## B7    Problems and Suggestions

1. Compute the root term for different values of v: For cars, airplanes, rockets etc. What does it mean for Newton's absolute time, when one considers only ‘earthly’ speeds?
2. How quickly does one have to move, in order that “one hour takes only 3599 s”?
3. How long would the running of ‘24 hours of Le Mans’ last for the drivers, if they drive on average (somewhat exaggerated) at 324 km/h?
The answer may depend on the pocket calculator that is used…
4. How far does light actually travel in a nanosecond? What distance corresponds to this precisely measurable time interval?
5. Provide a table of the distances of the planets from the sun, measured in ‘light minute’ units.
6. Two rockets fly past each other at 0.6 • c. A measures the length of the other rocket B to be 40 m. What is the rest length of the rocket B, and how much are the clocks at the tip and at the end of rocket B for A de-synchronized, given that they are synchronized for B? And which of the two clocks is running fast for A?
7. How fast does a clock have to move, in order to halve its running-time?
8. Signal travel times: The singing of Mick Jagger is broadcast directly from the microphone to a radio listener 300 km away. The listener sits 6.8 m from the loudspeaker. How long does the radio signal travel through the ‘ether’? How long do the acoustic waves need to travel from the loudspeaker to the ear of the listener? How long does it take for someone who is at the ‘live’ performance and sits 34 m from the loudspeakers to receive the acoustic waves?
9. What would actually happen with the length of an object, which moves with double the speed of light? And how slowly would such a fast-moving clock tick??
10. Yet another Pythagorean Triple: The root is also quite pretty if v / c take the values 5/13 or 12/13 … The pair 3/5 and 4/5 should already be familiar to you.
11. Again two rockets, flying past each other at high speed: A measures when flying by that the two rockets are the same length. What does B measure? a) A is the same length as B    b) A is longer than B    c) A is shorter than B   ?
12. Are fast-moving clocks, which are synchronized in their system, really synchronized or not? The question is just as meaningful as asking about the season: Is it now really winter or summer? If you are not sure, then call your uncle in Australia…
13. (Challenging) Derive the length contraction from observing a fast-moving light clock that is lying on its side! The flash of light travels back and forth in the same direction as the clock is moving and thus the ‘tick’ and ‘tock’ are not equivalently long to an observer at rest…

Einstein's 'entry ticket' to the Swiss Federal Institute of Technology (ETH Zürich): The Matura diploma of the Kantonsschule Aarau. It is often repeated that he was a weak student, but this is a misinterpretation: In Germany, 1 is the best mark and 6 the worst, while in Switzerland the scale runs from 6 for the best mark down to 1.