A 30-m-long rocket train car is travelingfrom Los Angeles to New York at 0.8 c w

Question

A 30-m-long rocket train car is travelingfrom Los Angeles to New York at 0.8c when a light at the center of the carflashes. When the light reaches the front of the car, itimmediately rings a bell. Light reaching the back of the carimmediately sounds a siren. (a) Are the bell and siren simultaneous events for a bicyclistwaiting to cross the tracks?If not, by how much time? (b) Are the bell and siren simultaneous events for a passengerseated in the car? If not, by how much time? (a) Are the bell and siren simultaneous events for a bicyclistwaiting to cross the tracks?If not, by how much time? (b) Are the bell and siren simultaneous events for a passengerseated in the car? If not, by how much time?

Explanation / Answer

Events in the car are simultaneous for an observer in the car- the wave front reaches the front and the back of the car simultaneously. Simultaneous events in one frame are never simultaneous in aframe moving with respect to the frame in which the simultaneous events occur t2 = [t1 - vx1 / c2] / (1 - v2 /c2) t1 = 0   the events aresimultaneous x1 = 30 m    the events occur30 m apart in the train 1 / (1 - v2 / c2) = 1 / (1- .64) = 1.67 t2 = 1.67 * .8 c * 30 / c2 = 13.3= 40.1 / 3 * 10E8 = 1.34 * 10E-7 sec Note: t2 is negative and the siren ringsbefore the bell sounds. This makes sense because an observer on the groundopposite the light in the middle of the car would see the back of the car approaching the wavefront whilethe front of the car would be receding from the wavefront.

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