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Chapter 2Motion in One Dimension
MULTIPLE CHOICE
1. The position of a particle moving along the x axis is given by x = (21 + 22t 6.0t2)m, where t is in s.
What is the average velocity during the time interval t
Physics 105 (Fall 2012) Week #4 Notes: Introduction to
Symmetries and Conservation Laws
A.E. Charman
Department of Physics, University of California, Berkeley
(Dated: 10/10/12)
Here we elaborate and expand on the material of Taylor, Classical Mechanics (2
Physics 105 (Fall 2012) Week #3 Notes:
Comments on Newtons Laws and Forces
A.E. Charman
Department of Physics, University of California, Berkeley
(Dated: 9/5/12; Revised 9/21/12)
Here we continue our review of vector mechanics, particularly the meaning of
Physics 105 (Fall 2012) Week #5 Notes:
Conservative Forces and Conservation of Energy
A.E. Charman
Department of Physics, University of California, Berkeley
(Dated: 9/21/12)
Here we continue our review of vector mechanics, particularly the handling of sys
Physics 105 (Fall 2012) Supplementary Notes: Chain Rules
H. Haggard and A.E. Charman
Department of Physics, University of California, Berkeley
(Dated: 9/29/12)
These are some supplementary notes on the care and feeding of chain rules. They are an attempt
Making Sense of the Legendre Transform
R. K. P. Zia1 , Edward F. Redish2 , and Susan R. McKay3
arXiv:0806.1147v2 [physics.ed-ph] 4 Mar 2009
1
Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061 USA
2
Department
Rep. b o g . Phys. 56 (1993) 7 91458. Printed in the U K
General covariance and the foundations of general relativity:
eight decades of dispute
John D Norton
Department of History and Philosophy of Science, Univeniry of Pinsburgh. Pinsburgh. PA 15260,USA
Notes on Index Notation
The purpose of these notes is to introduce you to a very powerful tool used by physicists in
vector analysis, linear algebra, and tensor analysis: index notation. These notes are intended to
complement professor Charmans lecture no
Dierential Equations: Greens Function and Fourier Series
Methods
Fourier Series
Suppose youd like to solve the dierential equation
x+
b
k
F (t)
x+ x=
m
m
m
where F (t) is a periodic function with period T (hence frequency = 2/T ). Since F (t) is periodic,
A Primer on Dimensions and Units
Glen Thorncroft
Mechanical Engineering Department
Cal Poly State University, San Luis Obispo
1. Dimensions vs. Units
Nearly every engineering problem you will encounter will involve dimensions: the
length of a beam, the ma
UNIVERSITY OF CALIFORNIA BERKELEY Structural Engineering,
Department of Civil Engineering
Mechanics and Materials
Fall 2002
Professor: S. Govindjee
A Quick Overview of Curvilinear Coordinates
1
Introduction
Curvilinear coordinate systems are general ways
Introduction to the Calculus of Variations
Jim Fischer
March 20, 1999
Abstract
This is a self-contained paper which introduces a fundamental problem in the calculus of variations, the problem of nding extreme values
of functionals. The reader should have
Homework # 14 Solutions
1. Georgi 3.5
(a) Let x1 and x2 be the positions of mass 1 and 2 with respect to the left wall. x1 and x2
are small quantities.
1
1
T = m1 x2 + m2 x2 = M =
1
2
2
2
m1 0
0 m2
1
1
1
U = k1 x2 + k2 (x2 x1 )2 + k3 (L x2 )2
1
2
2
2
The
Physics 105 (Fall 2012) Supplemental Notes: Coupled Harmonic
Oscillators and Normal Modes
A.E. Charman
Department of Physics, University of California, Berkeley
(Dated: 11/30/12)
Some explorations of tackling coupled oscillations via normal mode expansion
Physics 105 (Fall 2012) Week #4 Notes: Systems of Particles and
Conservation Laws
A.E. Charman
Department of Physics, University of California, Berkeley
(Dated: 9/5/12; Revised 9/21/12)
Here we continue our review of vector mechanics, particularly the han
Physics 105 (Fall 2012) Week #2 Notes: Comments on Coordinates
A.E. Charman
Department of Physics, University of California, Berkeley
(Dated: 8/27/12)
Here we explore some important aspects of coordinate systems and changes of coordinates, focusing on how
Chapter 12-The Laws of Thermodynamics
Student: _
1. The volume of an ideal gas changes from 0.40 to 0.55 m3 although its pressure remains constant at 50 000 Pa.
What work is done on the system by its environment?
A. -7 500 J
B. -200 000 J
C. 7 500 J
D. 20
Chapter 10-Thermal Physics
Student: _
1. Which best describes the relationship between two systems in thermal equilibrium?
A. no net energy is exchanged
B. volumes are equal
C. masses are equal
D. zero velocity
2. The zeroth law of thermodynamics pertains
Chapter 9-Solids and Fluids
Student: _
1. Which state of matter is associated with the very highest of temperatures?
A. liquid
B. plasma
C. gas
D. solid
2. A copper wire of length 2.0 m, cross sectional area 7.1 10-6 m2 and Young's modulus 11 1010 N/m2 ha
Chapter 11-Energy in Thermal Processes
Student: _
1. Arrange from smallest to largest: the BTU, the joule, and the calorie.
A. BTU, J, cal
B. J, cal, BTU
C. cal, BTU, J
D. J, BTU, cal
2. Of the following systems, which contains the most heat?
A. 100 kg of
Multiple Choice
1. Which is not true of acceleration?
a. Speed can be constant, but acceleration can still take place.
b. It is a change in velocity per unit of time.
c. It is the slope of the displacement - time plot.
d. It can be both positive and negat
Chapter 2-Motion in One Dimension
Student: _
1. A change in a physical quantity w having initial value wi and final value wf is given by which of the
following?
A. wi - wf
B. wf - wi
C. (wf + wi)/2
D. none of the above
2. Displacement is which of the foll
Chapter 1-Introduction
Student: _
1. Since 1983 the standard meter has been defined in terms of which of the following?
A. specific alloy bar housed at Sevres, France
B. wavelength of light emitted by krypton-86
C. distance from the Earth's equator to the
Assignment 12: Physics 105 Spring 2010
December 9, 2010
Problem: 16.4
If we make the change of variables
= x ct, = x + ct
=
+
,
= c
+c
x
t
Thus
2
2
c2 2
t2
x
u = c2
+
2
+
2
u = 4c2
2u
Problem: 16.5
(a) Wave equation:
2u
=0
which and are dened in
University of California, Berkeley
Physics 105 Practice Problems
A.E. Charman, E. Kur
Fall 2012
9. Molecular Mishmash [30 points]
Richard Feynman one remarked that, in the even of the collapse of civilization, if he could pass on one
sentence to future hu
Midterm # 2 Solutions
1. (a) In the non-inertial frame of the rotating Earth, the river experiences the gravitational,
centrifugal, and Coriolis forces. The combination of gravity and the centrifugal force
denes what we mean by down, as well as sets the v
Physics 105, Fall 2011
Classical Mechanics
Haggard & Jeevanjee
List of Problems to Study for the Final Exam
Problem 1. (Sloshing wine)
Consider a wine glass which has a spherically shaped bowl. Assume that this glass is lled halfway
with wine, so that the
Department of Physics
UC Berkeley
Fall 2012
Some Tips for Solving Physics Problems
Here are a few suggested frameworks, approaches, and strategies attempting to summarize,
formalize, or capture what is it we do when trying to solve a physics problem.
Desp
Homework # 13 Solutions
1. (a)
L =L+
Pi =
dF
F
F
= L + i qi +
dt
q
t
L
F
L
F
= i + i = pi + i
i
q
q
q
q
(b) The quick way to show this is to check if (q i , pi ) (q i , Pi ) is a canonical transformation.
cfw_q i , q j = 0
since the q s didnt change.
cfw
Homework # 12 Solutions
1. Energy is conserved since there is no work done by the non-conservative force the ground
exerts on the block (be it frictional or normal). If the edge of the block is constrained not to
slide, then the motion is purely rotationa