meson traveling through a laboratory of length x at speed v decays after a lifetime T as determined by a laboratory observer at rest. What is the lifetime of a meson while it is at rest in a laboratory? Symbolically express your response in terms of the variables given and the speed of light.
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A meson traveling through a laboratory of length x at speed v decays after a lifetime T as determined by a laboratory observer at rest. What is the lifetime of a meson while it is at rest in a laboratory? Symbolically express your response in terms of the variables given and the
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- measured by this observer to be 10 times longer than its lifetime when at rest relative to the observer? 3. The lifetime of a free neutron is 886 s. If a neutron moves with a speed of 2.9 x 108m/s relative to an observer in the lab, what does the observer measure the neutron's lifetime to be? 4. A computer in a laboratory requires 2.50 us to make a certain calcu- lation, as measured by a scientist in the lab. To someone moving past the lab at a relative speed of 0.995c, how long will the same cal- culation take? 5. The formula for length contraction gives the length of an interval on a ruler moving with velocity v relative to an observer as V1-v²/c² times the length of the same interval on a ruler at rest with respect to the observer. By what fraction is the length of a meter stick reduced if its velocity relative to you is measured to be 95 percent the speed of light? 6. If an electron is speeding down the two-mile-long Stanford Linear Accelerator at 99.98 percent the speed of light,…An observer measures a spacecraft’s length to be exactly half of its rest length. a) What is the speed of the ship relative to the observer’s frame of reference? b) By what factor do the spaceship’s clocks run slow relative to clocks in the observer’s frame?Determine an expression for the total travel time of the light pulse, as measured by the following: A) an observer in the S frame (Use the following as necessary: c, d, and v.) B) an observer on the spacecraft (Use the following as necessary: c, d, and v.) What If? If the transmitted light beam has a wavelength λT, determine an expression for the shift in the wavelength of the light beam, as measured by the following C) an observer in the S frame (Use the following as necessary: c, v, and λT.) D) an observer on the spacecraft (Use the following as necessary: c, v, and λT.)
- An elementary particle produced in a laboratory experiment travels 0.230 mm through the lab at a relative speed of 0.960c before it decays (becomes another particle). (a) What is the proper lifetime of the particle? (b) What is the distance the particle travels as measured from its rest frame?At relativistic speeds near that of light, the half-life of an unstable particle moving at high speed is longer than when it is at rest. an object is longer when moving than when it is stationary. O light emitted by a moving source moves at the same speed with the same frequency. effects precede causes in some inertial frames. lengths and times only appear different and have no effect on other measurable quantities.When pions are brought to rest their lifetime is 1.77´10-8 s. A beam of pions is produced in an accelerator and moves at a speed of 0.99c relative to the laboratory. After moving 39 m as measured in the la, half the pions have decayed. a) from the viewpoint of an observer in the lab frame and b) from an observer at rest in the frame of the moving pions that the two numerical results given in the problem for the half-life of the pions are consistent.
- Einstein concluded that the speed of light is the same in all inertial frames. Prove that the analysis of the Michelson-Morley experiment (see attached image) is in error.Alice and Mary are twins. Mary moves away from the Earth to a distant planet 12 light years away from the Earth. a) With what MINIMUM speed should Mary move in order to return to the Earth N=6 years younger than her sister? b) Explain the resolution of "twin paradox"? ( The twins seem to be in a symmetrical situation, why is one of them younger.)Suppose a cosmic ray colliding with a nucleus in the Earth's upper atmosphere produces a muon that has speed v = 0.99c. The muon then travels at constant speed and lives 1.5 μs as measured in the muon's frame of reference. (You can imagine this as the muon's internal clock.)Randomized Variablesv = 0.99 ct = 1.5 μs Part (a) How many kilometers does the muon travel according to an Earth-bound observer? Part (b) How many kilometers of the Earth pass by as viewed by an observer moving with the muon? Base your calculation on its speed relative to the Earth and its lifetime (proper time).
- The mean lifetime of mesons (pions) is 26 ns. A beam of pions is travelling at 0.93c. As measured in the laboratory: a) What is their mean lifetime? b) How far would they travel before they decay?In the Marvel comics universe, Quicksilver is awfully fast. Let's say he can run at a velocity of 0.74c. He measures a trip as having a distance of 1.36e+05 m. How much time does Quicksilver measure this trip as taking? Does Quicksilver measure the proper or dilated time? Quicksilver's sister, Wanda Maximoff, is standing stationary near where he is running. How much time does Wanda measure this trip as taking? S What distance does Wanda measure for Quicksilver's trip? mAn unstable high-energy particle is created in the laboratory, and it moves at a speed of 0.992c. Relative to a stationary reference frame fixed to the laboratory, the particle travels a distance of 1.05 × 10-3 m before disintegrating. What is (a) the proper distance and (b) the distance measured by a hypothetical person traveling with the particle? Determine the particle's (c) proper lifetime and (d) its dilated lifetime. (a) Number Units (b) Number Units (c) Number Units (d) Number Units