Muon. A muon produced by nuclear reaction in a space station is moving at 0.950c towards Earth. Its lifetime is 2.2 x 10“s. (a) a) How far does the muon travel according to an observer on Earth? (b) Basing your calculation on the velocity relative to the Earth and its proper time, how far does it travel as viewed by an observer moving with it? (c) How much is the length contraction?
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- How far from the earth would you be able to travel in a lifetime of 88 years if you were able to travel at a constant speed of 0.67c?To make the numbers simple we will regard the travelling twin as travelling at 0.866c during the trip (=2) to a planet 10.4 light-years away (this distance was chosen so that the trip time to destination = 12 years in earth frame). The total trip as measured in the earth frame is 24 years. Using the following information above, resolve the question on who is really younger by: a. Applying length contraction, time dilation and relativity of simultaneity.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 0.990c, and an observer who is stationary in a laboratory measures the pion's lifetime to be 2.6 × 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 i (b) Number i Units Units
- Suppose a cosmic ray colliding with a nucleus in the Earth's upper atmosphere produces a muon that has speed v = 0.82c. 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.) 1)how many meters does it travel as observed on the earth? 2)how many meters is this in muon's frame?1. A spaceship A (at rest in inertial frame A) of proper length L, =75.0m is moving in the +x direction at a speed v= 0.650c as measured in the Earth frame. Another spaceship B (at rest in inertial frame B) is moving on a parallel path in the opposite direction (-x) with u, =-0.720c as measured in the Earth frame. The two spaceships pass each other. a. What is the velocity and speed parameter of spaceship B in inertial frame A, u,,B' ? b. In inertial frame A, how long does it take for the tip of spaceship B to move from the tip of spaceship A to the tail of spaceship A? c. In inertial frame B, how long does it take for the tip of spaceship B to move from the tip of spaceship A to the tail of spaceship A? d. In the Earth frame, how long does it take for the tip of spaceship B to move from the tip of spaceship A to the tail of spaceship A?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 Units
- 1. You are an observer in a 100-m long spacecraft traveling from the earth to the moon at 0.8c. (a)What is the proper length of the spacecraft? (b) For a proper time interval of 1 sec., the relativistic time interval for the spacecraft measured from the earth reference frame would be: (c)Time dilation does not apply to all time-dependent physical and biological processes. T/F? (c) What is the relativistic length, DL measured from the reference frame of earth? (d) An APOLLO crew left a flat mirror reflector on the surface of the moon (for all you deniers out there, in the 50th anniversary year of APOLLO 11!). If the average surface-to-surface distance from the earth to the moon is 3.83 x 10^8 m, then how long does it take moonlight to reach earth?6. A particle has a speed of 96% of the speed of light and a mass of 1u. The particle is unstable and its lifetime is 150 ns. It passes through a room where we stand and observe. (a) How long do we think the lifetime of the particle is? (b) The room is 10 m long, but how far does the particle feel as it passes? (c) How much of the particle's total energy is rest mass?Suppose a cosmic ray colliding with a nucleus in the Earth's upper atmosphere produces a muon that has speed v = 0.765c. The muon then travels at constant speed and lives 1.6 μs as measured in the muon's frame of reference. (You can imagine this as the muon's internal clock.)Randomized Variablesv = 0.765 ct = 1.6 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).
- A borg spaceship is in the shape of a cube of side 100.0 m when it is at rest with respect to an observer. What length, width, and height will be the observer witness if the ship flies by at 0.62c going right to left? b) two borq crewmembers are arm wrestling, and it takes 6.0 seconds for the contest to end as measured by a third crewmember. As the ahip flies past the earth at 0.62c, how long will the match last according to an observer on earth?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?The measured mean lifetime of an elementary particle when it is at rest in the lab is measured to be 2.6x10-8 s. If the particle is observed while traveling at a speed v=0.9 c with respect to the lab. What will be the value of the measured mean lifetime while the particle is moving?