ch37 - 1417 Chapter 37 1 From the time dilation equation t...

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Unformatted text preview: 1417 Chapter 37 1. From the time dilation equation t = t (where t is the proper time interval, 1 1 2 / , and = v / c ), we obtain F H G I K J 1 2 t t . The proper time interval is measured by a clock at rest relative to the muon. Specifically, t = 2.2000 s. We are also told that Earth observers (measuring the decays of moving muons) find t = 16.000 s. Therefore, 2 2.2000 s 1 0.99050. 16.000 s 2. (a) We find from 1 1 2 / : 2 2 1 1 1 1 0.14037076. 1.0100000 (b) Similarly, 2 1 10.000000 0.99498744. (c) In this case, 2 1 100.00000 0.99995000. (d) The result is 2 1 1000.0000 0.99999950. 3. (a) The round-trip (discounting the time needed to “turn around”) should be one year according to the clock you are carrying (this is your proper time interval t ) and 1000 years according to the clocks on Earth, which measure t . We solve Eq. 37-7 for : 2 2 1y 1 1 0.99999950. 1000y t t 1418 CHAPTER 37 (b) The equations do not show a dependence on acceleration (or on the direction of the velocity vector), which suggests that a circular journey (with its constant magnitude centripetal acceleration) would give the same result (if the speed is the same) as the one described in the problem. A more careful argument can be given to support this, but it should be admitted that this is a fairly subtle question that has occasionally precipitated debates among professional physicists. 4. Due to the time-dilation effect, the time between initial and final ages for the daughter is longer than the four years experienced by her father: t f daughter – t i daughter = (4.000 y) where is the Lorentz factor (Eq. 37-8). Letting T denote the age of the father, then the conditions of the problem require T i = t i daughter + 25.00 y , T f = t f daughter – 25.00 y . Since T f T i = 4.000 y, then these three equations combine to give a single condition from which can be determined (and consequently v ): 54 = 4 = 13.5 = 0.9973. 5. In the laboratory, it travels a distance d = 0.00105 m = vt , where v = 0.992 c and t is the time measured on the laboratory clocks. We can use Eq. 37-7 to relate t to the proper lifetime of the particle t : 2 2 2 1 1 0.992 0.992 1 / t v d t t t c c v c which yields t = 4.46 10 –13 s = 0.446 ps. 6. From the value of t in the graph when = 0, we infer than t o in Eq. 37-9 is 8.0 s....
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ch37 - 1417 Chapter 37 1 From the time dilation equation t...

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