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Problem Set 7

# Problem Set 7 - Problem Set VII Assign Due November 1 2006...

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Problem Set VII- Assign October 23, 2006 Due November 1, 2006. Fall 2006 Physics 200a R. Shankar 1. The earth and sun are 8.3 light-minutes apart. Ignore their relative motion for this problem and assume they live in a single inertial frame, the Earth-Sun frame. Events A and B occur at t = 0 on the earth and at 2 minutes on the sun respectively. Find the time difference between the events according to an observer moving at u = . 8 c from Earth to Sun. Repeat if observer is moving in the opposite direction at u = . 8 c . 2. Return to the Earth-Sun case above. (a) What is the speed of a spacecraft that makes the trip from the Sun to the Earth in 5 minutes according to the on board clocks? (b) What is the trip time in the Earth-Sun frame? (c) Find the square of the space-time interval between them in light-seconds. (You may need to come back to part (c) after I do space-time intervals in class. Do not just jump in and use some formula. Think in terms of events, assign as many possible space-time coordinates as you can to each event in any frame and use the LT. Measure time in minutes, distance in light-minutes. Imagine a rod going from earth to the sun, if that helps. Note that the spatial coordinate difference between events in spacecraft frame are not the same as distance between Earth and Sun in that frame. Even pre-Einstein, if I sit in my car going at 60 mph, I leave New Haven at t=0 (Event 1) and arrive at Boston at t= 2hrs (Event 2), the two events have the same coordinate in my frame (i.e., where I am in the car) Δ x = 0 , but that is not the distance between these towns.) 3. A muon has lifetime of 2

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