- French: Chapter 5, Problem 1.
- Write down the Lorentz transformation equations the give
(x,ct) in terms of (x',ct'), but simply refer to the Lorentz
factor as
, instead of its
expression that you know, as a function of v/c. Likewise write
down the Lorentz transformation equations that give (x',ct') in
terms of (x,ct), again involving an unknown .
Insert these values for (x',ct'), from the second set of equations, into the first set, so that you have equations of the form- x = something involving x, ct, v, and ,
and
- t = something involving x, ct, v, and .
, must have
in order for them to be true.
- x = something involving x, ct, v, and
- 3 reasonably quick problems, on WebAssign, due tonight.
No. XXI: due viernes, 14 de marzo,
- A reasonably lengthy paper problem due Friday at classtime:
A space probe leaves earth and travels at a speed of 0.975c. Clocks on earth and on the space probe are all set to zero at launch. Every day mission control sends a signal (traveling at speed c) to the probe requesting a status report. The probe immediately sends back a reply that includes the reading on the probe clock at the time the signal was received. For the first such signal, please calculate- the time, according to Earth clocks, at which the reply is received on earth,
- and the time that is reported in the reply sent by the probe's computer.
- Also calculate the distance of the probe from earth when the signal is received by the probe, as measured by mission control
- and calculate the distance of the probe from earth when the signal is received by the probe, as determined by the computer on the space probe.
- Lastly, please estimate how many signals
will be sent from Earth to the probe before the first
acknowledgement signal will be received at Earth.
This is of course quite relevant if, for instance, that first acknowledgement signal indicates that the probe has been boarded by hostile aliens.
It is quite helpful to note various events:- As well it would be helpful to note these events on an
appropriate spacetime diagram, although that it is not required.
- the sending of the first message to the probe from earth,
- the receipt of the first message at the probe's computer,
- the receipt of the first probe reply, back again on earth,
- the event on earth that is simultaneous, by Earth's measurements, with the probe's receipt of the message, and
- the event on earth that is simultaneous, by the probe's measurements, with the probe's receipt of the message.
- There will be NO WebAssign problems this (Friday) night.
Have a happy Spring Break, but do note that there will be WebAssign problems due on the Monday night that you return.
due on Monday, 24 March, right after spring break.
In Halliday, Resnick, and Walker, Chapter 38: Problem 53, on superluminal jets.
However, the problem asks that you determine some algebraic expressions for the apparent speed of the jet in terms of its true speed and its angle relative to the direction of earth. It then asks that you evaluate this apparent speed for a particular value of the angle and the true speed. They ask this because this pair of values does indeed give an apparent speed much larger than c.
However, I want you to do slightly more. First, use two true speeds, the one they ask, namely v = 0.98c, and also a slower one, v = 0.80c. Then, in addition to determining the values for a particular angle, create a good graph of the variation of the apparent speed, divided by c, as a function of the angle theta, as it varies from 0 to
radians, for each of these two
true speeds. You will find that the curves begin quite slowly, rise
to a maximum apparent speed, and then slow down again as the angle
increases toward 2. For each of these
two true speeds, determine the angle which gives this maximum value
of the apparent speed.
A complete solution to this problem may be accessed after it is due by clicking right here.
No. XXII: due lunes, 24 de marzo,
- There is one paper problem due today, at classtime:
French 5-12. - There are 5, mostly fairly simple WebAssign problems due tonight.
Complete solutions to HW 22 may be accessed after they are due by clicking right here.
No. XXIII: due miercoles, 26 de marzo,
- There are 2 paper problems due today.
- French 5-19. However, when doing part (c), please draw
a separate space-time diagram for the situations described there
in each of the 3 relevant frames: the frame S (on earth),
in the frame S' (the outgoing
astronaut's frame) and the frame S" (the incoming astronaut's frame).
On these diagrams, you should locate the worldlines of
the earth, the star, and the outgoing and returning
worldlines of the astronaut; however, you do not need to draw the
various radio signals that were sent out except on the spacetime
diagram drawn in the earth's reference frame!
For part (d), the question about the Doppler effect refers to changes in perception of frequency, of sending out, and receiving, signals, as measured in the two frames. - Please do Problem 38.52 in your text.
However, be sure that, in addition to answering the questions posed, you also create correct space-time diagrams for the situation, with events 1 and 2 clearly noted, as well as the worldlines of the car and both garage doors, both from the point of view of the garageman and the person driving the limousine.
- French 5-19. However, when doing part (c), please draw
a separate space-time diagram for the situations described there
in each of the 3 relevant frames: the frame S (on earth),
in the frame S' (the outgoing
astronaut's frame) and the frame S" (the incoming astronaut's frame).
On these diagrams, you should locate the worldlines of
the earth, the star, and the outgoing and returning
worldlines of the astronaut; however, you do not need to draw the
various radio signals that were sent out except on the spacetime
diagram drawn in the earth's reference frame!
- There are 2 brief WebAssign problems due tonight.
Complete solutions to HW 23 may be accessed after they are due by clicking right here.
No. XXIV: due viernes, 28 de marzo,
- There are 3 paper problems due today:
- French, 6-1;
- French, 6-2, however, for part(b), please express the rest mass in GeV/c2, in addition to amu's;
- French, 6-3.
- There are no WebAssign problems for tonight.
No. XXV: due lunes, 31 de marzo,
- There is one paper problem due at classtime on Monday:
- French, 7-1
- There are 4 quite simple, "practice" problems on WebAssign and one slightly more serious problem, concerning collisions of very short wavelength light rays with electrons in atoms; all due Monday night.
Complete solutions to HW 25 may be accessed after they are due by clicking right here.
SECOND EXAM will be on Wednesday, 2 April.
-
Coverage will be all the material we have discussed on Special
Relativity.
- A listing of equations for the exam, in Acrobat format, may be accessed here. You may bring these sheets with you to the exam itself, and write on the backs if you so desire.
- Solutions may be accessed here.
The "repeat" part of the second exam was given on 11 April, 2003. It covered only special relativistic kinematics, in space and time. Solutions may be accessed here.
Grade distributions for the respective exams may be found at the end of the solutions.
Back to Phys. 262 Home Page.
Last updated/modified: 14 April, 2003 - A listing of equations for the exam, in Acrobat format, may be accessed here. You may bring these sheets with you to the exam itself, and write on the backs if you so desire.