Worksheet: Relativistic Momentum

In this worksheet, we will practice applying Lorentz transformation to find the momentum of objects that are subject to relativistic velocity transformations.


What is the velocity of an electron that has a relativistic momentum of 3.040×10 kg⋅m/s?

Electron rest mass is 9.109×10 kg.

  • A2.984×10 m/s
  • B2.980×10 m/s
  • C2.988×10 m/s
  • D2.982×10 m/s
  • E2.986×10 m/s


Find the momentum of a helium nucleus having a mass of 6.68×10 kg that is moving at 0.200𝑐.

  • A3.74×10 kg⋅m/s
  • B3.83×10 kg⋅m/s
  • C4.00×10 kg⋅m/s
  • D4.09×10 kg⋅m/s
  • E3.91×10 kg⋅m/s


Calculate the speed of a 1.00-μg-mass dust particle that has the same momentum as a proton moving at 0.999𝑐. The rest mass of a proton is 1.67×10 kg.

  • A1.21×10 m/s
  • B1.39×10 m/s
  • C1.46×10 m/s
  • D1.30×10 m/s
  • E1.12×10 m/s


A 1.00×10 km asteroid is heading toward Earth at 30.0 km/s. At velocities such as these, 𝛾1+𝑣2𝑐.

Calculate the approximate momentum of the asteroid to the first two nonzero significant digits that occur after the leading digit.

  • A3.000000015×10 kg⋅m/s
  • B3.000000010×10 kg⋅m/s
  • C3.000000020×10 kg⋅m/s
  • D3.000000025×10 kg⋅m/s
  • E3.000000017×10 kg⋅m/s

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.

  • A1.0000000011
  • B1.0000000091
  • C1.0000000031
  • D1.0000000051
  • E1.0000000071


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?


Find the force needed to accelerate a mass of 1.00 kg by 1.00 m/s2 when it is traveling at a velocity of 𝑐2.


A 9,000 kg satellite is orbiting at 500 km/s. Find the difference between the relativistic momentum and the classical momentum by using the approximation that 𝛾=1+12𝑣𝑐 at low velocities.


Find the velocity of a proton that has a momentum of 5.38×10 kg⋅m/s.

  • A0.695𝑐
  • B0.732𝑐
  • C0.735𝑐
  • D0.710𝑐
  • E0.705𝑐


What is the momentum of an electron traveling at 0.990𝑐?

  • A1.36×10 kg⋅m/s
  • B1.56×10 kg⋅m/s
  • C1.92×10 kg⋅m/s
  • D2.70×10 kg⋅m/s
  • E2.70×10 kg⋅m/s

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