What is the Time Read by a Moving Clock in Basic Relativity?

[DukeLuke]

Homework Statement

A clock moves along the x-axis at a speed of 0.590c and reads zero as it passes the origin.
What time does the clock read as it passes x = 180 m?

Homework Equations

I believe that this is some sort of basic Lorentz Transformation, but I have just started learning about relativity so I might be wrong.

\Delta x' = \gamma(\Delta x - v\Delta t)
\Delta t' = \gamma(\Delta t - v\Delta x/c^2)

The Attempt at a Solution

I started by putting these variables into the second equation
x= 180m
v= .590c
t= 0s
\gamma=1.269

\Delta t' = \gamma(\Delta t - v\Delta x/c^2)
\Delta t' = 1.269(0 - (180m)(.590c)/c^2)

This gave me -4.49537e-7 secs which was wrong. I'm most confused on what conditions are used to determine whether given variables are regular or prime (').

 

[naresh]

The prime refers to variables in a moving frame of reference. You need to therefore clearly define two frames of reference in this problem. Let's say one of them is the laboratory (no primes) and the other is the clock's frame (primes). Why do we choose the clock's frame? Because we want the time shown by the clock. (The time shown by the clock is the time difference between two events as measured in its frame).

Can you identify what the four variables in your equations? Specifically, what are \Delta x and \Delta x'?

 

[DukeLuke]

Thanks for the help, but I'm still having trouble with this problem.

For the reference frame moving with the clock I took the variables to be.
v'= 0 because the frame is moving with the clock
x'= 0 because the frame is moving with the clock
t'= ? this is what I'm trying to find

For the stationary laboratory frame I have
v= .59c
x= 180m
t= ?

From this I have two unknowns (t, t') and two equations. I used the first equation below to find t for the lab frame and put that value into the second equation to find t'. This still gave me the wrong answer. Am I associating the given variables with the right frames? Also, should I be thinking about the lab frame being stationary at the origin?

\Delta x' = \gamma(\Delta x - v\Delta t)
\Delta t' = \gamma(\Delta t - v\Delta x/c^2)

 

[Doc Al]

To use those equations, you need to start somewhere. Which of these quantities do you already know?
Δx = ?
Δx' = ?
Δt = ?
Δt' = ? (That's the one you're trying to figure out.)

Hint: You should know two of them right off the bat, which will allow you to find the others.

 

[DukeLuke]

When I attempted it I used
Δx = 0
Δx' = 180m

With these I found Δt using the first equation and put that into the second equation to find Δt', but this gave me the wrong answer.

 

[Doc Al]

When I attempted it I used
Δx = 0
Δx' = 180m

You have these backwards. In the prime frame the clock isn't moving, so Δx' = 0.

 

[DukeLuke]

Thanks, that did the trick.