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If a meson at rest decays 2 μs after it is created, what is its lifetime according to laboratory clocks when moving at 0.99c?
If a meson at rest decays 2 μs after it is created, what is its lifetime according to laboratory clocks when moving at 0.99c?
What distance is required for the intensity of a beam of pi mesons traveling at speed v = βc to be halved if they have a half-life of T?
What distance is required for the intensity of a beam of pi mesons traveling at speed v = βc to be halved if they have a half-life of T?
If a meson moving through a laboratory of length x at speed v decays after a lifetime T, what would its lifetime be if it were at rest in the laboratory?
If a meson moving through a laboratory of length x at speed v decays after a lifetime T, what would its lifetime be if it were at rest in the laboratory?
A meter stick moves sideways at 0.95c. What is its length according to measurements taken in the laboratory?
A meter stick moves sideways at 0.95c. What is its length according to measurements taken in the laboratory?
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At rest, pi mesons have a half-life of T. If a beam of pi mesons travels at speed v = βc, what happens to the intensity of the beam?
At rest, pi mesons have a half-life of T. If a beam of pi mesons travels at speed v = βc, what happens to the intensity of the beam?
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According to the theory of relativity, what is mass considered as?
According to the theory of relativity, what is mass considered as?
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What happens to the mass of moving particles according to the theory of relativity?
What happens to the mass of moving particles according to the theory of relativity?
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In high-speed collisions according to the theory of relativity, what is conserved?
In high-speed collisions according to the theory of relativity, what is conserved?
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How is the length of a rod moving rapidly sideways (perpendicular to its length) affected?
How is the length of a rod moving rapidly sideways (perpendicular to its length) affected?
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If a source emits light of frequency $f_0$ while moving to the right with speed $c/4$ relative to frame S, and a detector measures the frequency to be $f$, what can be concluded about the detector's movement?
If a source emits light of frequency $f_0$ while moving to the right with speed $c/4$ relative to frame S, and a detector measures the frequency to be $f$, what can be concluded about the detector's movement?
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If the kinetic energy of a free particle is much less than its rest energy, how is its kinetic energy related to the magnitude of its momentum?
If the kinetic energy of a free particle is much less than its rest energy, how is its kinetic energy related to the magnitude of its momentum?
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An electron with a speed of 0.95c has a momentum magnitude closest to which value?
An electron with a speed of 0.95c has a momentum magnitude closest to which value?
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When light from a stationary spaceship is observed and then the spaceship moves directly away at high speed, what happens to the light seen by the observer?
When light from a stationary spaceship is observed and then the spaceship moves directly away at high speed, what happens to the light seen by the observer?
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In the scenario of a fast-moving train (v = 0.6c) with an engineer (E) at the front, a guard (G) at the rear, and a passenger (S') exactly halfway between them, what color signaling lamps do both E and G have?
In the scenario of a fast-moving train (v = 0.6c) with an engineer (E) at the front, a guard (G) at the rear, and a passenger (S') exactly halfway between them, what color signaling lamps do both E and G have?
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When a source emits light of frequency $f_0$ and moves to the right with speed $c/4$ relative to frame S, what happens if a detector measures the frequency to be $f = f_0$?
When a source emits light of frequency $f_0$ and moves to the right with speed $c/4$ relative to frame S, what happens if a detector measures the frequency to be $f = f_0$?
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In an observation where light from a spaceship is initially seen and then it moves directly away at high speed, what phenomenon accounts for the change in light frequency?
In an observation where light from a spaceship is initially seen and then it moves directly away at high speed, what phenomenon accounts for the change in light frequency?
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If light from a stationary spaceship is initially observed and then the spaceship moves directly towards an observer at high speed, what will happen to the light seen by the observer?
If light from a stationary spaceship is initially observed and then the spaceship moves directly towards an observer at high speed, what will happen to the light seen by the observer?
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In reference frame S', what is the coordinate where the leading edges of two light flashes meet?
In reference frame S', what is the coordinate where the leading edges of two light flashes meet?
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In reference frame S', what is the time when the leading edges of two light flashes meet?
In reference frame S', what is the time when the leading edges of two light flashes meet?
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What is the speed of the clock that measures the proper time between the sending and receiving of the capsule relative to us?
What is the speed of the clock that measures the proper time between the sending and receiving of the capsule relative to us?
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In which direction does the clock that measures the proper time between the sending and receiving of the capsule travel?
In which direction does the clock that measures the proper time between the sending and receiving of the capsule travel?
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What is the speed of frame S' with respect to frame S?
What is the speed of frame S' with respect to frame S?
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What is the speed of a particle that moves in the positive x direction as measured by an observer in S'?
What is the speed of a particle that moves in the positive x direction as measured by an observer in S'?
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According to an observer moving in the positive x direction, how do two simultaneous events occurring on the y axis of a reference frame S appear?
According to an observer moving in the positive x direction, how do two simultaneous events occurring on the y axis of a reference frame S appear?
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A train traveling at 0.6c passes a station. According to both the station master (S) and an observer (S') on the train, which of the following statements is true about the signals sent by the engineer (E) and the guard (G)?
A train traveling at 0.6c passes a station. According to both the station master (S) and an observer (S') on the train, which of the following statements is true about the signals sent by the engineer (E) and the guard (G)?
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According to the observer (S') on the train, how do the signals sent by the engineer (E) and the guard (G) appear when the train is passing the station?
According to the observer (S') on the train, how do the signals sent by the engineer (E) and the guard (G) appear when the train is passing the station?
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A station master (S) observes a train traveling at 0.6c. According to S, how do the signals sent by the engineer (E) and the guard (G) appear?
A station master (S) observes a train traveling at 0.6c. According to S, how do the signals sent by the engineer (E) and the guard (G) appear?
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A train traveling at 0.6c passes a station. According to the observer (S') exactly halfway between the engineer (E) and the guard (G), how do the signals sent by E and G appear?
A train traveling at 0.6c passes a station. According to the observer (S') exactly halfway between the engineer (E) and the guard (G), how do the signals sent by E and G appear?
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A train traveling at 0.6c passes a station. According to the station master (S), how do the distances from the engineer (E) and the guard (G) to the station compare when they send their signals?
A train traveling at 0.6c passes a station. According to the station master (S), how do the distances from the engineer (E) and the guard (G) to the station compare when they send their signals?
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Study Notes
Relativity
- Meson decay:
- At rest, decays 2 μs after creation
- When moving at 0.99c, its lifetime is 14 μs according to laboratory clocks
- Pi mesons:
- Half-life is T at rest
- When traveling at speed v = βc, the distance in which the beam intensity is halved is cβT(1 – β^2)^(-1/2)
- Time dilation:
- A meson moving at speed v through a laboratory of length x decays after a lifetime T
- If the meson were at rest in the laboratory, its lifetime would be T(1 – v^2/c^2)^1/2
- Length contraction:
- A meter stick moving sideways at 0.95c has a length of 0.31 m according to laboratory measurements
- Relativity principles:
- Mass is a form of energy
- Moving particles do not lose mass
- Momentum is conserved in high-speed collisions
- A rod moving rapidly sideways is shorter along its length
- Kinetic energy:
- If the kinetic energy of a free particle is much less than its rest energy, its kinetic energy is proportional to the square of the magnitude of its momentum
- Particle momentum:
- An electron with a speed of 0.95c has a momentum of 8.3 × 10^(-22) kg ⋅ m/s
- A particle with mass m and momentum 2mc has a speed of 0.89c
- Photon energy:
- A particle with zero mass and energy E carries momentum E/c
- Doppler shift:
- When a source moves to the right with speed c/4 relative to a detector, the frequency measured by the detector is greater than the proper frequency
- When a spaceship moves away from an observer at high speed, the light seen by the observer has a lower frequency and a longer wavelength
- Special relativity:
- A clock that measures the proper time between the sending and receiving of a message capsule travels at 0.95c relative to the observer
- Two events occur simultaneously at separated points on the y-axis of a reference frame; according to an observer moving in the positive x direction, the events are simultaneous
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Description
Test your understanding of events occurring simultaneously in special relativity from the perspective of an observer moving in the positive x direction. Determine the correct sequence of events and the impact of observer's speed on simultaneity.
