Korea Advanced Institute of Science and Technology
PHYSICS 101

Winter 2002
HM) #U So\u+0V\
\ (a) For Made Sysm, 0( 'Iw) W: J IN (003.9(4)
For whe( a'one
I
M = I, ( w; + (41%)
For
SPMCQ Cruf'e lu'kkowl wheel
FFOM ) (/05 _ ._ Mt
(IIw) "
From QM
@ W: = m M = itt'if M 1
Iv k. ._ ' K.
m 9 _ + + M II MM)
5 Ownw i) (f) .H :_ M c
Korea Advanced Institute of Science and Technology
PHYSICS 101

Winter 2002
ME 251 Dynamics
Issued at Dec. 2, 2015
Handout #HW 12
Due by Dec. 9, 2015
Honor Code: I have neither given nor received the details of the problems from anyone
and/or any existing solutions prepared by others when completing the final written work.
Name:
Korea Advanced Institute of Science and Technology
PHYSICS 101

Winter 2002
ME 251 Dynamics
Issued 2015 Nov. 18th
Handout #HW 10
Due by 2015 Nov. 25th
Honor Code: I have neither given nor received the details of the problems from anyone
and/or any existing solutions prepared by others when completing the final written work.
Name:
Korea Advanced Institute of Science and Technology
PHYSICS 101

Winter 2002
ME 251 Dynamics
Issued 2015 Nov. 25th
Handout #HW 11
Due by 2015 Dec. 2nd
Honor Code: I have neither given nor received the details of the problems from anyone
and/or any existing solutions prepared by others when completing the final written work.
Name:
Korea Advanced Institute of Science and Technology
Quantum Mechanics I
PHYSICS ph503

Spring 2014
Supplement
2A
The Fourier Integral
and Delta Functions
Consider a function f(x) that is periodic, with period 2L, so that
f(x) f(x 2L)
(2A1)
Such a function can be expanded in a Fourier series in the interval (L, L), and the series
has the form
f(x)
A
Korea Advanced Institute of Science and Technology
Quantum Mechanics I
PHYSICS ph503

Spring 2014
Supplement
1A
Einsteins Approach
to Plancks Law
In 1917 Albert Einstein wrote a remarkable paper in which he used classical statistical mechanics and elements of the old Bohr theory to derive the Planck distribution and to relate
spontaneous emission, as
Korea Advanced Institute of Science and Technology
Electromagnetics
PHYSICS 241

Spring 2014
Newtons Shell Theorem
Abstract
One of the principal reasons Isaac Newton was motivated to invent the Calculus was to show that in
applying his Law of Universal Gravitation to sphericallysymmetric massive bodies (like planets, stars, and the
like), one ca
Korea Advanced Institute of Science and Technology
Quantum Mechanics I
PHYSICS ph503

Spring 2014
2.20 Marine Hydrodynamics, Fall 2011
Lecture 14
c 2011 MIT  Department of Mechanical Engineering, All rights reserved.
Copyright
2.20  Marine Hydrodynamics
Lecture 14
Chapter 6  Water Waves
6.1 Exact (Nonlinear) Governing Equations for
Surface Gravity
Korea Advanced Institute of Science and Technology
Quantum Mechanics I
PHYSICS ph503

Spring 2014
21
Molecular Universe, HS 2009, D. Fluri, ETH Zurich
2 Atomic Spectroscopy
We will first have a look at spectroscopy, starting with atoms in this chapter and followed by
molecules in the next chapter. This will give us the necessary basis for understandin
Korea Advanced Institute of Science and Technology
Quantum Mechanics I
PHYSICS ph503

Spring 2014
Jeffrey Hellrung
Monday, April 30, 2007
Physics 105A, Homework 04
a. For the equation
x
+ 2 x + 02 x = 0,
critical damping occurs for 2 = 02 (when the characteristic polynomial has precisely one root). From
scalar ODE theory, we know the general solution
Korea Advanced Institute of Science and Technology
PHYSICS 101

Winter 2002
'T 'v VA, ~"? T "' a! a" v 1" ' er " \ a W .: e V7 v7 * ,s r '
l . : .
\V \m/ \J V V V V v v V V v V V V V V V v V v V v v V v V V v v v w \l
kw z? E 1 its? we MI! Bi: 113/: I,
9! E cfw_norm A;
My: L on (LIL/1119): 7L U I; 9)
vv; "Ayn/cam
Korea Advanced Institute of Science and Technology
PHYSICS 101

Winter 2002
11. According to the Archimedes Principle, the objects stop rising when their
mass become equal to the weight of the original fluid volume. In other words,
objects
density
and
original
fluid
density
become
same.
In
the
case
of
heliumfilled balloon, densi
Korea Advanced Institute of Science and Technology
PHYSICS 101

Winter 2002
26
The wave speed corresspond to root(gh). See eq 14.5
34
Lets suppose speed of light is infinity. Time delay is 100m/ (334m/s). Almost 0.3s
44
By eq 14.15, new f is f / (1 (17/343)=380/0.95=400
48
Amplitude is 3cm, wavelength is 8cm, T is 10.4s, and spe
Korea Advanced Institute of Science and Technology
PHYSICS 101

Winter 2002
Chapter 9 odd number solutions
41.
Since the cone has constant density, we know by inspection that the centre of mass is along the
axis of the cone. We need to find out how high the centre of mass is along the axis i.e.
.
The volume of each mass elements
Korea Advanced Institute of Science and Technology
PHYSICS 101

Winter 2002
16.(a) The change in the internal energy of the water is U mcT , and the work done by it (i.e., the
negative of the work done on it) is given. Therefore, Equation 18.1 gives
Q U W (0.5 kg)(4.184 kJ/kg K)(3 K) (9.0 kJ) 6.28 kJ 9.0 kJ 2.72 kJ. (The
negative
Korea Advanced Institute of Science and Technology
PHYSICS 101

Winter 2002
11.
In this problem we want to find the work done by the frictional force in moving a block from
one point to another over two different paths.
Figure 7.16 is a plan view of the horizontal surface over which the block is moved, showing
the
paths (a) and (
Korea Advanced Institute of Science and Technology
PHYSICS 101

Winter 2002
40.
With the carbon atom end of either spring fixed, the frequency of either oxygen atom is=
2=
f
Therefore k= (2 4 1013 Hz) 2 (16 1.66 1027 kg)= 1.68 103 N/m.
50.
INTERPRET In this problem we want to find the radius of the solid disk such that its verti
Korea Advanced Institute of Science and Technology
PHYSICS 101

Winter 2002
26.
problem)
A 3.0mdiameter merrygoround with rotational inertia
is spinning freely at 0.50 rev/s.
Four 25kg children sit suddenly on the edge of the merrygoround. (a) Find the new angular
speed, and (b) determine the total energy lost to friction
Korea Advanced Institute of Science and Technology
PHYSICS 101

Winter 2002
Ch.4 Solutions for Even number
16. Let the initial speed as v0. The final speed is obviously 0. We can examine the stopping force,
f=ma by using Eq. 2.11, v 2 =
v02 + 2a ( x x0 ). Using v=0, the stopping distance is given by (since a<0)
02
=  =
2 0 
Th