughly in the [111] direction the energies of a
Homework # 6 - Solution
Problem # 1: Show that the kinetic energy of a three-dimensional electron gas of N electrons at zero temperature is U=3/5NEF. For free electrons the density of states is given by
V 2m D( E ) = 2 2 2
3/ 2
E1/ 2 .
Using the formula
Homework # 6 (due Thursday, March 3)
1. Show that the kinetic energy of a three-dimensional electron gas of N electrons at zero temperature is U=3/5NEF. 2. Show that the density of states of a free-electron gas in two dimensions is independent of energy.
Homework # 5 - Solution
Problem #1 The dispersion relation for the 1D monoatomic lattice is
=
4C qa qa sin = m sin , M 2 2
where m is the maximum frequency. The density of vibrational modes is given by D( ) = 1 . d / dq
1
L
By differentiating we obtain
a
Homework # 5 (due Thursday, 17 February)
1. Using the dispersion relation for the monoatomic linear lattice of N atoms with nearest neighbor interactions, show that the density of vibrational modes is given by 2N 1 , where m is the maximum frequency. D (
Homework # 4 Solution
Problem #1 (a) The total energy of the wave is the sum of the kinetic energy Ekin and the potential energy Epot. The kinetic energy is the sum of the kinetic energies of all atoms, i.e.
Ekin 1 du = M n , 2 n dt
2
dun is the velocity
Homework # 4 (due Thursday, 10 February)
1. Consider a longitudinal wave un = A cos ( qna t ) in a monoatomic linear lattice of atoms of mass M, spacing a and nearest-neighbor interaction C. (a) Show that the total energy of the wave is given by
1 E= M 2
Homework # 3 Solution
Problem #1 (a) The equilibrium interatomic distance R0 is determined by the minimum of the binding energy as a function of interatomic distance R. The binding energy per atom is given by
U=
6 A q2 , Rn R
(1)
where it is assumed that
Homework # 3 (due Thursday, 3 February)
1. Consider an ionic solid which has the sodium chloride structure and in which the
repulsive potential between two atoms is represented by A/Rn, where constants A and n
are phenomenological parameters. (a) Show tha
Homework # 2 - Solution
Problem #1 The primitive vectors in the simple cubic lattice are a1 = ax; a 2 = ay; a3 = az . The reciprocal lattice vectors are 2 2 2 b1 = x; b 2 = y; b3 = z. a a a We can now build vectors G: 2 2 2 G = hb1 + kb 2 + lb 3 = h x+k y