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, sho 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 by his position (call this event E) and stopping it when Alice passes his position again (call this 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 the first time, and Dave happens to pass Brian just as Alice passes Brian the second time. Assume that the clocks used by Alice, Brian, and Cara are close enough together that we can consider them all to be "present" at event E; similarly, that those used by Alice, Brian, and Dave are "present" at event F. Assume that the ground frame is an inertial reference frame.

(a) Who measures the shortest time between these events? Who measures the longest?

(b) If Brian measures 100s between the events, how much less times does Alice measure between events?

(c) 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 Brain's time? Explain carefully.

Answer: (a) Alice is the shortest, Dave/Cara is the longest (b) 2 ps (c) 0.5 ps longer

sse The halksle of a muon at rest is 1.52 us. One can store anuions or a much longer tbione (as measured the laboratory) by acelerating them to a speed (1 + x. Apply equation R5.23 and the cha this function to arrive at equation R517 Event F Event E Car dives by Alio Car driven by Alice o Brian Dave a) Figure R5.8 Train in the situation described in problem R5S.3. (b) Event F in the situation described in problem R5S.3.

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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