Chapter 26, Problem 22P

26.3-26.6 Simultaneity, Time Dilation, Length Contraction, and Spacetime Diagrams

22 * A pole and barn “paradox" A barn of width 4.0 m is at rest in reference frame S. Let us take a pole of length 8.0 m and accelerate it to a velocity such that its length in frame S becomes equal to 4.0 m. Then at a certain moment the pole, flying through the barn (let's say from left to right), fits entirely within it. However, for an observer in reference frame S ’attached to the pole, the barn is moving to the left, and so it is the barn width that becomes reduced by half, and consequently the pole (8.0 m) does not fit in the barn (2.0 m). (a) Determine the speed of the pole relative to the barn. (b) Determine the time interval between the following two events, as observed by the observer in reference frame S and the observer in reference frame S: event 1: the right end of the pole meets the right side of the barn; event 2: the left end of the pole meets the left side of the barn. (c) Why is there no paradox in this situation? Explain (d) Represent the situation with spacetime diagrams for the observer in the reference frame S and the observer in the reference frame S :