In the muon decay experiment discussed in Section 2.9 as a verification of time dilation, the muons move in the laboratory with a momentum of 3094 MeV/c. Find the dilated lifetime in the laboratory frame. (The proper lifetime is 2.198 ?s.)

Q: Is the relativistic Doppler effect consistent with the classical Doppler effect in the respect that…

A: Doppler effect is an effect in the frequency or wavelength of light due to the motion of the motion…

Q: For what value of υ does γ = 1.010 0? Observe that for speeds lower than this value, time dilation…

A: It is given that,

Q: An unstable high-energy particle is created in the laboratory, and it moves at a speed of 0.991c.…

A:

Q: What happens to the relativistic Doppler effect when relative velocity is zero? Is this the expected…

A: Relativistic Doppler effect is defined as the change in wavelength of radiation, which is moving…

Q: A particle of rest energy 140 MeV moves at a sufficiently high speed that its total relativistic…

A: The expression from relativity,

Q: What is the speed of an electron having the same momentum with a proton having speed 0.005c? (Just…

A: Given data: Speed of proton is, v=0.005c.

Q: A spaceship flies past you and you measure its length to be 99 m. If you know its rest length is 193…

A:

Q: The elementary particle called a muon is unstable and decays in about 2.20μs, as observed in its…

A:

Q: How fast would a rocket be traveling if a stationary observer noticed its length was contracted to…

A:

Q: Particles called π -mesons are produced by accelerator beams. If these particles travel at 2.70×108…

A: Given:  velocity, v = 2.7 x 108 m/s t = 2.6 x 10-8 s

Q: The origins of two frames coincide at t = t' 0 and the relative speed is 0.991c. Two micrometeorites…

A: t=277μS x=83500 m

Q: How does relativistic time dilation prohibit neutrino oscillations if they are massless?

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Q: Observers in reference frame S see an explosion located at x1= 480 m. Asecond explosion occurs 5μs…

A:

Q: How fast will a space ship be moving, if the observer on earth notices that the time on the…

A: The equation for the time dilation is given by

Q: How fast must a meter stick be moving if its length is observed to shrink to half a meter by an…

A: l=l01-v2c2

Q: A spacecraft is measured to be 250.00 m long while it is at rest with respect to earth-based…

A: GivenLength of spaceship at rest with respect to observer, Lo=250 mSpeed of spaceship, v=0.8 c

Q: A meter stick in frame S' makes an angle of 30° with the x'axis. If that frame moves parallel to the…

A: Since the frame is moving along the x-axis, Now, Also,

Q: A muon has a lifetime 2.2 microseconds in its own rest frame. In a frame of reference where the muon…

A: Write a given values of this question. Muon lifetime. τ∘=2.2 microseconds Velocity of muon. v=0.6c

Q: What are the rest energy, the kinetic energy, and the total energy of a 1.0 g particle wit of 0.7c?

A:

Q: If a high-speed spaceship appears shrunken to half its normal length, how does its momentum compare…

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Q: A rod lies parallel to the x axis of reference frame S, moving along this axis at a speed of 0.630c.…

A:

Q: If relativistic effects are to be less than 3%, then γ must be less than 1.03. At what relative…

A:

Q: In an Earth reference frame, a star is 49 light-yearsaway. How fast would you have to travel so that…

A: If particle or an object travel at relativistic speed its length contraction occurs. Formula of…

Q: A supertrain of proper length 100 m travels at a speed of 0.95c as it passes through a tunnel having…

A:

Q: If relativistic effects are to be less than 1%, then γ must be less than 1.01. At what relative…

A:

Q: Suppose a cosmic ray colliding with a nucleus in the Earth’s upper atmosphere produces a muon that…

A: Speed of light, c = 3×108 m/sVelocity of muon, v = 0.95cTime period, ∆t0 = 1.52×10-6 s β = vcβ =…

Q: A ground observer made a measurement on a wooden box and the length was found to be 2.3 m. At what…

A:

Q: Does the relativistic postualte of constancy of velocity of light hold for inertial frames only or…

A: This holds for all inertial frames.

Q: At what speed does the classical momentum, p=mv, give an error, when compared with the relativistic…

A:

Q: The measured mean lifetime of an elementary particle when it is at rest in the lab is measured to be…

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Q: A spaceship, 180 m long as seen on board, moved by the earth at 0.980c. What is it's length in m as…

A: Given data: Original Length (L0) = 180 m Speed (v) = 0.980 c Required: The length of spaceship…

Q: Consider a particle that, once it comes to existence, decays on average after a short time t, where…

A: Given  t = average time of decay of particle in its own frame. Therefore t= proper time Speed of…

Q: What are the kinetic energy, the rest energy, and the total energy of a 1.0 g particle with a speed…

A: The mass of rhe particle is m=1.0 g×1 kg1000 g=0.001 kg. The speed of the particle is…

Q: In a nuclear reaction two identical particles are created,traveling in opposite directions. If the…

A: Given Data: The speed of the first particle is, u = -0.82c. The speed of the second particle is, v…

Q: An astronaut at rest has a heart rate of 66 beats/min. What will her heart rate be as measured by an…

A:

Q: An armada of spaceships that is 1.00 ly long (as measured in its rest frame) moves with speed 0.800c…

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Q: A golf ball travels with a speed of 90.0 m/s. By what fraction does its relativistic momentum…

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Q: The positive muon (?+), an unstable particle, lives on average 2.20?10−16 ? (measured in its own…

A: Given: A positivive mu+ Time ∆to = 2.20 × 10-16 s u = 0.900c To determine: Average lifetime and…

Q: Is the C.M. frame an inertial frame?

A:

Q: A spaceship, 200 m long as seen on board, moves by the Earth at 0.970c . What is its length as…

A: The given values are,

Relativistic Energy and Momentum

According to classical physics, time flow is the same for every observer. But according to einstein's theory, time flow is different for different observers. The idea that time flow is not the same for all may sound strange because we may not experience this effect in everyday life. This effect is only observed when an object moves with some velocity comparable to the velocity of light. This velocity is termed relativistic velocity.