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

In summary, the problem involves a clock moving at a speed v=\frac{c}{2} and the Lorentz transformation is used to find out what our clock will read when the moving clock reads 10 seconds. The attempt at a solution involved using the equation t=\gamma(x^{'}+\frac{Vt^{'}}{c^{2}}) and plugging in values for v and t, but the final answer did not match the correct answer of 11.5 seconds. The question raises some confusion about the initial values and possible errors in calculations.
  • #1
harvellt
95
0

Homework Statement


A clock is moving past us at speed [tex]v=\frac{c}{2}[/tex] reads [tex]t^{'}=0[/tex] 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


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


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 [tex]x^{'}[/tex] 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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  • #2
our clocks will read 0. What does the question really say?
 
  • #3
that s wasnt real sorry and fixed the rest of the problem should be a little better now
 

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

1. How do you solve Lorentz transformation homework?

The Lorentz transformation is solved using the equations t' = γ(t - vx/c^2) and x' = γ(x - vt), where γ is the Lorentz factor, t is the time in the original frame, t' is the time in the transformed frame, x is the distance in the original frame, x' is the distance in the transformed frame, v is the relative velocity between the two frames, and c is the speed of light. By plugging in the given values and solving for t, you can find the time in the original frame when t' = 10s.

2. What is the Lorentz factor?

The Lorentz factor, denoted by γ, is a term used in special relativity to account for the effects of time dilation and length contraction. It is given by the equation γ = 1/√(1 - v^2/c^2), where v is the relative velocity between two frames and c is the speed of light. It is a factor that is greater than or equal to 1, and it approaches infinity as v approaches c.

3. How does the Lorentz transformation relate to Einstein's theory of special relativity?

The Lorentz transformation is a mathematical tool used to describe how measurements of time and space are affected by the relative motion between two frames of reference. It is a crucial component of Einstein's theory of special relativity, which states that the laws of physics are the same for all observers in uniform motion. The Lorentz transformation allows us to understand how time and space measurements change for different observers, and it is a fundamental concept in understanding the effects of relativity.

4. Can the Lorentz transformation be applied to any frame of reference?

Yes, the Lorentz transformation can be applied to any frame of reference, as long as the two frames are moving at a constant velocity relative to each other. This means that it can be used to describe the effects of relativity for objects moving at any speed, as long as their relative velocity is constant. However, it does not apply to objects that are accelerating or changing direction.

5. Are there any real-world applications of the Lorentz transformation?

Yes, the Lorentz transformation has many real-world applications, especially in the fields of physics and engineering. It is used in the design and analysis of particle accelerators, such as the Large Hadron Collider, and in the development of GPS technology. It is also crucial in understanding the behavior of high-speed particles, such as those in nuclear reactions, and in the study of astronomical phenomena like black holes and supernovae.

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