| Date | May 2014 | Marks available | 3 | Reference code | 14M.3.SL.TZ1.8 |
| Level | Standard level | Paper | Paper 3 | Time zone | Time zone 1 |
| Command term | Calculate, Discuss, and Explain | Question number | 8 | Adapted from | N/A |
Question
This question is about relativistic kinematics.
State what is meant by an inertial frame of reference.
A spaceship travels from space station Alpha to space station Zebra at a constant speed of 0.90c relative to the space stations. The distance from Alpha to Zebra is 10ly according to space station observers. At this speed γ=2.3.
Calculate the time taken to travel between Alpha and Zebra in the frame of reference of an observer
(i) on the Alpha space station.
(ii) on the spaceship.
Explain which of the time measurements in (b)(i) and (b)(ii) is a proper time interval.
The spaceship arrives at Zebra and enters an airlock at constant speed. O is an observer at rest relative to the airlock. Two lamps P and Q emit a flash simultaneously according to the observer S in the spaceship. At that instant, O and S are opposite each other and midway between the lamps.
Discuss whether the lamps flash simultaneously according to observer O.
Markscheme
a co-ordinate system (in which measurements of distance and time can be made);
which is not accelerating;
in which Newton’s laws are valid;
(i) \(\left( {\frac{{10}}{{0.90{\rm{c}}}} = } \right)11{\rm{yr}}\);
\(\left( { = 3.5 \times {{10}^8}{\rm{s}}} \right)\);
This is a question testing units for this option. Do not award mark for an incorrect or missing unit.
(ii) distance according to spaceship observer \( = \frac{{10}}{{2.3}}\left( { = 4.3{\rm{ly}}} \right)\);
so time for spaceship \( = \frac{{4.3}}{{0.90}} = 4.8\left( {{\rm{yr}}} \right)\);
between two events occurring at the same point in space / shortest time measured;
so proper time interval measured by observer on spaceship;
Do not award second marking point unless a reason has been attempted.
speed of light is the same for both observers O and S / events simultaneous in stationary reference frame are not (necessarily) simultaneous in moving reference frame;
S is moving so PS will be longer than QS when light reaches S;
so if light arrives simultaneously then light from P will have been in transit for longer than Q;
therefore P emits a flash before Q;
Examiners report
There were a large variety of answers to (a). Many candidates stated that the frame of reference is not accelerated. Many candidates did not explain the term “frame of reference” in terms of a “co-ordinate system”. It was a rare answer that earned more than one mark.
In (b)(i), the majority of candidates properly calculated the time. Some wrote the incorrect unit (ly) instead of y or s. There is room for improvement in responses to (b)(ii). The vast majority of candidates used the formula for time dilation. They did not notice that it is not normal for the observer on the spaceship to know the time measured on the space station. The correct calculation, length and speed measured, appeared only very rarely.
There was a good variety of answers to (c). Many candidates still do not know the term proper time interval, clearly defined in relativity. Many incorrectly referred to both events occurring in one frame of reference rather than one point in space in their answer. Most did attempt a reason.
In (d) many candidates proved that they understood the concept of simultaneity. However, many did not respond to the command term “discuss”. Many candidates were confused between object (in a specific frame of reference) and event.
