Worksheet: Lorentz Transformation

In this worksheet, we will practice using Lorentz transformation to relate the distance and time measurements of observers in relative motion.

Q1:

If relativistic effects are to modify time and length values by less than 1%, then the Lorentz factor 𝛾 must be less than 1.01. At what relative velocity is 𝛾 = 1 . 0 1 ?


Q2:

What is the Lorentz factor 𝛾 produced by a relative velocity of 0 . 2 5 0 𝑐 ?

Q3:

What is the Lorentz factor 𝛾 produced by a relative velocity of 0 . 5 0 0 𝑐 ?

Q4:

At what relative velocity is the Lorentz factor 𝛾 = 2 . 0 0 ?

Q5:

At what relative velocity is the Lorentz factor 𝛾 = 1 0 . 0 ?

  • A 0 . 9 3 4 𝑐
  • B 0 . 9 1 9 𝑐
  • C 0 . 9 5 8 𝑐
  • D 0 . 9 9 5 𝑐
  • E 0 . 9 7 1 𝑐

Q6:

What is the Lorentz factor for a proton having a mass energy of 938.3 MeV accelerated through an effective potential of 1.00 teravolts?

  • A
  • B
  • C
  • D
  • E

Q7:

If relativistic effects are to be less than 4 % , then 𝛾 must be less than 1.04. At what velocity is 𝛾 = 1 . 0 4 ?

  • A 0 . 1 9 6 𝑐
  • B 0 . 0 7 5 𝑐
  • C 0 . 2 5 0 𝑐
  • D 0 . 2 7 5 𝑐
  • E 0 . 1 7 8 𝑐

Q8:

An object initially moves at 0 . 2 0 0 𝑐 and then, sometime later, it moves at 0 . 8 0 0 𝑐 .

What is the Lorentz factor 𝛾 when 𝑣 = 0 . 2 0 0 𝑐 ?

What is the Lorentz factor 𝛾 when 𝑣 = 0 . 8 0 0 𝑐 ?

Q9:

A proton has a momentum of 1 . 1 2 Γ— 1 0 βˆ’ 1 7 kgβ‹…m/s.

Calculate 𝛾 for the proton.

Calculate the proton’s speed.

  • A 0 . 9 9 9 𝑐
  • B 0 . 9 6 2 𝑐
  • C 0 . 9 7 8 𝑐
  • D 0 . 9 9 2 𝑐
  • E 0 . 9 6 8 𝑐

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