Solved Examples on Lorentz Factor
Problem 1: If the relative velocity between the two observers is 120 m/s, Determine the Lorentz factor. (Speed of light is 3 x 108 m/s).
Solution:
Given:
Relative Velocity (v) = 120 m/s
Speed of light (c) = 3 x 108 m/s
Therefore, Lorentz factor is given as,
γ = 1 / √(1-(v/c)2)
γ = 1 / √(1-(120/3 x 108)2)
= 1 / √(1 – (14400 / 9 x 1016))
= 1
Problem 2: If the relative velocity between the two observers is 300 m/s, Determine the Lorentz factor. (Speed of light is 2.99 x 108 m/s).
Solution:
Given:
Relative Velocity (v) = 300 m/s
Speed of light (c) = 2.99 x 108 m/s
Therefore, Lorentz factor is given as,
γ = 1 / √(1-(v/c)2)
γ = 1 / √(1 – (300/3 x 108)2)
= 1 / √(1 – (90000 / 8.9401 x 1016))
= 1
Problem 3: The ratio of v to c is given as 26.7 x 10-8, Determine the Lorentz factor. (Speed of light is 2.99 x 108 m/s).
Solution:
Given:
The ratio of v to c (v/c) = β = 26.7 x 10-8
Therefore, Lorentz factor is given as,
γ = 1 / √(1-(v/c)2)
γ = 1 / √(1-(26.7 x 10-8)2)
= 1
Problem 4: If the time interval is 25 seconds and the observer velocity is 30,000 m/s, Find the relative time.
Solution:
Given,
Time interval (Δt0) = 25 seconds
Observer velocity (v) = 30,000 m/s
Relative time Δt = Δt0 / √(1 – v²/c²)
= 25 / √(1 – 30,000²/299,792,4582)
= 25 sec
Therefore, the relative time is 25 seconds.
Problem 5: Find the relative time, If the time interval is 32 seconds and the observer velocity is 50,000 m/s.
Solution:
Given,
Time interval (Δt0) = 32 seconds
Observer velocity (v) = 50,000 m/s
Relative time Δt = Δt0 / √(1 – v²/c²)
= 32 / √(1 – 50,000²/299,792,4582)
= 32 sec
Therefore, the relative time is 32 seconds.
Lorentz Transformations
Lorentz factor, often known as the Lorentz term, is a measurement that describes an object’s measurements of time, length, and other physical properties, which vary when it moves. The expression occurs in derivations of the Lorentz transformations and is found in a number of special relativity equations.
It is named after the Dutch physicist Hendrik Lorentz, the term originates from its earlier use in Lorentzian electrodynamics.
Table of Content
- Lorentz Factor Definition
- Inertial Frame of Reference
- Non-Inertial Frame of Reference
- Difference between Inertial Frame of Reference and Non-Inertial Fames of Reference
- Lorentz Transformation
- The formula for Lorentz transformation can be given as,
- Time Dilation
- Properties of Lorentz Factor
- Solved Examples on Lorentz Factor