Elements of Physics II

Transcription

1 Physics 132: Lecture 23 Elements of Physics II Agenda for Today Special Theory of relativity Inertial vs. non-inertial reference frames Postulates of SR Consequences of SR Time dilation Length contraction Physics 201: Lecture 1, Pg 1

2 Students: Relativity This stuff is so confusing =( the preclass video blew my mind. i think going through different examples than the ones in the video would be helpful as its difficult to imagine everything described in the video with only one example for each topic aaaaaaaaaattttttttttttttttttttgffffffffffff Physics 201: Lecture 1, Pg 2

3 Students: Relativity I force myself to believe that speed of light is constant to anyone. But, what is light? If the light is the wave, it does not perform as sound. Speed of sound is not constant to anyone(according to the pre-class video.) If the light is an object, I don't know how I can grab the light. So, what is light? Physics 201: Lecture 1, Pg 3

4 Maxwell s Theory of Electromagnetic Waves A changing electric field creates a magnetic field, which then changes in just the right way to recreate the electric field, which then changes in just the right way to again recreate the magnetic field, and so on. This is an electromagnetic wave. Physics 201: Lecture 1, Pg 4

5 Galilean-Newtonian Relativity Reference frame: The place of reference that one can make measurement of distance velocity etc from. Inertial reference frame: A reference frame that is not undergoing an acceleration (moving at constant velocity) Relativity Principle The laws of physics are the same for all inertial reference frames. Physics 201: Lecture 1, Pg 5

6 Reference Frames The figure shows two reference frames called S and S. The coordinate axes in S are x, y, z and dthose in S are x, y, z. Frame S moves with velocity v relative to S. Physics 201: Lecture 1, Pg 6

7 Galilean Transformations Physics 201: Lecture 1, Pg 7

8 Clicker Question 1: Which of these quantities change when you change your inertial reference frame? a) position u / x u x v b) velocity c) acceleration d) all of the above e) only a) and b) Physics 201: Lecture 1, Pg 8

9 Inertial Reference Frames Physics 201: Lecture 1, Pg 9

10 Galilean-Newtonian relativity The laws of physics are the same for all inertial reference frames. There is no preferred or more correct frame When you are in a constantly tl moving object (that t travels smoothly) you can not tell if you are still or moving. (No experiment can either) Lengths of objects and time that passes between events are constant (absolute) meter sticks are always a meter If a ball drop it takes 6 s for it to fall in all frames Physics 201: Lecture 1, Pg 10

11 Example: Dropping ball Frame moving with car Car does not move Ball falls straight down 1-D kinematics prob Frame standing still Car does move Ball takes parabolic path. 2-D kinematics prob Different motion, but laws of physics are the SAME! F = ma Physics 201: Lecture 1, Pg 11

12 Example: Driving down freeway Example 1: You are driving down the highway at a constant speed 50 mph V = 0 V = -50 mph In you reference frame you see all objects trees and stuff moving past you at a constant speed a = 4 m/s 2 F = ma always works!!! F Physics 201: Lecture 1, Pg 12

13 IRF Physics 201: Lecture 1, Pg 13

14 Clicker Question 2: All of the boats on the bay have foghorns of equal intensity. One night on the shore, you hear two horns at exactly the same time one is loud and the other is softer. What do you conclude from this? a) softer one sounded first b) louder one sounded first c) both sounded at the same time d) unable to conclude anything Physics 201: Lecture 1, Pg 14

15 Trouble Maxwell predicted EM waves will travel with a velocity of c. His theory did not explain about relative velocity. People were perplexed. Physics 201: Lecture 1, Pg 15

16 Airplanes Two planes travel To the bottom plane the top 500 mph plane is travelling 300 mph v T = = 300 mph To an observer on the ground who is not moving the top plane goes 500 mph 200 mph Physics 201: Lecture 1, Pg 16

17 Chewbacca here sees the EM wave travelling at a speed of c = m/s EM (Light) waves This is bad for physics! v = c EM wave Using Newton s and Gallileo s way Luke would measure: v L = c - c/2 = c/2 v = c/2 However this is not correct Chewbacca s frame is better than Luke s frame because it correctly figures the speed of the wave Physics 201: Lecture 1, Pg 17

18 Postulates of Special Relativity 1) The laws of Physics have the same form in all inertial reference frames. (Moving with constant velocity) 1B) The speed of light (in a vacuum) is always c, independent of the observer. Physics 201: Lecture 1, Pg 18

19 Pre-Class Quiz Teenagers Sam and Tom are playing chicken in their rockets. As figure shows, an experimenter on earth sees that each is traveling at 0.95 as he approaches the other. Sam fires a laser beam toward Tom. What is the speed of the laser beam relative to Sam? A) 0.95 c B) 0 Student: Is it possible to perceive something travelling faster C) c D) 1.95 c E) 0.05 c than the speed of light, since nothing in the universe can travel faster than the speed of light, so in the rocket question, the speed of the laser tom sees cannot exceed c? Student: Can you explain why the speed of light has to be constant? I didn't get it from the video. Thank you. What is the speed of the laser beam relative to Tom? Physics 201: Lecture 1, Pg 19

20 Consequences This may not seem to be revolutionary In order to measure c = m/s, different frames must measure distance and time intervals differently! v distance time Physics 201: Lecture 1, Pg 20

21 Simultaneity The two events are simultaneous in Ryan s reference frame. Physics 201: Lecture 1, Pg 21

22 Simultaneity As seen in Ryan s reference frame. Physics 201: Lecture 1, Pg 22

23 Simultaneity As seen in Peggy s reference frame. The two events are not simultaneous in Peggy s reference frame! This is called the relativity of simultaneity. Physics 201: Lecture 1, Pg 23

24 Clicker Question 3: The figure below shows a rocket traveling from left to right. At the instant it is halfway between two trees, lightning simultaneously (in the rocket's frame) hits both trees. Do the light flashes reach the rocket pilot simultaneously? If not, which reaches her first? (a) The light flashes reach the rocket pilot simultaneously. (b) The left flash reaches the rocket pilot first. (c) The right flash reaches the rocket pilot first. Physics 201: Lecture 1, Pg 24

25 Incorrect: Clicker Question 3: The pilot is approaching the right tree, thereby making the distance between the two objects smaller. Therefore, it takes a shorter amount of time to see the right lightning bolt. In the perspective of the rocket, lightning i would appear to be traveling faster on the right and slower on the left. Correct: From the rocket's perspective, both lightning strikes occurred simultaneously. This is because the flashes arising from the lightning both reach the rocket at the same time. Thus to the pilot who is travelling within the rocket, the two flashes are observed to have occurred at the same time. The light travels the same distance. The events were defined as simultaneous with respect to the rocket's frame of reference. The light flashes are traveling at c, and will reach the rocket simultaneously. Physics 201: Lecture 1, Pg 25

26 Clicker Question 3:

27 Clicker Question 4: The figure below shows a rocket traveling from left to right. At the instant it is halfway between two trees, lightning simultaneously (in the rocket's frame) hits both trees. A student was sitting on the ground halfway between the trees as the rocket passed overhead. According to the student, were the lightning strikes simultaneous? If not, which tree was hit first? (a) The light flashes reach the student simultaneously. (b) The left flash reaches the student pilot first. (c) The right flash reaches the student pilot first. Physics 201: Lecture 1, Pg 27