pset1 - the front with speed u with respect to the train....

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Physics 260, Problem Set 1 due: Tuesday, September 20 at Noon Please place your completed problem sets in the “Physics 260” box in the physics department mailroom (Rutherford 103b). You are encouraged to discuss these problems with your colleagues, but you must write up your own solutions; the solutions you hand in should reflect your own work and understanding. Late problem sets will be penalized 10% per day late, unless an extension has been obtained from me or a TA before the due date. Reading : Chapter 2 of Bernstein et al. 1. Chapter 2, problem 6. 2. Chapter 2, problem 8. 3. Chapter 2, problem 10. 4. Chapter 2, problem 18. 5. A train of length L (as measured in the frame where the train is at rest) moves a speed v with respect to the ground. When the front of the train passes a tree on the ground, a ball is simultaneously (as measured in the ground frame) thrown from the back of the train toward
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Unformatted text preview: the front with speed u with respect to the train. Show that it is possible to choose a value of u so that the ball hits the front of the train simultaneously (as measured in the train frame) with the tree passing the back of the train. You should nd that this can only happen if v is less than a critical value v which you should compute. Draw a diagram of this setup. 6. Suppose that I observe two events which happen at positions x 1 and x 2 and at times t 1 and t 2 . Under what circumstances is it possible to nd an observer moving at constant velocity who will see these events happening simultaneously? Draw a diagram of this setup. What is the velocity (relative to me) of the observer who sees these events as simultaneous? What is this velocity in the limit where | x 1-x 2 | approaches c | t 1-t 2 | ? 1...
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