A cube of metal with sides of length a sits at rest in a frame S with one edge parallel to the x-axis. Therefore, in S the cube has volume a3 . Frame S′ moves along the x-axis with a speed u. As measured by an observer in frame S′, what is the volume of the metal cube?
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A cube of metal with sides of length a sits at rest in a frame S with one edge parallel to the x-axis. Therefore, in S the cube has volume a3 . Frame S′ moves along the x-axis with a speed u. As measured by an observer in frame S′, what is the volume of the metal cube?
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- There is a spaceship that moves past us with a speed of (3/5)c and it has a rest length of 1000 m. Two clocks on the ship's nose and tail have been synchronized with each other in the ship's frame of reference. (On the ground, we have many clocks that are synchronized with each other in our frame.) When the nose of the spaceship reaches us, both our clock as well as the clock in the ship's nose read t = 0. At this time (t = 0 to us), what will the clock in the ship's tail read and in what time will the tail reach us?In frame S, event B occurs 2 ms after event A and at Dx = 1.5 km from event A. (a) How fast must an observer be moving along the +x axis so that events A and B occur simultaneously? (b) Is it possible for event B to precede event A for some observer?(c) Draw a spacetime diagram that illustrates your answers to (a) and (b). (d) Compute the spacetime interval and proper distance between the events.Two rockets, A and B, approach the earth from opposite directions at speed 0.800c. The length of each rocket measured in its rest frame is 100 m. What is the length of rocket A as measured by the crew of rocket B?
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