Solve Lorentz Transformation Homework: Find t When t'=10s

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SUMMARY

The discussion centers on solving a Lorentz transformation problem where a moving clock reads t' = 10 seconds while the stationary clock's time t needs to be determined. The relevant equation used is t = γ(x' + (Vt'/c²), where V = c/2. The user initially misapplied the time dilation formula, arriving at an incorrect result of 11.5 seconds, but struggled to correctly apply the Lorentz transformation, resulting in a calculated time of 14 seconds. Clarifications were made regarding the variables involved, particularly the value of x'.

PREREQUISITES
  • Understanding of Lorentz transformations in special relativity
  • Familiarity with the concept of time dilation
  • Knowledge of the speed of light (c) and its significance in relativity
  • Ability to manipulate algebraic equations involving gamma (γ) factor
NEXT STEPS
  • Review the derivation and application of the Lorentz transformation equations
  • Study the concept of the Lorentz factor (γ) and its calculation
  • Practice solving additional problems involving time dilation and Lorentz transformations
  • Explore the implications of relativistic effects on simultaneity and measurement
USEFUL FOR

Students of physics, particularly those studying special relativity, educators teaching relativity concepts, and anyone seeking to deepen their understanding of time dilation and Lorentz transformations.

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Homework Statement


A clock is moving past us at speed v=\frac{c}{2} reads t^{'}=0 when our clock read t=0. Using the Lorentz tranformation, find out what our clock will read when the moving clock reads 10s.


Homework Equations


t=\gamma(x^{'}+\frac{Vt^{'}}{c^{2}})


The Attempt at a Solution


Alright so I know I have this one wrong if I use the equation for time dilation I get 11.5 seconds and it is correct, but I am having trouble using the lorenz transformation to get the same answer. For x^{'} I am using the equation Vt=x and get 5cs (light seconds), but I am ending up with a t=14. seconds.
I have some small silly disconnect somewhere. Help?
 
Last edited:
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our clocks will read 0. What does the question really say?
 
that s wasnt real sorry and fixed the rest of the problem should be a little better now
 

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