Worksheet: The Lorentz Factor

In this worksheet, we will practice calculating the Lorentz factor for objects moving at given speeds relative to an observer.

Q1:

Which of the following is the correct formula for the Lorentz factor, 𝛾 ?

  • A 𝛾 = 1 1
  • B 𝛾 = 1 1 +
  • C 𝛾 = 1 1
  • D 𝛾 = 1 1 𝑣 𝑐
  • E 𝛾 = 1 1

Q2:

What is 𝛾 1 for an object moving at a speed of 0 . 0 0 5 𝑐 relative to an observer? Give your answer to 3 significant figures.

  • A 2 . 5 1 × 1 0
  • B 5 . 0 3 × 1 0
  • C 2 . 5 3 × 1 0
  • D 5 . 0 1 × 1 0
  • E 1 . 2 5 × 1 0

Q3:

Object A has a Lorentz factor of 1.25. Object B has a Lorentz factor that is ten times that of object A. What is the ratio of the speed of object B to the speed of object A? Give your answer to 3 significant figures.

Q4:

What is the Lorentz factor of an object moving at 50% of the speed of light relative to an observer? Give your answer to 3 significant figures.

  • A0.800
  • B1.33
  • C1.41
  • D0.894
  • E1.15

Q5:

An electron in a particle accelerator has a Lorentz factor of 2,500, relative to the accelerator facility. What is the difference between the speed of the electron, relative to the accelerator facility, and the speed of light? Give your answer in meters per second to 2 significant figures.

Q6:

What is 𝛾 1 for an object moving at a speed of 10,000 m/s relative to an observer? Give your answer to 3 significant figures.

  • A 5 . 5 6 × 1 0
  • B 1 6 . 7 × 1 0
  • C 3 3 . 3 × 1 0
  • D1.00
  • E 1 . 1 1 × 1 0

Q7:

What is 𝛾 1 for an object moving at 1% of the speed of light relative to an observer? Give your answer to 3 significant figures.

  • A 5 . 0 3 × 1 0
  • B 5 . 0 0 × 1 0
  • C 1 . 0 0 × 1 0
  • D 5 . 5 0 × 1 0
  • E 1 0 . 0 × 1 0

Q8:

What is the Lorentz factor for an object moving at a speed of 3 0 0 0 0 km/s relative to an observer? Give your answer to 6 significant figures.

  • A1.05409
  • B1.01010
  • C0.995037
  • D1.00504
  • E0.953463

Q9:

The Large Hadron Collider near Geneva can accelerate protons to speeds faster than 0.99 C. What is the Lorentz factor for a proton moving at a speed of 0.99 C? Give your answer to 3 significant figures.

  • A10.0
  • B0.505
  • C50.3
  • D0.711
  • E7.09

Q10:

The Large Hadron Collider near Geneva can accelerate protons to a speed just 3.1 m/s slower than the speed of light. What is the Lorentz factor for a proton moving at this speed? Give your answer to 3 significant figures.

  • A 9 6 . 8 × 1 0
  • B 9,840
  • C 4 8 . 4 × 1 0
  • D 6,960
  • E 4,840

Q11:

What is the Lorentz factor for an object moving at a speed of 0.2 C relative to an observer? Give your answer to 6 significant figures.

  • A0.980581
  • B1.25000
  • C0.961538
  • D1.04167
  • E1.02062

Q12:

If an object has a Lorentz factor of 2, how fast is it moving relative to the observer? Give your answer in meters per second to 3 significant figures.

  • A 2 . 1 2 × 1 0 m/s
  • B 4 . 6 4 × 1 0 m/s
  • C 1 . 0 0 × 1 0 m/s
  • D 2 . 6 0 × 1 0 m/s
  • E 2 . 2 3 × 1 0 m/s

Q13:

A spacecraft traveling from Earth to the Alpha Centauri system has a Lorentz factor of 1.02 as measured on Earth. How fast is the spacecraft moving relative to Earth as a percent of the speed of light? Give your answer to 3 significant figures.

  • A 1 4 . 0 %
  • B 1 . 9 6 %
  • C 2 0 . 1 %
  • D 1 9 . 7 %
  • E 3 . 8 8 %

Q14:

If an object has a Lorentz factor of 1.25, how fast is it moving relative to an observer? Give your answer as a multiple of the speed of light, 𝑐 .

  • A 0 . 6 0 0 𝑐
  • B 0 . 4 4 7 𝑐
  • C 0 . 2 0 0 𝑐
  • D 0 . 7 5 0 𝑐
  • E 0 . 3 6 0 𝑐

Q15:

Voyager 1 is a robotic probe that was launched into space in 1977 to explore the outer limits of the solar system. It is currently traveling at a speed of 17 km/s relative to the Sun. What is 𝛾 1 of Voyager 1 relative to the Sun? Give your answer to 3 significant figures.

  • A 3 . 2 1 × 1 0
  • B 5 . 6 7 × 1 0
  • C 1 . 6 1 × 1 0
  • D 8 . 5 0 × 1 0
  • E 2 . 8 3 × 1 0

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.