HOMEWORK
set 2B
DUE WEDNESDAY NOON, OCTOBER 29, 1997
SPECIAL RELATIVITY, LECTURES 18-23
WORTH 6 POINTS, 6 PERCENT OF YOUR GRADE
Come to discussion sections or use FirstClass for homework help or call me at 262-3827 or email me at
bdurand@theory3.physics.wisc.edu
NUMBERS 19 AND 23 REQUIRE DISCUSSING AND COMPOSING AN ANSWER AS A GROUP, WITH ONLY ONE PAPER TURNED IN FOR THE WHOLE GROUP. KEEP THE SAME GROUP AS BEFORE UNLESS I REASSIGN YOU. PLEASE CONTACT ME AT ONCE IF YOU WANT TO BE SWITCHED.
18. one point, from Lectures 17 and 18, explanations, pictures, possibly an equation in one of the explanations
20. one point, from Lectures 20 and 22, picture and calculations.
21. one point, from Lectures 20 and 22, pictures and calculations.
22. one point, from Lectures 21 and 22, diagrams, explanation on second diagram.
23. one point, from Lecture 23, a group question, short answers.
You can get help from the Writing Center with written homework assignments.
Revised October 19, 1997.
DON'T FORGET TO SAVE YOUR FILE AND MAKE A PHOTOCOPY OF YOUR COMPLETED PAPER IN CASE THE ORIGINAL GETS LOST.
(a) .3 The Famous Gamma Factor.
Define the gamma factor in an equation (.1), with a right triangle (draw it carefully, and label all three sides) (.1), and by drawing a graph of it (.1). See page 95 of March's book for help with the gamma factor graph. Be sure you draw the graph carefully and label key values.
(b) .2 New Rule
What is the new rule for ``hard'' and ``soft'' catches for light? (.1) How does the second postulate imply this rule? (.1)
(c) .2 Nature's Speed Limit.
How does the second postulate imply that nothing can travel faster than the speed of light? (.2)
(d) .3 Measuring Moving Length.
Using a set of 3 pictures of the moving eraser example, carefully labeled, to show incorrect and correct measurements of moving length. (.3)
19. one point, from Lectures 18 and 19, a group question, explanations, pictures, pretty hard
(a) .2 It's All in Your Head!
What is a ``Gedanken'' experiment (.1), and when do physicists need to do one? (.1)
(b) .4 Simultaneity is Relative.
Explain the Gedanken Experiment in the Albert--Henry video which shows that simultaneity is relative. (.4) You must start your explanation from Einstein's Second Postulate. While this might be easier with pictures, even then it's hard, so DON'T use pictures. Do not use the book or lecture examples; use the video example.
(c) .4 Moving Length is Relative.
Contrast the examples from the lecture (.2) and the book (pp. 109-111) (.2) which were used to show that a moving train is measured to be shorter than a train at rest. You must be very clear on what is different between the two presentations. I prefer my way of doing it to the book's, but I want to know which way you think works better. Please say which way you prefer and why. Do not draw pictures.
Problems 20 and 21 are on the numerical effects of relativity. Be sure you understand all of these effects, including that they are reciprocal for the two observers!
In Prob. 20, you and I have relative velocity v=(4/5)c. Use the
appropriate spacetime triangle and the formulas for length contraction, time
dilation (clock slowdown), and mass increase to get the answers. Show all of
your work!
(a) .2 The Gamma Triangle.
Use a triangle (draw it to scale and label it) to get gamma. (.2)
(b) .2 How Fast?
What is our actual relative speed in m/s? (c=3× 10^8m/s) (.2)
(c) .2 I Measure Your Meterstick
You are carrying a meterstick (100 centimeters in one meter). How many centimeters long do I measure it to be? (.2)
(d) .2 I Measure Your Time Passage.
While one minute passes on my clock, how much time do I measure
passing on your clock? (.2)
(e) .2 I Measure Your Mass.
Your rest mass is 60 kg on your own scale. What do I measure your mass to be? (.2)
In Prob. 21, parts (a) through (d), you and I have relative velocity such that
gamma=13/5. Use the appropriate spacetime triangle and the
formulas for length contraction, time dilation (clock slowdown), and mass
increase to get the answers. Show all of your work.
(a) .1 The Gamma Triangle.
Use a triangle (draw it to scale and label it) to get v/c. (.1)
(b) .2 You Measure my Bike.
I am riding a bike which is 1.3 meters long at rest. How long do you measure it to be? (.2)
(c) .2 You Measure My Time Passage.
It takes you 6.5 hours by your own clock to do this homework. How much time do you measure passing on my clock while you are doing your homework? (.2)
(d) .2 You Measure My Mass.
Doing all this homework made me lose mass down to 50 kg on my own scale. How much mass do you measure me to have? (.2)
(e) .3 The Gamma Factor for Time Passage.
Draw a series of pictures (.3), carefully labeled, of the tick-tock light clock from lecture, the video, or the book to describe how a factor of gamma fewer seconds pass on a moving clock than on a clock at rest.
(a) .6 Six Spacetime Diagrams on One Graph.
Draw carefully and accurately, with the ct axis vertical and x axis horizontal, a spacetime diagram with six points or lines on it (.1 apiece) representing an event, the worldline of an object at rest, the worldline of an object traveling with constant speed less than c, the worldline of light, the worldline of an object traveling with constant speed greater than c (not physically possible), and the worldline of an object accelerating from rest to near the speed of light, but not quite getting there. Label both axes and all the worldlines or points. Make just one picture, big enough to clearly show all six motions.
(b) .4 Graphing Nature's Speed Limit.
Draw a graph showing how mass increases as relative velocity increases. Label the graph to show clearly how Nature's Speed Limit (say what this is!) is enforced. (.4)
(a) .2 Nuclear Fission.
What are the physics (.1) and historical (.1) connections between nuclear fission and the equation E=mc²?
(b) .2 Nuclear Fusion.
Give two examples of nuclear fusion which have a clear effect on your daily life, explaining those effects. (.2)
(c) .6 Fusion and Fission Energy Diagrams.
In the energy diagrams for nuclear fusion and nuclear fission, what are mothers and daughters (.1), hills (.1), and tunneling (.1)? Why is fusion hard to get started? (.1) How are critical mass and chain reaction in fission related to each other? (.2)
writing center help
Please email any questions, comments, or suggestions to
Professor Bernice Durand, bdurand@theory3.physics.wisc.edu.
Images and layout © 1997, Shane Hamilton