The positive muon (?+), an unstable particle, lives on average 2.20?10−16 ? (measured in its own frame of reference) before decaying. (a) If such as particle is moving, with respect to the laboratory, with a speed of 0.900?, what average lifetime is measured in the laboratory? (b) What average distance, measured in the laboratory, does the particle move before decaying?

Q: A spacecraft receding from the earth emits radio waves at a constant frequency of 10^9 Hz. If the…

A: Let the difference between the classical and relativistic frequency of the radio wave be 1 Hz. For…

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

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Q: A particle of the rest energy (0.624 GeV) moves with respect to the laboratory at speed u=0.8 c. the…

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Q: A particle travels at 1.90 x 108 m/s and lives 2.10 x 10-8 s when at rest relative to an observer.…

A: The decay time in the rest frame is, The particle’s velocity is,

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

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Q: alculate the interval Δs2 between two events with coordinates (x1 = 55m, y1 = 0m, z1 = 0m, t1 = 1…

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Q: Recall, from this chapter, that the factor gamma (γ) governs both time dilation and length…

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Q: A neutral -meson is a particle that can be created by accelerator beams. If one such particle lives…

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Q: Calculate the interval ∆s2 between two events with coordinates (x1 = 50 m, y1 = 0, z1 = 0, t1 = 1…

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Q: At what speed, as a fraction of c, will a moving rod have a length 60% that of an identical rod at…

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

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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: 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: Suppose that a father is 23.00 y older than

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Q: An observer on the earth sees a spaceship approaching at 0.52c. The ship then launches an…

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

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Q: Inertial frame S' moves at a speed of 0.60c with respect toframe S. Further, x = x' = 0 at t = t' =…

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Q: Frame S' has a speed v = 0.6c relative to S in x direction which is parallel to x'. The clocks on S…

A: Given : Speed of S' with respect to S, v = 0.6c The clocks on S and S' are adjusted so that t= t'= 0…

Q: A spacecraft receding from the earth emits radio waves at a constant frequency of 109 Hz. If the…

A: Given data: Frequency f = 109 Hz

Q: Suppose that a person is 20.00 y older than their sibling. The person wants to travel outward from…

A: We have to use concept of time dilation here.

Q: A particle travels at 1.90×108 m/s and lives 2.10×10−8 s when at rest relative to an observer. How…

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Q: Space cruisers A and B are moving parallel to the positive direction of an x axis. Cruiser A is…

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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 particle moves along the x' axis of frame S' with velocity 0.40c. Frame moves with velocity 0.60c…

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Q: At what speed is a particle’s momentum twice its Newtonian value?

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Q: At what speed, in m/s,  would a moving clock lose 1.1 ns in 1.0 day according to experimenters on…

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

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Q: In the experiment to verify time dilation by flying the cesium clocks around the Earth, what is the…

A: The concept of time dilation explains that the measured interval in a moving system is greater than…

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

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Q: The positive muon (µ), an unstable particle, lives on average 2.20 x 10 reference) before decaying.…

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Q: Consider a space shuttle traveling at 8 × 103 m/s above the earth. How much time per day is an…

A: Given: velocity 'v' of the space shuttle = 8 x 103 m/s

Q: An airplane has rest length 40.0 m and speed 630 m/s. To a ground observer, (a) by what fraction is…

A: (a) The expression for the length contraction is:

Q: Suppose that a father is 20.00 y older than his daughter. He wants to travel outward from Earth for…

A: The formula for the time dilation is: The father is 20 years older than his daughter but after…

Q: Derive the Lorentz transformation connecting a frame S (the lab frame) to a frame S′ that moves with…

A: SOlution: To derive the  Lorentz transformation connecting a frame S (the lab frame) to a frame S'.

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: 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: 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: Suppose a spacecraft of mass 17000 kg is accelerated to 0.200 c. How much kinetic energy would it…

A: Given:- Mass(m)=17000 kg Velocity (V)=0.20 c Now, The relativistic kinetic energy of the particle.…

Q: Calculate the interval ∆s2 between two events with coordinates ( x1 = 50 m, y1 = 0, z1 = 0, t1 = 1…

A: Einstein with his special theory of relativity brought in an entirely new understanding of the world…

Q: In the Marvel comics universe, Quicksilver is awfully fast. Let's say he can run at a velocity of…

A:

Proper Length

The theory of special relativity explains the connection between space and time to objects that move in a straight line at a constant speed. The objects move at the speed of light. When an object approaches light speed, its mass is endless and cannot move faster than light. The most crucial postulate of Einstein's special relativity is that the laws of nature do not change in each frame of reference.