| Date | May 2015 | Marks available | 3 | Reference code | 15M.3.SL.TZ2.11 |
| Level | Standard level | Paper | Paper 3 | Time zone | Time zone 2 |
| Command term | Calculate and State | Question number | 11 | Adapted from | N/A |
Question
This question is about relativistic kinematics.
A spacecraft leaves Earth and moves towards a planet. The spacecraft moves at a speed 0.60c relative to the Earth. The planet is a distance of 12ly away according to the observer on Earth.
Determine the time, in years, that it takes the spacecraft to reach the planet according to the
(i) observer on Earth.
(ii) observer in the spacecraft.
The spacecraft passes a space station that is at rest relative to the Earth. The proper length of the space station is 310 m.
(i) State what is meant by proper length.
(ii) Calculate the length of the space station according to the observer in the spacecraft.
F and B are two flashing lights located at the ends of the space station, as shown. As the spacecraft approaches the space station in (b), F and B turn on. The lights turn on simultaneously according to the observer on the space station who is midway between the lights.
State and explain which light, F or B, turns on first according to the observer in the spacecraft.
Markscheme
(i) \(\left( {\frac{{12{\rm{ly}}}}{{0.60{\rm{c}}}} = } \right)20\left( {{\rm{yr}}} \right)\) or 6.3×108 (s);
(ii) \(y = \left( {\frac{1}{{\sqrt {1 - {{0.60}^2}} }} = } \right)1.25\);
\(\Delta {t_0} = \left( {\frac{{\Delta t}}{y} = \frac{{20}}{{1.25}} = } \right)16\left( {{\rm{yr}}} \right)\) or 5.0×10 8 (s); (allow ECF from (a)(i));
This question is worth [2], but it is easy to accidentally award [1].
(i) the length of a body in the rest frame of the body;
Do not accept “event” instead of “object/body”.
Do not accept “in the same frame” unless rest (OWTTE) is mentioned.
(ii) \(l = \frac{{310}}{{1.25}}\); (allow ECF from (a)(ii))
=250(m);
This question is worth [2], but it is easy to accidently award [1].
according to the spacecraft observer, the space station observer receives light from B and F at the same time;
for the spacecraft observer the space station observer moves away from the waves from B/towards the waves from F;
but the speed of light is constant;
according to the spacecraft observer light from B must be emitted first;
Do not award second marking point for answers that refer to light the spacecraft observer SEES or to distances to the spacecraft.
Examiners report
Part (a) was answered very well. This year almost nobody worked in seconds and so the answers were easily obtained. As usual there were candidates who got time dilation the wrong way round. The time interval for the Earth clocks is dilated (longer) but some candidates think that the time interval on the “moving” clock is dilated. It is best not to think of motion, but to realise that the single clock at both events records the shortest time interval.
In (b) a very common misconception with proper length is to just say that the object must be measured in the same frame of reference as the observer. Well this is always true of course, but only if the object is at rest in the observer’s frame is it proper length. Everything is in everything else’s frame. Gradually more and more candidates are answering simultaneity questions correctly. This year almost 3% could correctly explain why light B emits waves before light F as perceived from the spacecraft frame. The other 97% thought that the question was asking about which light the spacecraft observer sees first.
