Hints for HW 4

General Advice: The mathematical skills you need for this problem set include algebra and an understanding of what a differential (like dv) means (go back to your math book and look it up if you cannot explain it in words to a friend). You also need to be able to work with differential and integral calculus. Finally, Taylor series expansions enter too. On the physics side, you need to understand what the frequency of light is.

Hints on specific problems:

Problem L-14: This is a long problem that involves a fair amount of sophisticated math. For part d, the only way to make the argument rigorous is to discuss a relevant integral and evaluate it. For part e, be sure to answer all questions, since we have covered Chapter 6 already. Part f is important to think about, in essence if you understand this you understand the crux of what length contraction really is.
Problem 5-5: As with any paradox, draw a diagram. If you draw the right one and understand it, the rest of the problem will be easy. Note that not all answers to 5-5 in the book are correct!
Problem 5-6 If you have ever gotten a speeding ticket or wondered what the doppler radar discussed on the weather reports is, then this problem is for you. The key is to express to yourself what the figure means in words, and fully understand what the different parts of the figure mean. Be sure to divide delta f by f, and be sure you know how to perform the relevant Taylor series expansion.
Problem 5-7 Carefully draw your diagram to scale, and this problem will go quickly.

Last modified August 11, 2004

Jim Freericks, Professor of Physics, freericks at physics dot georgetown dot edu