Physics 1 Problem Solutions 290

Physics 1 Problem Solutions 290 - 286 Chapt 38 Special...

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286 Chapt. 38 Special Relativity 038 qfull 00300 2 3 0 moderate math: alternate Fitzgerald contraction 3. The Fitzgerald contraction formula is = 0 radicalbig 1 β 2 , where 0 is the proper length of object (i.e., length measured in the rest frame of the object) moving at speed β relative to some other inertial frame (let’s call it the lab frame) and is the corresponding length in the lab frame: note the lengths are both parallel to the direction of motion. The formula is derived from the Lorentz transformations assuming that the measurement of the location of the ends of the length was simultaneous in the lab frame. But there is another way one can measure the length of the moving object in the lab frame: measure the time Δ τ (i.e., the time in the “length form” equal to c Δ t ) between the front end of the object passing a fixed point in the lab frame and the rear end passing the same point, and multiply by the speed of the object. Call this length , where = β Δ τ .
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