Calculating elapsed time in different frames

[Abhishek11235]

Homework Statement

Consider the following problem. A stick passes with speed v though a breadthless person whose(the stick) proper length is L. How does:

Stick See the time elapsed on my clock?

I see time elapsed on my clock?

The second part is easy. In my frame ,the stick is length contracted. So the time elapsed is $T_{my}= L/\gamma v$

Now the first part. The stick measures the time L/v for the person to pass from one end of stick to another. The stick measures proper time of L/v. Hence he should see the time elapsed on my clock to be
$T_{me}= \gamma T= \gamma L/v$

However if I calculate using Lorentz transformation, I get same answer as in a. Where is flaw in my reasoning of 2? Thanks in advance

Relevant Equations

$T= \gamma T'$

The attempt is above

 

[TSny]

Does the stick measure proper time?

In general, how do you decide which frame measures the proper time interval between two events?

 

[Abhishek11235]

Does the stick measure proper time?

In general, how do you decide which frame measures the proper time interval between two events?

If the 2 events occur are measured at same position ,it is proper frame. I think I got idea. Please correct me if I am wrong. In the frame of stick,the events(when the ends come and then pass through person) are spatially separated(by length L),the stick can't constitute proper frame. It is the person who is proper frame(he measures events occurring at same position). Hence the time should be $T_{me}=T/\gamma$. Is it right?

 

[TSny]

Yes. Good.