# 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 must be less than 1.01. At what relative velocity is ?β¨

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Q2:

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

Q3:

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

Q4:

At what relative velocity is the Lorentz factor ?

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Q5:

At what relative velocity is the Lorentz factor ?

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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 teravolt?

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Q7:

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

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Q8:

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

What is the Lorentz factor when ?

What is the Lorentz factor when ?

Q9:

A proton has a momentum of kgβm/s.

Calculate for the proton.

Calculate the protonβs speed.

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