In this lesson, we will learn how to apply Lorentz transformation to find the momentum of objects that are subject to relativistic velocity transformations.

Q1:

A 1 . 0 0 × 1 0 9 -kg asteroid is heading towards Earth at 30.0 km/s. At velocities such as the velocity of this asteroid, 𝛾 ≃ 1 + 1 2 𝑣 / 𝑐 2 2 .

Calculate the approximate momentum of the asteroid. Find the value to a precision giving the first two nonzero significant digits that occur after the leading digit.

Find the ratio of the asteroid’s approximate momentum to the classical value of its momentum. Find the value of the ratio to a precision giving the first nonzero significant digit that occurs after the leading digit.

Q2:

A muon has a rest energy of 105.7 MeV. The muon decays into an electron and a massless particle.

If all of the mass of the muon was converted into kinetic energy of the electron, what would be the ratio of the speed of the electron to the speed of light? Use six figure precision in your answer.

If all of the mass of the muon was converted into kinetic energy of the electron, what Lorentz factor 𝛾 would be associated with the velocity of the electron.

Q3:

Find the force needed to accelerate a mass of 1.00 kg by 1.00 m/s^{2} when it is traveling at a velocity of 𝑐 2 .

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