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A rod moving with a speed v along the horizontal direction

Physics for Scientists and Engineers with Modern Physics | 9th Edition | ISBN: 9781133954057 | Authors: Raymond A. Serway John W. Jewett ISBN: 9781133954057 230

Solution for problem 30 Chapter 39

Physics for Scientists and Engineers with Modern Physics | 9th Edition

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Physics for Scientists and Engineers with Modern Physics | 9th Edition | ISBN: 9781133954057 | Authors: Raymond A. Serway John W. Jewett

Physics for Scientists and Engineers with Modern Physics | 9th Edition

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Problem 30

A rod moving with a speed v along the horizontal direction is observed to have length , and to make an angle u with respect to the direction of motion as shown in Figure P39.29. (a) Show that the length of the rod as measured by an observer at rest with respect to the rod is ,p 5 ,[1 2 (v 2 /c 2) cos2 u]1/2. (b) Show that the angle up that the rod makes with the x axis according to an observer at rest with respect to the rod can be found from tan up 5 g tan u. These results show that the rod is observed to be both contracted and rotated. (Take the lower end of the rod to be at the origin of the coordinate system in which the rod is at rest.)

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Koshar Amy Brogan March 6 & 8, 2016 Week 13 Cryptography Part 2 Review  Shift Cipher o A code that replaces letters with other letters Code the message “Send Ammo” using the Vignere key “SHOE” (18-7-14-4) S E N D A M M O 18 4 13 3 0 12 12 14 S H O E S H O E 18 7 14 4 18 7 14 4 36 11 27 7 18 19 26 18 10 1 0 K L B H S T A S Now that we have the coded message, try to decode it like as if you received it and needed to read it without knowing what it said. K L B H S T A S 10 11 1 7 18 19 0 18 At this point to work backwards, we need to subtract the code word from what we have, but some of the numbers won’t be big enough sowe have to add 26. K L B H S T A S 10 11 1 7 18 19 0 18 +26 = 36 +26 = 27 +26 = 26 S H O E S H O E -18 -7 -14 -4 -18 -7 -14 -4 18 4 13 3 0 12 12 14 S E N D A M M O Decode this: Key: OUT T I K K U K R Modular Arithmetic  Addition operation o Sum after adding  Multiplication operation o Product after repeated adding  Subtraction operation o Difference after subtracting  Division operation o Quotient after repeated subtracting  Modular Arithmetic o Remainder after dividing With Modular Arithmetic, the answer will be what is left over after dividing the value in question. It doesn’t matter how many timesa number goes into another, only what is left over. With small numbers this is easiest to see using long division Ex 1: 1 = 3 mod2  2 goes into 3 and there is 1 left over (3-2=1) Ex 2: 23 mod5 = 3 20 / 5, 3 left over Ex 3: mod 5 = 0, 1, 2, 3, 4 (all numbers before the value is 5) Ex 4: 27 mod4 = 3 27/4, 3 left over Ex 5: 66 mod11 =0  66 = 11*6 +0 Keep in mind that all of the “=” isn’t reallyan equal sign. It’sreally “≡”, “equivalent”, but I don’t have that symbol in an easy type-able form. With large numbers, it’s easier to put the value in question into a calculator and find out the remainder, but then it will be in decimal form, andwe need it in whole numbers. So: Ex 6: 673 mod 17  673/17 = 39.588  17*39 = 663 673-663 =10 673 mod17 =10 Ex 7: 492 mod 16  492/16 = 30.7516*30 = 480  492-480 = 12  492 mod 16 = 12 Try these: 7 mod 5 = 26 mod 3 = 129 mod4 = Decimation Code In decimation code, instead of adding values from a key word, multiply a value that the sender and receiver will know. Ex: Code HEAD SOUTH, code: 3 H E A D S O U T H 7 4 0 3 18 14 20 19 7 x3 21 12 0 9 54 42 60 57 21 26mod2=2 = 16 =8 =5 V M A J C Q I F V Now decode: V M A J C Q I F V 21 12 0 9 2 16 8 5 21 /3 Where valuesare two small to divide by three, keep adding 26 till the value is a multiple of the key 2+26=28 16=42 8+26=34 5=57 +26=54 60 7 4 0 3 18 14 20 19 7 H E A D S O U T H With this code, A willalways beA because 0 multiplied by any number willalwaysbe 0.  Advantages o Simple to code o More difficult to decode  Disadvantages o Does not encode repeat letters o A is always A o Even with a small-valued key, the numbers to code will be large, and they will onlyget larger with bigger keys o The kay can’t be just anything; it has to work when decoding. Some values will be too large to decode with, and others will be confused with similar values. Try decoding: key = 5 R H U U  SymmetricCartography o Same key to code and decode o Private key  AsymmetricCartography o Public key to encode o Private code to decode How is AsymmetricCartography possible Through prime factorization, a method discovered and developed by Rivest, Shamir, and Adleman in 1977; it is known as the RSA publickey encryption scheme. Ex: 24 = 2x2x2x3 Ex: 90 = 2x3x3x5 9x10  9=3x3;10=2x5 Using both modular arithmetic (24=4 mod 20)and prime factorization, they wereable to create a complex coding system. Two prime numbersaremultiplied to get the public key, and then only the decoder knows the prime numbers to factorize by. Ex: 11,483*45,161 = 518,583,763 Ex: 3,130,832,609 =31,91*100,699 Where we are looking at smaller values, they use numbers that aremillions of digits long. Even with a quick computer it would take a long time to find the prime factors of the numbers. Answers: T I K K UK R  FO R W AR D T I K K U K R 19 8 10 10 20 10 17 +26=34 +26=36 36 36 -14 -20 -19 -14 -20 -14 -19 5 14 17 22 0 17 3 F O R W A R D 7 mod 5 =2 26 mod 3 =2 129 mod4 = 1 R H U U;Key = 5  TR E E R H U U 17 7 20 20 +26=43+26=69+26=95 +26=33+26=59+26=85 /5 /5 19 17 4 4 T R E E

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Chapter 39, Problem 30 is Solved
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Textbook: Physics for Scientists and Engineers with Modern Physics
Edition: 9
Author: Raymond A. Serway John W. Jewett
ISBN: 9781133954057

This textbook survival guide was created for the textbook: Physics for Scientists and Engineers with Modern Physics, edition: 9. The answer to “A rod moving with a speed v along the horizontal direction is observed to have length , and to make an angle u with respect to the direction of motion as shown in Figure P39.29. (a) Show that the length of the rod as measured by an observer at rest with respect to the rod is ,p 5 ,[1 2 (v 2 /c 2) cos2 u]1/2. (b) Show that the angle up that the rod makes with the x axis according to an observer at rest with respect to the rod can be found from tan up 5 g tan u. These results show that the rod is observed to be both contracted and rotated. (Take the lower end of the rod to be at the origin of the coordinate system in which the rod is at rest.)” is broken down into a number of easy to follow steps, and 138 words. Since the solution to 30 from 39 chapter was answered, more than 235 students have viewed the full step-by-step answer. Physics for Scientists and Engineers with Modern Physics was written by and is associated to the ISBN: 9781133954057. This full solution covers the following key subjects: . This expansive textbook survival guide covers 46 chapters, and 3681 solutions. The full step-by-step solution to problem: 30 from chapter: 39 was answered by , our top Physics solution expert on 01/09/18, 08:01PM.

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A rod moving with a speed v along the horizontal direction