First Sample Test for PC 124

1. We have a meter stick. People travelling past us at half the speed of light measure our meter stick to be how long?

2. Is there a reference frame in which our meter stick is more than one meter long?

3. Your friend takes a vacation on which he flies a total of 10,000 miles at 600 miles/hour. Because of this, he has aged how much less than you?

4. Describe all the inertial reference frames in which our meter stick is exactly one meter long.

5. The book describes an experiment in which muons travel at .995c and thus live about ten times as long as their proper lifetime of 2 microseconds. We would like some muons to live for about a thousand times their normal life, or 2 ms, before decaying. How fast must these muons be travelling? Is it much faster than .995c? What quantity might we compare, instead of speed, that wll show how different these two situations are?

6. In Wonderland, where c=10 miles/hour, the bank robbers have a car that can travel at 7 miles an hour. The cops have a car that can go only 4 miles/hour, but they have guns that shoot bullets at 4 miles/hour. If the robbers are ahead of the cops in a high-speed chase, can the cops shoot the robbers' tires?

7. You would like to read Proust's Remembrance of Things Past in the original French, but fear you will not live long enough to do so. You decide to be put into a high-speed orbit in order to prolong your life. Ignoring the question of technical feasibility, will this strategy give you the extra time you need to fulfill your literary longings?

Interval questions:

(You might want first to read the page on intervals.)

8. At 5 o'clock, according to the perfectly-synchronized clocks in Wonderland, Evelyn accidentally fires a death-blaster. At 5:03, Louis is wounded by what appears to be a blast from the same model of death-blaster. Louis was standing half a mile away from where Evelyn was messing around. (a) Could Evelyn be responsible for Louis's injury? (b) Eugene testifies that he was present at and witnessed both events, and that he's therefore certain that Evelyn is the responsible party. Can Eugene's testimony be trusted?

9. All the clocks in Wonderland are indeed synchronized, but we know that that doesn't mean they're synchronized in all reference frames. If two clocks are 8 miles apart, Is there a reference frame in which one clock is an hour behind the other?