Alice is driving a race car around an essentially circular track at a constant s

Question

Alice is driving a race car around an essentially circular track at a constant speed of 60 m/s. Brian, who is sitting at a fixed position at the edge of the track, measures the time that Alice takes to complete a lap by starting his watch when Alice passes his position (event E) and stopping when Alice passes his position again (event F). This situation is also observed by Cara and Dave, who are passengers in a train that passes very close to Brian. Cara happens to be passing Brian just as Alice passes Brian for the first time, and Dave happens to pass Brian just as Alice passes Brian the second time. Assume the clocks used by Alice, Brian, and Cara are close enough together so we can consider them all to be "present" at event E; simarly that those used by Alice, Brian, and Dave are "present" at event F. Assume that the ground frame is an inertial reference frame.

1) if Brian measures 100s between the events, how much less time does Alice measure between the events?

CORRECT ANSWER: 2 ps

2) if the train carrying Cara and Dave moves at a speed of 30 m/s, how much larger or smaller is the time that they measure compared to Brian's time? explain carefully.

CORRECT ANSWER: 0.5 ps larger

Explanation / Answer

Lets represent by following notation

: A- Alice, B- Brian, CD- Cara and Dave

(a) The Shortest time- A and B measures r Because B measures s also, and A is moving (therefore time moves slower for her) – Alice measures the shortest time.

The longest time- B and CD measures t B measures s which is the shortest possible t. Since CD don’t measure s they measure the longest time interval.

(b) Converting the speed the SR units: 60m/s=20108(SR) tABBrian=100s

Manipulating the equation by subtracting t in order to get the answer:

rABAlicetAB=(10.5v2)tABtAB=(10.5v21)tAB=

=21012s
Time is 2 picosec

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