Homework 1 Solutions
Problem 1
The kaons are moving with respect to the lab frame, so they will
experience a time-dilation as viewed in the lab frame. Let
t = the kaon lifetime in the lab frame,
t = the kaon lifetime in the kaon rest frame.
The equation f
Physics 225 Homework #1
due in 225 homework box1 by Thu, 2 pm
Please supply your solutions to these problems on separate sheets of paper. All solutions must be
written in English and must clearly show the steps and reasoning you used to arrive at your res
Physics 225 Homework #1
due in 225 homework box1 by Thu, 11 am
All solutions must be written in English and must clearly show the steps and reasoning you used to
arrive at your result. You will lose points for poorly written solutions as well as for incor
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
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 extend the t
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
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 recent lectures and units weve studied the physical meaning of the differential operations gradient,
divergence, and curl. Here
NAME: _ ID#: _
SIGNATURE: _
Spring 2010 - Physics 225 Final Exam
14 May (1:30 pm 4:30 pm)
Instructions:
Work the problems in your exam answer booklets. Remember to put your name and ID number
on the answer booklets (you may use more than one). Also, sign
Phys 225 - Homework 9 Solutions
Problem 1: Unit Vector Transformations
3
(v ri ) ri , we can write
(a) Using the equation provided in the question v =
i=1
r = ( r x) x + ( r y ) y + ( r z ) z
= ( x) x + ( y ) y + ( z ) z
= ( x) x + ( y
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 .
We note that, using (E/c, px , py , pz ) as the Energy-momentum four vector, the
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
Physics 225
Relativity and Math Applications
Unit 1
Special Relativity: Do you c what I c?
N.C.R. Makins, G. Gollin1
University of Illinois at Urbana-Champaign
2013
1
The innovative guided-discovery format of these units was developed by Prof. George Goll
Physics 225 Homework #9
due in 225 homework box1 by 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
Physics 225 Homework #13
due in 225 homework box1 by 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
Physics 225 Homework #6
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points for poorly written solutions or incorrect reasoning / explanations; answers given
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 easier to
Phys 225 - Homework 5 Solutions
Problem 1 - Spacestation
(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
Physics 225 Homework #7
due in 225 homework box1 by Thu, 2 pm
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points for poorly written solutions or incorrect reasoning / explanations; answers given
Physics 225 Homework #10
due in 225 homework box1 by 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
Physics 225 Homework #5
due in 225 homework box1 by Thu, 2 pm
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points for poorly written solutions or incorrect reasoning / explanations; answers given
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
Physics 225 Homework #2
due in 225 homework box1 by Thu, 2 pm
Please supply your solutions to these problems on separate sheets of paper. All solutions must be
written in English and must clearly show the steps and reasoning you used to arrive at your res
15
<- Values given by
incorrect figure
labels on
uncorrected exam
Alternate approach: Consider invariant of total momentum 4-vector for system of
two Y-particles.
i.e. For two Y particles, p_tot = 0 + 3/4 = 3/4 A.U./c
E_tot = 2/5 + 17/20 = 25/20 A.U.
Thus
Physics 225
Relativity and Math Applications
Unit 5
2
E = mc
N.C.R. Makins
University of Illinois at Urbana-Champaign
2013
The innovative guided-discovery format of these units was developed by Prof. George Gollin for the Phys
199HO course he introduced i
Physics 225
Relativity and Math Applications
Unit 12
Multidimensional Integration II
& Maxwells Equations
N.C.R. Makins
University of Illinois at Urbana-Champaign
2013
The innovative guided-discovery format of these units was developed by Prof. George Gol
Physics 225
Relativity and Math Applications
Unit 7
The 4-vectors of Kinematics
N.C.R. Makins
University of Illinois at Urbana-Champaign
2013
The innovative guided-discovery format of these units was developed by Prof. George Gollin for the
Phys 199HO cou
Physics 225
Relativity and Math Applications
Unit 9
Vector Fields and Curvilinear Coordinates
N.C.R. Makins
University of Illinois at Urbana-Champaign
2013
The innovative guided-discovery format of these units was developed by Prof. George Gollin for the
Physics 225
Relativity and Math Applications
Unit 11
Multidimensional Integration I
N.C.R. Makins
University of Illinois at Urbana-Champaign
2013
The innovative guided-discovery format of these units was developed by Prof. George Gollin for the
Phys 199HO
Physics 225
Relativity and Math Applications
Unit 6
Conservation, Conversion, and
Nuclear Power
N.C.R. Makins
University of Illinois at Urbana-Champaign
2013
The innovative guided-discovery format of these units was developed by Prof. George Gollin for th
Physics 225
Relativity and Math Applications
Unit 8
Differential Calculus:
Now in 3D
N.C.R. Makins
University of Illinois at Urbana-Champaign
2013
The innovative guided-discovery format of these units was developed by Prof. George Gollin for the
Phys 199H