Frigillana 1
131 Physics Lab, Section 19
Experiement #4
The Atwood Machine (2/6/13)
Name: Daryl Frigillana, Partner: Ryan Folk
Introduction:
Newtons second law assumes that a system with mass and acceleration has a net force which
is directly proportional
131 Homework 5 Solutions
February 19, 2013
1
1.1
1: Page 122
4
A is 2 4, B is 3 2, and C is 3 3. The only sensible products involving 2
matrices are BA and CB, and C 2 . Therefore, the only allowed triple products
are CBA and C 2 B.
14 4
(1)
CB = 1 19
1
131 Homework 7 Solutions
March 5, 2013
1
Problem 1:
f (z)
=
u(x, y) + iv(x, y)
(1)
dz
=
dx + idy
(2)
f (z)dz
=
udx vdy + i(vdx + udy)
(3)
Here we can see that if f (z)dz = ax dx + ay dy + i(bx dx + by dy), then:
ax
= u
(4)
ay
= v
(5)
bx
= v
(6)
by
= u
(7)
131: Mathematical Methods HW 2 Solutions
January 24, 2013
1
Problem 1
We want to consider a gravitational potential (r) = k/r, where k is a constant.
To consider gravity on the surface of the earth, it is conventional to refer to a
height z as the height
March 6, 2013
Mathematical Methods with Boas
Physics 131. Mathematical Methods. Winter 2013
Instructor Chris Fronsdal
1
Orientation
This may be your rst upper division course, and if so please be prepared to nd it a
wee bit dicult. The solution is to work
Physics 1AH, Fall 2016:
Physics for Scientists and Engineers: Mechanics (Honors)
Prof. J. Rosenzweig
3-174C Knudsen Hall
Ph: 310-205-4541
rosen@physics.ucla.edu
When:
Lecture TR 12:00-1:50 PM
Discussion R 8:00-8:50 PM (TA: Eric Sawyer)
Rosenzweig office h
Physics 131
Fall 2016
Instructor
Josh Samani
jsamani@physics.ucla.edu
Office: PAB 1-707L
Office Hours: MWF 1 PM - 2 PM
Teaching Assistants
Please refer to CCLE for updated information.
Exams
There will be two midterm exams and a final exam.
Exam
Midterm
Two equal masses are at the ends of a massless 50-cm-long rod.
The rod spins at 2.0 rev/s about an axis through its midpoint.
Suddenly, a compressed gas expands the rod out to a length of 160
cm. What is the angular velocity after the expansion?
A U-shaped tube open to the air at both ends contains some
mercury. Water is carefully poured into the left arm of the tube
until the vertical height of the water column is 15 cm.
What is the gauge pressure at the water-mercury interface?
Calculate the
A 34-kg child runs with a speed of 2.8 m/s tangential to the rim of a
stationary merry-go-round. The merry-go-round has a moment of
inertia of 510 kgm2 and a radius of 2.31 m. When the child jumps
on the merry-go-round the entire system begins to rotate.
The block floats in a liquid with 4.6 cm of the side of the block
submerged. When the block is placed in water, it also floats but with
5.8 cm submerged. What is the density of the unknown liquid?
A 5.0 kg rock whose density is 4800 kg/m3 is suspended by a string
such that half of the rocks volume is under the water. What is the
tension in the string?
In the figure, a wheel of radius 0.2 m is mounted on a frictionless
horizontal axle. A massless cord is wrapped around the wheel and
attached to a 2.0 kg box that slides on a frictionless surface inclined
at an angle 20 with the horizontal. The box accele
An object in SHM oscillates along the x-axis with a frequency of 2.5
Hz. At t = 0 its position and velocity are 1.1 cm and -15 cm/s,
respectively.
Find the acceleration of the object at t = 0
Write equations giving the position and velocity of the objec
Fourier Transforms
1. The uses thereof. I am pretty sure that the most important applications of Fourier
transforms have to do with solving linear dierential equations. It is therefore appropriate
to begin with an illustration.
Consider a simple, forced h
131 Midterm 1 Solutions
Winter 2013
Problem 1
Given any sequence, of real or complex numbers:
a0 , a1 , a2 , .an , an+1 , .,
(a) what property makes it an arithmetic sequence?
In an arithmetic sequence, subsequent terms dier by the same additive constant,
Phys 131
Hw 1
1. Show that a (b c ) ( a c )b ( a b )c
2. Prove that a , b , c are coplanar if and only if a (b c ) 0
3. Given a ( 2, 1, 1) , b ( 2, 3, 1) , c (0, 1, 1) , find:
( a b ) c ; ( a b ) c ; a (b c )
4. Find the unit normal to the pla
Phys 131
Hw 2
1. Show by direct calculation that the inertia tensor for a uniform sphere is isotropic (its
components are the same in any Cartesian coor. System centered at the CM).
2. Find the tensor of inertia for the following distribution of point mas
Phys 131
Hw 6
1. Consider a semi-infinite rectangular plate of width L; the bottom edge is held at
T T0 cos(2 x / L) T0 , the other sides (including at infinity) at T 0 . Find T ( x, y ) on
the plate.
2. Find the Laplace transform of:
a) f ( x ) 1
b) f (
Phys 131
Hw 3
1. Show that for a central field, meaning: u u( r ) r , u 0 .
2. Find a vector potential A(x ) which gives rise to a uniform B field along z , i.e. a
magnetic field B A (0, 0, B ) .
3. Find the circulation of the field u ( x ) ( y , x,
Phys 131
Hw 4
1. Calculate the volume element in spherical coordinates from the Jacobian of the
transformation to Cartesian coordinates.
2. Consider the vector space of square integrable functions on [0, 2]. Show that the form:
2
( f , g ) f ( x ) g ( x )
Phys 131
Hw 5
1. Solve the problem of the guitar string of length L plucked at the position L/4 from one
end.
2. Solve the problem of the piano string hit by a hammer in the middle. Assume that the
initial velocity f ( x, t ) / t of the string is a piecew
b) 5: \ 3;: (DIG-F Z )xj
9 K t, (:4 *Zw funk Z fom X.
- : J4 g A \ .4
1) 1'8 I'M 1th 1421/1 ,'m,uf,5 3 7 : M : .E;ZX 4.
X I MID/M'- 3 _\
( U ) K : Cox ]
(Matt imaj 0" " Z013 .
E: g zwwf = Z Jim/w;
FIQCIS
_ H .4 1
($65%u<aw9z)%am - mail(tow)
wl=/:D/2 o,+(
January 15, 2013
Mathematical Methods with Boas
Physics 131. Mathematical Methods. Winter 2013
Instructor Chris Fronsdal
1
Orientation
This may be your rst upper division course, and if so please be prepared to nd it a
wee bit dicult. The solution is to w
Physics 131 HW 8 Expanded Solutions
Winter 2013
Problem 1
See page 112. If we set (r, ) = eim g(r), then the function f satises the equation
1
m2
2
r + r 2 + k 2 g(r) = 0.
r
r
We expect to nd a solution that is regular everywhere in the region 0 r 1, so i
Physics 131 HW 1 Expanded Solutions
Winter 2013
1. We wish to show that
N
i=
i=1
N (N + 1)
.
2
(1)
We go through the steps of math induction:
Step 1: test whether this is true for N = 2. By plugging in N = 2 into the RHS and LHS separately, we
indeed see
Physics 131 HW 3 Expanded Solutions
Winter 2013
1,2. Boas 3.3, #1,2: there are various ways of doing these using the determinant manipulations you have
learned (see Boas p. 91). The idea is to try to have at least one, and ideally two, zero entries in one