Physics 6C. Special Relativity. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Transcription

1 Physis 6C Speial Relatiity

2 Two Main Ideas The Postulates of Speial Relatiity Light traels at the same speed in all inertial referene frames. Laws of physis yield idential results in all inertial referene frames.

3 Two Main Ideas The Postulates of Speial Relatiity Light traels at the same speed in all inertial referene frames. Laws of physis yield idential results in all inertial referene frames. Inertial referene frames refer to obserers moing at onstant eloity with respet to eah other.

4 Two Main Ideas The Postulates of Speial Relatiity Light traels at the same speed in all inertial referene frames. Laws of physis yield idential results in all inertial referene frames. Inertial referene frames refer to obserers moing at onstant eloity with respet to eah other. If there is a nonzero aeleration, the frames are not inertial, and we would need to use General Relatiity. Way too muh math for this ourse sorry

5 Two Main Ideas The Postulates of Speial Relatiity Light traels at the same speed in all inertial referene frames. Laws of physis yield idential results in all inertial referene frames. Inertial referene frames refer to obserers moing at onstant eloity with respet to eah other. If there is a nonzero aeleration, the frames are not inertial, and we would need to use General Relatiity. Way too muh math for this ourse sorry The relationship between what is seen in the two referene frames is found ia the Lorentz Transformation. We will see the following fator in all of our equations: 1 1 Here is the relatie speed of the frames, and is the speed of light.

6 The main results of Speial Relatiity are the following: 1) Time Dilation - if an objet is moing, an obserer will measure times to be longer (ompared to the frame of the objet itself) t t t t 1 t refers to the objet at rest in its own frame

7 The main results of Speial Relatiity are the following: 1) Time Dilation - if an objet is moing, an obserer will measure times to be longer (ompared to the frame of the objet itself) t t t t 1 t refers to the objet at rest in its own frame ) Length Contration if an objet is moing, an obserer will measure lengths to be shorter in the diretion of motion (ompared to the frame of the objet itself) L L L L 1 L refers to the objet at rest in its own frame

8 The main results of Speial Relatiity are the following: 1) Time Dilation - if an objet is moing, an obserer will measure times to be longer (ompared to the frame of the objet itself) t t t t 1 t refers to the objet at rest in its own frame ) Length Contration if an objet is moing, an obserer will measure lengths to be shorter in the diretion of motion (ompared to the frame of the objet itself) L L 1 L L L refers to the objet at rest in its own frame 3) Addition of eloities is more ompliated than in the non-relatiisti ase. At low speeds, we just add or subtrat the relatie eloities and it works fine, but near the speed of light we need to be more areful. Here s a formula: = V V 1 V is the relatie speed between the frames, and and are the eloities of the objet in eah frame. This formula is triky to use, so pratie seeral examples.

9 The main results of Speial Relatiity are the following: 1) Time Dilation - if an objet is moing, an obserer will measure times to be longer (ompared to the frame of the objet itself) t t t t 1 t refers to the objet at rest in its own frame ) Length Contration if an objet is moing, an obserer will measure lengths to be shorter in the diretion of motion (ompared to the frame of the objet itself) L L L L 1 L refers to the objet at rest in its own frame 3) Addition of eloities is more ompliated than in the non-relatiisti ase. At low speeds, we just add or subtrat the relatie eloities and it works fine, but near the speed of light we need to be more areful. Here s a formula: = V V 1 V is the relatie speed between the frames, and and are the eloities of the objet in eah frame. This formula is triky to use, so pratie seeral examples. 4) Energy and Mass are equialent (E rest =m ). We an also get formulas for relatiisti momentum and total energy. p m 1 E total m 1 K E rest

10 Visual demonstrations of speial relatiity.

11 In the year 84, a spaeraft flies oer Moon Station III at a speed of.8. A sientist on the moon measures the length of the moing spaeraft to be 14 m. The spaeraft later lands on the moon, and the same sientist measures the length of the now stationary spaeraft. What alue does she get?

12 In the year 84, a spaeraft flies oer Moon Station III at a speed of.8. A sientist on the moon measures the length of the moing spaeraft to be 14 m. The spaeraft later lands on the moon, and the same sientist measures the length of the now stationary spaeraft. What alue does she get? Use the length ontration formula with L=14m and =.8. We are looking for L. L L 1

13 In the year 84, a spaeraft flies oer Moon Station III at a speed of.8. A sientist on the moon measures the length of the moing spaeraft to be 14 m. The spaeraft later lands on the moon, and the same sientist measures the length of the now stationary spaeraft. What alue does she get? Use the length ontration formula with L=14m and =.8. We are looking for L. L L 1 14m L 1.8

14 In the year 84, a spaeraft flies oer Moon Station III at a speed of.8. A sientist on the moon measures the length of the moing spaeraft to be 14 m. The spaeraft later lands on the moon, and the same sientist measures the length of the now stationary spaeraft. What alue does she get? Use the length ontration formula with L=14m and =.8. We are looking for L. L L 14m L 14m L L 1 33m Notie that anels out. This usually happens when you use speeds written in terms of. Our result is onsistent with the onept of length ontration. The ship is measured to be shorter when it is moing.

15 Inside a spaeship flying past the earth at ¾ the speed of light, a pendulum is swinging. a) If eah swing takes 1.5 s as measured by an astronaut performing an experiment inside the spaeship, how long will the swing take as measured by a person at mission ontrol on earth who is wathing the experiment? b) If eah swing takes 1.5 s as measured by a person at mission ontrol on earth, how long will the swing take as measured by an astronaut inside the spaeship?

16 Inside a spaeship flying past the earth at ¾ the speed of light, a pendulum is swinging. a) If eah swing takes 1.5 s as measured by an astronaut performing an experiment inside the spaeship, how long will the swing take as measured by a person at mission ontrol on earth who is wathing the experiment? b) If eah swing takes 1.5 s as measured by a person at mission ontrol on earth, how long will the swing take as measured by an astronaut inside the spaeship? We will be using the time dilation formula. Notie the differene between part a) and part b) In part a) the time as measured on the spaeship is gien. This is Δt beause the pendulum is at rest relatie to the ship.

17 Inside a spaeship flying past the earth at ¾ the speed of light, a pendulum is swinging. a) If eah swing takes 1.5 s as measured by an astronaut performing an experiment inside the spaeship, how long will the swing take as measured by a person at mission ontrol on earth who is wathing the experiment? b) If eah swing takes 1.5 s as measured by a person at mission ontrol on earth, how long will the swing take as measured by an astronaut inside the spaeship? We will be using the time dilation formula. Notie the differene between part a) and part b) In part a) the time as measured on the spaeship is gien. This is Δt beause the pendulum is at rest relatie to the ship. t t 1

18 Inside a spaeship flying past the earth at ¾ the speed of light, a pendulum is swinging. a) If eah swing takes 1.5 s as measured by an astronaut performing an experiment inside the spaeship, how long will the swing take as measured by a person at mission ontrol on earth who is wathing the experiment? b) If eah swing takes 1.5 s as measured by a person at mission ontrol on earth, how long will the swing take as measured by an astronaut inside the spaeship? We will be using the time dilation formula. Notie the differene between part a) and part b) In part a) the time as measured on the spaeship is gien. This is Δt beause the pendulum is at rest relatie to the ship. t t 1.5s t t.3s The people on earth measure a longer (dilated) time for eah swing, as expeted.

19 Inside a spaeship flying past the earth at ¾ the speed of light, a pendulum is swinging. a) If eah swing takes 1.5 s as measured by an astronaut performing an experiment inside the spaeship, how long will the swing take as measured by a person at mission ontrol on earth who is wathing the experiment? b) If eah swing takes 1.5 s as measured by a person at mission ontrol on earth, how long will the swing take as measured by an astronaut inside the spaeship? We will be using the time dilation formula. Notie the differene between part a) and part b) In part a) the time as measured on the spaeship is gien. This is Δt beause the pendulum is at rest relatie to the ship. t t 1.5s t t.3s The people on earth measure a longer (dilated) time for eah swing, as expeted. Part b) uses the same formula, but now we are gien Δt instead.

20 Inside a spaeship flying past the earth at ¾ the speed of light, a pendulum is swinging. a) If eah swing takes 1.5 s as measured by an astronaut performing an experiment inside the spaeship, how long will the swing take as measured by a person at mission ontrol on earth who is wathing the experiment? b) If eah swing takes 1.5 s as measured by a person at mission ontrol on earth, how long will the swing take as measured by an astronaut inside the spaeship? We will be using the time dilation formula. Notie the differene between part a) and part b) In part a) the time as measured on the spaeship is gien. This is Δt beause the pendulum is at rest relatie to the ship. t t 1.5s t t.3s The people on earth measure a longer (dilated) time for eah swing, as expeted. Part b) uses the same formula, but now we are gien Δt instead. t t t 1.5s t s Again the people on earth measure a longer time beause the lok is moing relatie to them.

21 Two partiles are reated in a high-energy aelerator and moe off in opposite diretions. The speed of one partile, as measured in the laboratory, is.65, and the speed of eah partile relatie to the other is.95. What is the speed of the seond partile, as measured in the laboratory?

22 Two partiles are reated in a high-energy aelerator and moe off in opposite diretions. The speed of one partile, as measured in the laboratory, is.65, and the speed of eah partile relatie to the other is.95. What is the speed of the seond partile, as measured in the laboratory? Pitures will probably help here =? 1 -V=.65 = V V 1 this is the lab This is what you see in the laboratory frame. Partile 1 is moing at.65, and Partile is moing the other diretion.

23 Two partiles are reated in a high-energy aelerator and moe off in opposite diretions. The speed of one partile, as measured in the laboratory, is.65, and the speed of eah partile relatie to the other is.95. What is the speed of the seond partile, as measured in the laboratory? Pitures will probably help here =? 1 -V=.65 = V V 1 this is the lab This is what you see in the laboratory frame. Partile 1 is moing at.65, and Partile is moing the other diretion. V=-.65 = This is the same senario in the referene frame of Partile 1. Partile is moing away at -.95, and Partile 1 is at rest in its own frame.

24 Two partiles are reated in a high-energy aelerator and moe off in opposite diretions. The speed of one partile, as measured in the laboratory, is.65, and the speed of eah partile relatie to the other is.95. What is the speed of the seond partile, as measured in the laboratory? Pitures will probably help here =? 1 -V=.65 = V V 1 this is the lab This is what you see in the laboratory frame. Partile 1 is moing at.65, and Partile is moing the other diretion..95 (.65) V=-.65 = So in the lab, Partile looks like it is moing to the left at speed.78. This is the same senario in the referene frame of Partile 1. Partile is moing away at -.95, and Partile 1 is at rest in its own frame.

25 Here s a sample problem: The sun produes energy by nulear fusion reations, in whih matter is onerted to energy. The rate of energy prodution is 3.8 x 1 6 Watts. How many kilograms of mass does the sun onert to energy eah seond?

26 Here s a sample problem: The sun produes energy by nulear fusion reations, in whih matter is onerted to energy. The rate of energy prodution is 3.8 x 1 6 Watts. How many kilograms of mass does the sun onert to energy eah seond? We only need to use Einstein s E=m for this one.

27 Here s a sample problem: The sun produes energy by nulear fusion reations, in whih matter is onerted to energy. The rate of energy prodution is 3.8 x 1 6 Watts. How many kilograms of mass does the sun onert to energy eah seond? We only need to use Einstein s E=m for this one J m 9 m 4. 1 kg m s Remember, a Watt is a Joule per seond