Spaceship Special relativity

  • Thread starter struggles
  • Start date
  • #1
50
0

Homework Statement


  1. A spaceship travels from Earth to the vicinity of the star that is measured by astronomers on Earth to be six light-years away. The spaceship and its occupants have a total rest mass of 32 000 kg. Assume that the spaceship travels at constant velocity. The time taken as measured by clocks on the spaceship is 2.5 years.
    1. (i) Compute the velocity of the spaceship. [3 marks]

    2. (ii) How long does the trip take as measured by clocks in the Earth’s

      inertial rest frame? [3 marks]

Homework Equations



x' = γ(x-ut)
t' = γ(t - ux/c2) where the dash frame is the object rest frame, u is the relative speed between frames
γ = 1/√(1-u2/c2)
v' = v-u/1-u2v/c2

The Attempt at a Solution



So I'm a bit stuck my the first part of the question.
So far I have determined that x = 6ly, t' = 2.5yrs. I'm getting a bit puzzled as to what I'm looking to find. Is it u
or v or are they the same thing in this case? regardless I cannot think of a way in which i have enough variables that allows me to compute a value. Any help would be greatly appreciated!
 

Answers and Replies

  • #2
Doc Al
Mentor
44,986
1,253
Sometimes you have to chip away at it. See if you can solve for x'. (Hint: You'll need a different version of your first equation.)

I'm getting a bit puzzled as to what I'm looking to find. Is it u
or v or are they the same thing in this case?
You are solving for u. v is irrelevant: there's only one velocity in this problem.
 
  • #3
50
0
Ok so I'm not sure if this works or not but this is what I've got:
t = γt' and t = x/u.
Combining this gives x/t' = uγ and then expanding this all out and rearranging gives a value for u. Would this method work?
 
  • #4
Doc Al
Mentor
44,986
1,253
Ok so I'm not sure if this works or not but this is what I've got:
t = γt' and t = x/u.
Combining this gives x/t' = uγ and then expanding this all out and rearranging gives a value for u. Would this method work?
That will do it. Good! :thumbup:
 
  • #5
50
0
Thank you for your help!
 

Related Threads on Spaceship Special relativity

  • Last Post
Replies
0
Views
900
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
1
Views
919
Replies
3
Views
1K
  • Last Post
Replies
1
Views
630
  • Last Post
Replies
9
Views
576
Replies
0
Views
1K
Replies
1
Views
2K
Replies
6
Views
1K
  • Last Post
Replies
5
Views
1K
Top