Phys 225 - Homework 1 Solutions
0
Problem 1: KL meson decay
(a) How do you start every problem?
Make a sketch, with symbols for everything you
know and everything you want to know.
Now start coming up with relations involving these known & desired quantit
Phys 225 - Homework 10 Solutions
Problem 1: Div and Curl in Cylindrical Coordinates
(a) Step 1: write down the nine terms of divergence in Cartesian coordinates,
using the distributive property of the dot product:
( Ex + y Ey + z Ez )
x
+y
+z
x
y
z
=x
(
Phys 225 - Homework 11 Solutions
Problem 1: Div, Curl, and Maxwell in cylindrical
(a) To nd the volume charge density we need to compute E . Lets compute
rst out
1
1
out = 0 Eout = 0
)=0
(s
)= 0
(
s s 2 0 s
s s 2 0
We can see that out = 0, so there is no
Phys 225 - Homework 6 Solutions
Problem 1: 0 decay in 1D
(a) Let us set the x-axis along the direction of the motion of the pion. Since the
momentum is conserved,
p = p1 p2 ,
where p1 , p2 are the (magnitudes of the) momentum of the rst and the second
pho
Physics 225 Homework #6
due in 225 homework box1 by Thu, 11 am
All solutions must clearly show the steps or reasoning you used to arrive at your result. You will lose
points for poorly written solutions or incorrect reasoning / explanations; answers given
Physics 225 Homework #3
due in 225 homework box1 by Thu, 11 am
All solutions must clearly show the steps or reasoning you used to arrive at your result. You will lose
points for poorly written solutions or incorrect reasoning / explanations; answers given
Physics 225 Homework #12
due in 225 homework box Thu, 2 pm
All solutions must clearly show the steps or reasoning you used to arrive at your result. You will
lose points for poorly written solutions or incorrect reasoning / explanations; answers given
wit
Phys 225 - Homework 3 Solutions
Problem 1: Worldlines 101
(a) Please note that one is not able to plot the spaceships worldline all the way
back to Cape Canaveral on this graph because the spaceship is traveling slower on
the way back. You would need to e
Phys 225 - Homework 7 Solutions
Problem 1: Energy-Momentum 4-vectors
Write down the energy-momentum four-vectors for the following cases. In each
case, the particle has (rest) mass m0 .
(a) Q. A particle moves in the positive x direction in the laboratory
Phys 225 - Homework 9 Solutions
Problem 1: Vector Magnitudes Galore
(a) Proof of the Law of Cosines, from the dot-products geometric denition and
its distributive property:
|A + B | =
(A + B ) (A + B )
=
A A + B B + 2A B
=
A2 + B 2 + 2AB cos AB
(b)
|A + B
Phys 225 - Homework 2 Solutions
Problem 1: The Train-Tunnel Paradox
In order to resolve this apparent paradox, we will examine the three key events,
both in the rest frame of the tunnel and in the rest frame of the train. The setup
of the problem makes it
due in 225 homework box1 by Thu, 11 am
Physics 225 Homework #11
Reading: The Meaning of Grad, Div, Curl, and the GGS Theorem
In this weeks lecture, we studied the physical meaning of the differential operations gradient,
divergence, and curl. (The physica
Physics 225 Homework #10
due in 225 homework box1 by Thu, 11 am
All solutions must clearly show the steps or reasoning you used to arrive at your result. You will lose
points for poorly written solutions or incorrect reasoning / explanations; answers give
Phys 225 - Homework 5 Solutions
Problem 1: Space Station
(a) To boost the velocity u of a moving particle from a frame S to another frame
S , we will boost the separation x = (ct, x, y, z ) between two spacetime
points on the particles trajectory. For con
Phys 225 - Homework 13 Solutions
Problem 1: A Novel AC Circuit
(a)
1
R(iXC )
1
1
RXC
= iXL +
+
= XL +
R XC
R iXC
R + XC
2
2
RXC iR XC
= iXL +
(multiplied top and bottom by R + iXC )
2
XC + R2
2
R2 XC
RXC
+ XL 2
i.
=
2
XC + R2
XC + R2
Z = XL +
(b) As , Z i
Phys 225 - Homework 12 Solutions
Problem 1: Parabolic Mirror
(a) Revolving the line z = x2 /a around the z -axis mathematically corresponds
to replacing x with s. We parametrize the surface in cylindrical coordinates and
choose s and as our sweeping param
" F (r )! d !
The Procedure for Multidimensional Integration
i
!n
Definition of the essential
word PARAMETRIZE
as used in this context:
Express all quantities that vary over the integral in
terms of your integration parameters (IPs) & constants.
1. Parame
Physics 225 Homework #2
due in 225 homework box1 by Thu, 11 am
All solutions must clearly show the steps or reasoning you used to arrive at your result. You will lose
points for poorly written solutions or incorrect reasoning / explanations; answers given
due in 225 homework box1 by Thu, 11 am
Physics 225 Homework #4
All solutions must clearly show the steps or reasoning you used to arrive at your result. You will lose
points for poorly written solutions or incorrect reasoning / explanations; answers given
Physics 225 Homework #5
due in 225 homework box1 by Thu, 11 am
All solutions must clearly show the steps or reasoning you used to arrive at your result. You will lose
points for poorly written solutions or incorrect reasoning / explanations; answers given
Physics 225 Homework #9
due in 225 homework box1 by Thu, 11 am
All solutions must clearly show the steps or reasoning you used to arrive at your result. You will lose
points for poorly written solutions or incorrect reasoning / explanations; answers given
Physics 225 Homework #7
due in 225 homework box1 by Thu, 11 am
All solutions must clearly show the steps or reasoning you used to arrive at your result. You will lose
points for poorly written solutions or incorrect reasoning / explanations; answers given
Physics 225 Homework #12
due in 225 homework box1 by Thu, 11 am
All solutions must clearly show the steps or reasoning you used to arrive at your result. You will
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Phys 225 - Homework 4 Solutions
Problem 1: Scientists Toolkit to the Rescue
For this problem are several ways to justify why every answer is wrong; here are
some examples of correct answers:
(a) If a 0, we should obtain the force between two point charges