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=1.01?


Q2:

What is the Lorentz factor 𝛾 produced by a relative velocity of 0.250𝑐?

Q3:

What is the Lorentz factor 𝛾 produced by a relative velocity of 0.500𝑐?

Q4:

At what relative velocity is the Lorentz factor 𝛾=2.00?

Q5:

At what relative velocity is the Lorentz factor 𝛾=10.0?

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

Q6:

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

  • A 1 . 1 3 Γ— 1 0 
  • B 1 . 1 9 Γ— 1 0 
  • C 1 . 2 5 Γ— 1 0 
  • D 1 . 0 7 Γ— 1 0 
  • E 1 . 0 1 Γ— 1 0 

Q7:

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

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

Q8:

An object initially moves at 0.200𝑐 and then, sometime later, it moves at 0.800𝑐.

What is the Lorentz factor 𝛾 when 𝑣=0.200𝑐?

What is the Lorentz factor 𝛾 when 𝑣=0.800𝑐?

Q9:

A proton has a momentum of 1.12Γ—10 kgβ‹…m/s.

Calculate 𝛾 for the proton.

Calculate the proton’s speed.

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

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