Relativity problems?
Two trains (A and B), each of proper length 1 km run on parallel tracks. Train A has a velocity of 0.6 c while train B has a velocity of 0.8 c relative to the ground. How long does it take the faster train to fully pass the slower one (from the time when the front of B coincides with the rear of A to the time when the rear of B coincides with the front of A)? The answer is
(a) __according to observers in the ground frame;
(b) __according to observers in the frame of the slower train.
Two trains (A and B), each of proper length 1 km run on parallel tracks. Train A has a velocity of 0.6 c while train B has a velocity of 0.8 c relative to the ground. How long does it take the faster train to fully pass the slower one (from the time when the front of B coincides with the rear of A to the time when the rear of B coincides with the front of A)? The answer is
(a) __according to observers in the ground frame;
(b) __according to observers in the frame of the slower train.
1 Answer
(a) __according to observers in the ground frame;
(b) __according to observers in the frame of the slower train.
Explanation:
(a) __according to observers in the ground frame;
A and B both have proper lengths
In ground frame G, the velocity of B rel to A is
-
(a) the front of B coinciding with the rear of A to
-
(b) the rear of B coinciding with the front of A,
....B has to travel a distance
The time required for that is:
(b) __according to observers in the frame of the slower train.
Use inverse Lorentz transform between G and A:
Everything is known apart from
-
(a) the total distance travelled by B in
#Delta t_G# less B's contracted length, or -
(b) the total distance travelled by A in
#Delta t_G# plus A's contracted length.
So:
Or:
Hence: