| Date | November 2017 | Marks available | 3 | Reference code | 17N.3.SL.TZ0.6 |
| Level | Standard level | Paper | Paper 3 | Time zone | Time zone 0 |
| Command term | Draw | Question number | 6 | Adapted from | N/A |
Question
A train is passing through a tunnel of proper length 80 m. The proper length of the train is 100 m. According to an observer at rest relative to the tunnel, when the front of the train coincides with one end of the tunnel, the rear of the train coincides with the other end of the tunnel.
Explain what is meant by proper length.
Draw a spacetime diagram for this situation according to an observer at rest relative to the tunnel.
Calculate the velocity of the train, according to an observer at rest relative to the tunnel, at which the train fits the tunnel.
For an observer on the train, it is the tunnel that is moving and therefore will appear length contracted. This seems to contradict the observation made by the observer at rest to the tunnel, creating a paradox. Explain how this paradox is resolved. You may refer to your spacetime diagram in (b).
Markscheme
the length of an object in its rest frame
OR
the length of an object measured when at rest relative to the observer
world lines for front and back of tunnel parallel to ct axis
world lines for front and back of train
which are parallel to ct′ axis
realizes that gamma = 1.25
0.6c
ALTERNATIVE 1
indicates the two simultaneous events for t frame
marks on the diagram the different times «for both spacetime points» on the ct′ axis «shown as Δt′ on each diagram»
ALTERNATIVE 2: (no diagram reference)
the two events occur at different points in space
statement that the two events are not simultaneous in the t′ frame
