Problem

After being produced in a collision between elementary particles, a positive pion (π+) m...

After being produced in a collision between elementary particles, a positive pion (π+) must travel down a 1.90-km-long tube to reach an experimental area. A π+ particle has an average lifetime (measured in its rest frame) of 2.60 × 10-8 s; the π+ we are considering has this lifetime. (a) How fast must the π+ travel if it is not to decay before it reaches the end of the tube? (Since u will be very close to c, write u = (1 - Δ)c and give your answer in terms of Δ rather than u.) (b) The π+ has a rest energy of 139.6 MeV. What is the total energy of the π+ at the speed calculated in part (a)?

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