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Time Dilation for the Lifetime of a Muon A muon is an unstable subatomic particle with the same charge as the electron, but its mass is approximately 207 times the mass of the electron. Muons at rest decay in 2.20 ms on average. Cosmic rays hitting Earth’s atmosphere can create muons travelling near the speed of light. Assume that one of these muons has a speed of 0.990c. (a) What lifetime does an observer on the ground measure for the muon? (b) How far does the muon travel according to the observer?
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Space Travel A spaceship travels at 98.0% of the speed to light to an Exoplanet 45.0 Iy away. What distances do observers on Earth and on the spaceship measure for the trip What time does an observer on Earth measure for the one-way trip? What time do the occupants of the spaceship measure for the one-way trip?
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Spaceship Length Contraction A spaceship is 25.0 m long as measured in its own reference frame. What length do you measure as it moves past you at 90% of the speed of light?
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Transforming Space-time Coordinates There are two inertial reference frames, with the primed system travelling in the positive x-direction (similar to Figure 30-12) at a speed corresponding to β=√3/2. In the unprimed coordinate system, a space-time event is att=0,x=100.m,y=200.m,z=300.m. what will be the x’-coordinate of this space-time event?
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Matrix Form of the Lorentz Transformation Prove that the matrix form of the Lorentz transformation in Equation 30-21 is equivalent to the form expressed in Equation 30-19.
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Space time Intervals Karen sees two events occur at the same place but separated by 2.50 μs in time. Another observer, Tasha, sees the two events separated by 3.50 μs in time. According to Tasha, what is the spatial separation between the two events?
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Lorentz Transformation and Spacetime Intervals Consider two space-time events, A and B. From the point of view of observer 1, space-time event A happens t_1A=1.00 μs,x_1A=50.0 m,y_1A=z_1A=20.0 m, while Spacetime event B occurs at t_1B=2.00 μs,x_1B=10.0 m,y_1B=50.0 m,z_1B=60.0 m. From the point of view of reference frame 1, what will be the space-time interval between the two events? If a second reference frame 2 is in motion along the positive x-axis with v=√3/2 c, what will be the coordinates of the two space-time events according to this reference frame? (Assume that y is known precisely enough to justify answers to three significant digits.) Calculate the space-time interval from the point of view of the second reference frame using the results from (b).
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Mass–Energy Conversion in the Sun In the dominant reaction that produces energy in the core of the Sun, four hydrogen nuclei (protons) fuse into one helium nucleus (α-particle) and emit two positrons and two neutrinos of negligible mass. The rest mass of a proton is1.007 276 467 u, and the rest mass of an α-particle is 4.001 506 177 u, where u is the unified atomic mass unit(1 u=1.660 539 ×〖10〗^(-27) kg). Material in the interior of stars such as the Sun is essentially totally ionized, so we use the mass of the nuclei, not the neutral atoms, in the calculation. The rest mass of a positron is 9.109 38 ×〖10〗^(-31) kg. What is the mass loss in this fusion reaction? What percentage of the original mass is lost? How much energy is released by one reaction? Express the energy in joules and electron volts. The power output of the Sun 3.85×〖10〗^26 W. How many hydrogen fusion reactions per second are needed to provide this energy output?
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