What work has to be performed in order to increase the velocity of a particle of rest mass mo from 0.60 c to 0.80 c? Compare the result obtained with the value calculated from the classical formula.
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- 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?12. (a) A particle is traveling through the Earth's atmosphere at a speed of 0.750c. To an earth bound observer, the distance it travels is 2.5km. How far does the particle travel in the particle's frame of reference? (b) Calculate the momentum of an electron traveling at a speed 0.985c? The rest mass of the electron is 9.11 X 10-31 kg.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?
- Consider a general equation for the ratio the relativistic length to the proper length. Find an algebraic expression for v/c in terms of, ΔL/ΔLo Show the algebraic form of the equation that you apply and the final final expression.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.In a nuclear reaction two identical particles are created,traveling in opposite directions. If the speed of each particleis 0.82c, relative to the laboratory frame of reference, whatis one particle’s speed relative to the other particle?
- An object with a rest mass of 1.5 kg is moving at a speed of 0.91c. (a) Determine the relativistic momentum of the object. (b) Determine the total relativistic energy, in joules, of the object according to a stationary observer.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?
- Calculate the ratio of the relativistic kinetic energy to the classical energy kinetic energy for an electron (mass = 9.109x10^-31 kg) moving with constant speed of 0.75c.An astronaut at rest has a heart rate of 66 beats/min. What will her heart rate be as measured by an Earth observer when the astronaut’s spaceship goes by the Earth at a speed of 0.55 c?A golf ball travels with a speed of 90.0 m/s. By what fractiondoes its relativistic momentum magnitude p differfrom its classical value mu? That is, calculate the ratio(p mu)/mu.