| Date | November 2011 | Marks available | 4 | Reference code | 11N.3.SL.TZ0.9 |
| Level | Standard level | Paper | Paper 3 | Time zone | Time zone 0 |
| Command term | Calculate and Explain | Question number | 9 | Adapted from | N/A |
Question
This question is about special relativity, simultaneity and length contraction.
One of the two postulates of special relativity may be stated as:
“The laws of physics are the same for all observers in inertial reference frames.”
State
(i) what is meant by an inertial frame of reference.
(ii) the other postulate of special relativity.
In a thought experiment to illustrate the concept of simultaneity, Vladimir is standing on the ground close to a straight, level railway track. Natasha is in a railway carriage that is travelling along the railway track with constant speed v in the direction shown.
Natasha is sitting on a chair that is equidistant from each end of the carriage. At either end of the carriage are two clocks C1 and C2. Next to Natasha is a switch that, when operated, sends a signal to each clock. The clocks register the time of arrival of the signals. At the instant that Natasha and Vladimir are opposite each other, Natasha operates the switch. According to Natasha, C1 and C2 register the same time of arrival of each signal.
Explain, according to Vladimir, whether or not C1 and C2 register the same time of arrival for each signal.
The speed v of the carriage is 0.70c. Vladimir measures the length of the table at which Natasha is sitting to be 1.0 m.
(i) Calculate the length of the table as measured by Natasha.
(ii) Explain which observer measures the proper length of the table.
Markscheme
(i) (a reference frame) in which Newton’s first law holds true/that is not accelerating/that is moving with constant velocity;
(ii) the speed of light in a vacuum/free space is the same for all inertial observers;
Look for these main points:
signal from switch travels at same speed c to each lamp;
but during signal transfer C1 moves closer to/C2 moves away from source of signal;
since speed of light is independent of speed of source, signal reaches C1 before C2/C2 after C1;
according to Vladamir C1 registers arrival of signal before C2/C2 registers arrival of signal after C1;
(i) \(\gamma = \frac{1}{{\sqrt {1 - {{\left( {0.70} \right)}^2}} }} = 1.4\);
L0=γL;
=1.4m;
(ii) Natasha
since proper length is defined as the length of the object measured by the observer at rest with respect to the object;
