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?


  • A0.121𝑐
  • B0.110𝑐
  • C0.167𝑐
  • D0.190𝑐
  • E0.140𝑐

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?

  • A0.855𝑐
  • B0.838𝑐
  • C0.823𝑐
  • D0.866𝑐
  • E0.883𝑐

Q5:

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

  • A0.995𝑐
  • B0.958𝑐
  • C0.934𝑐
  • D0.919𝑐
  • E0.971𝑐

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?

  • A1.13Γ—10
  • B1.19Γ—10
  • C1.25Γ—10
  • D1.07Γ—10
  • E1.01Γ—10

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?

  • A0.250𝑐
  • B0.275𝑐
  • C0.178𝑐
  • D0.075𝑐
  • E0.196𝑐

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.

  • A0.968𝑐
  • B0.999𝑐
  • C0.962𝑐
  • D0.978𝑐
  • E0.992𝑐

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