High-energy particles are observed in laboratories by photographing the tracks they leave in certain detectors; the length of the track depends on the speed of the par- ticle and its lifetime. A particle moving at 0.993c leaves a track 1.15 mm long. What is the proper lifetime of the particle?
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- Chapter 37, Problem 045 In a high-energy collision between a cosmic-ray particle and a particle near the top of Earth's atmosphere, 110 km above sea level, a pion is created.The pion has a total energy E of 1.68 x 105 MeV and is traveling vertically downward. In the pion's rest frame, the pion decays 35.0 ns after its creation. At what altitude above sea level, as measured from Earth's reference frame, does the decay occur? The rest energy of a pion is 139.6 MeV. Number Units3.4. Cosmic ray muons are produced high in the atmosphere (at 8000 m, say) and travel toward the earth at very nearly the speed of light (0.998 c, say). (a) Given the lifetime of the muon (2.2 x 10-6 sec), how far would it go before disintegrating, according to prerelativistic physics? Would the muons make it to ground level? (b) Now answer the same question using relativistic physics. (Because of time di- lation, the muons last longer, so they travel farther.) (c) Now analyze the same process from the perspective of the muon. (In its reference frame it only lasts 2.2 x 10-6 sec; how, then, does it make it to ground?) + (d) Pions are also produced in the upper atmosphere. [In fact, the sequence is proton (from outer space) hits proton (in atmosphere) → p + p + pions. The pions then decay into muons: ¯ → μ¯ + D µ; πt → μ† + vµ.] But the lifetime of the pion is much shorter, a hundredth that of the muon. Should the pions reach ground level? (Assume that the pions also have a speed of…What is the momentum of the alpha particle that is moving at 0.5c. with mass equal to 7.0*10-27 kg.
- High-energy particles are observed in laboratories by photographingthe tracks they leave in certain detectors; the length of the trackdepends on the speed of the particle and its lifetime.A particle moving at 0.85 c leaves a track 1.25 mm long. What is the properlifetime of the particle?A particle known as a pion lives for a short time before breaking apart into other particles. Suppose a pion is moving at a speed of 0.986c, and an observer who is stationary in a laboratory measures the pion's lifetime to be 2.8 × 10-8 s. (a) What is the lifetime according to a hypothetical person who is riding along with the pion? (b) According to this hypothetical person, how far does the laboratory move before the pion breaks apart? (a) Number (b) Number MO Units UnitsA particle is found to have a lifetime of 30 ms. It is found moving at a speed of 0.999c. How long can the particle be observed in a laboratory if it is moving at the given speed.
- Derive an expression for E using the attached equation (Lorentz Force Law), and calculate a predicted value for E in N/C if a particle had v = 40 m/s, q = -0.001 C, m = 0.3 ⨉ 10 -3 kg, and B = 0.6 T.A particle known as a pion lives for a short time before breaking apart into other particles. Suppose a pion is moving at a speed of 0.992c, and an observer who is stationary in a laboratory measures the pion's lifetime to be 2.7 x 10-8 s. (a) What is the lifetime according to a hypothetical person who is riding along with the pion? (b) According to this hypothetical person, how far does the laboratory move before the pion breaks apart? (a) Number (b) Number i Units UnitsA particle's dynamics are considered "relativistic" when its velocity is a significant fraction of the speed of light. For example, the mass of a moving particle seen by a stationary observer increases in proportion to the square root of 1/(1 - (v/c)2). For typical speeds in the everyday world it is not noticeable, but take a fast moving fundamental particle and you may have apparent mass increases or changes in its lifetime as a consequence of time dilation. Look at this factor for the electron you measured at 100 V in the glass globe. Pick the best answer. The effect is less than 0.1 %. The effect is around 1%. The effect is around 10%. The effect is a factor of 2 change in mass.
- Consider a proton moving with speed = 0.94 c. (c is the speed of light.) What is the kinetic energy, in MeV? (in MeV) OA: 1160 OB: 1449 OC: 1812 OD: 2265 OE: 2831 OF: 3539 OG: 4423 OH: 5529A ship is heading off to Bernard's star at 0.700c. As it passes a space station (at rest with respect to the Earth) a few days out from Earth, the ship fires a "photon torpedo" in the forward direction and another in the reverse direction. the torpedoes have a speed relative to the ship of 0.700c. On a space-time diagram, determine the direction and speed of each torpedo as seen by the station. Check your answers using the relativistic addition of velocities formula.In the Marvel comics universe, Quicksilver is awfully fast. Let's say he can run at a velocity of 0.56c. He measures a trip as having a distance of 4.60e+05 m. How much time does Quicksilver measure this trip as taking? 2.73e-3 S Does Quicksilver measure the proper or dilated time? 2 proper time v Quicksilver's sister, Wanda Maximoff, is standing stationary near where he is running. How much time does Wanda measure this trip as taking? 3 3.29e-3 S What distance does Wanda measure for Quicksilver's trip? 4 Xm