Easy and quick Special Relativity before my exam

[mewmew]

Well I am having my exam tomorrow over special and very basic general relativity. I have one area I am still a bit fuzzy on now that I look back at our last exam. I am confused on when you can use just Lorenz time dilation/length contraction to when you need to use the full Lorenz transformation.

For example: In one problem we were given a spaceship leaves Earth to a star distance x away(in the Earth reference frame), the spaceship has a velocity of y with respect to the earth. How long does it take to get to to asteroid in the Earth reference frame? The ships? This you can use simple time dilation.

Our next problem was: Frame S' has a speed of x relative to S, clocks are adjusted so that t'=t=0. A photon is emitted in S at x=0 and absorbed at x=50 m, what time does this event occur in S'? This you need to use the full Lorentz transformation.

I am sure it is pretty simple to understand when and why you can use one or the other but I am a bit confused. Thanks for any help!

 

[Doc Al]

Simple time dilation describes the behavior of a single moving clock. That applies perfectly to your first example (the spaceship's clock is that single moving clock), but not to the second. In the second example, no single clock times the emission and absorption of that photon: multiple clocks in each frame are needed to measure the travel time. That requires the full Lorentz transformations.