Alice, Bruce, Chad, and Dave are enjoying a trip to the amusement park. Alice rides the Ferris Wheel (47.75 meters in diameter), but Bruce decides simply to watch. Chad and Dave are riding the monorail that passes along a straight track just below the Ferris Wheel's bottom. The monorail moves at a constant speed of 9 m/s. The first time that Alice passes Bruce (who is standing right next to Alice but on the ground), Alice and Bruce look at their watches, and Chad (who happens to be passing under Alice's seat on the Ferris Wheel at that instant) looks at the clock on her seat's fancy electronic display. This is event A. When Alice passes Bruce the next time (call this event B), Alice and Bruce again look at their watches, and Dave, who happens to be passing under Alice's position at just that instant, looks at his display (which we assume is synchronized with Chad's display). Everyone determines the time interval that they measure between these momentous events (Chad and Dave by subtracting Chad's value for event A from Dave's value for event B). Bruce measures exactly 50 seconds between events A and B. Who measures the shortest time between these events? Who measures the longest? Explain. (Hint: What kind or kinds of time does each person measure?) How much longer or smaller is the time that Alice measures than the time that Bruce measures? How much longer or smaller is the time that Chad and Dave measure than Bruce's time? Explain. (Hint: note that their time will be very close to Bruce's time.)
Alice, Bruce, Chad, and Dave are enjoying a trip to the amusement park. Alice rides the Ferris Wheel (47.75 meters in diameter), but Bruce decides simply to watch. Chad and Dave are riding the monorail that passes along a straight track just below the Ferris Wheel's bottom. The monorail moves at a constant speed of 9 m/s. The first time that Alice passes Bruce (who is standing right next to Alice but on the ground), Alice and Bruce look at their watches, and Chad (who happens to be passing under Alice's seat on the Ferris Wheel at that instant) looks at the clock on her seat's fancy electronic display. This is event A. When Alice passes Bruce the next time (call this event B), Alice and Bruce again look at their watches, and Dave, who happens to be passing under Alice's position at just that instant, looks at his display (which we assume is synchronized with Chad's display). Everyone determines the time interval that they measure between these momentous events (Chad and Dave by subtracting Chad's value for event A from Dave's value for event B). Bruce measures exactly 50 seconds between events A and B.
- Who measures the shortest time between these events? Who measures the longest? Explain. (Hint: What kind or kinds of time does each person measure?)
- How much longer or smaller is the time that Alice measures than the time that Bruce measures?
- How much longer or smaller is the time that Chad and Dave measure than Bruce's time? Explain. (Hint: note that their time will be very close to Bruce's time.)
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d) Chad and Dave are moving in the ground frame. Shouldn't they therefore measure less time between the events than Bruce? Explain why the "moving clocks run slow" idea is very misleading here.
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