Section 2.4: Minkowski diagrams 2.25. Pole in barn * (a) A pole with proper length L moves rightward at speed 3c/5 through a barn with proper length L. In the barn frame, what are the Ax and At separations between the "left end of pole passing left end of barn" and "right end of pole passing right end of barn" events? (b) If you analyze the setup in the pole frame, you will quickly see that the order of the above events is reversed from the order in the barn frame. By continuity, there should therefore be a frame in which the two events happen at the same time. Use a Minkowski diagram to find this frame. 1. Invariant interval. (60 points) Morin exercise 2.22 (p. 107). Please note that the speeds of B and C are both given with respect to the ground. You may use Lorentz transformations or the fundamental effects to find the coordinates, but you might find it useful practice to do it with Lorentz transformations. Section 2.3: The invariant interval 2.22. Passing a train ** Person A stands on the ground, train B with proper length L moves to the right at speed 3c/5, and person C runs to the right at speed 4c/5. C starts behind the train and eventually passes it. Let event E be "C coincides with the back of the train," and let event E be "C coincides with the front of the train." Find At and Ax between the events E and E2 in the frames of A, B, and C, and verify that c(At) (Ax) is the same in all three frames.