Problem%20Set%209%20Solutions

# Problem%20Set%209%20Solutions - 6 Due to the time-dilation...

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6. 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 = γ (4.000 y) where γ is 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 + 20.00 y , T f = t f daughter – 20.00 y . Since T f T i = 4.000 y, then these three equations combine to give a single condition from which γ can be determined (and consequently v ): 44 = 4 γ γ = 11 β = 2 30 11 = 0.9959.

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Note the limits of the vertical axis are +2 µ s and –2 µ s. We note how “flat” the curve is in this graph; the reason is that for low values of β , Bullwinkle’s measure of the temporal separation between the two events is approximately our measure, namely +1.0 µ s. There are no non-intuitive relativistic effects in this case. (c) A plot of t as a function of β in the range 0.1 1 < < is shown below: 25. (a) Using Eq. 2 of Table 37-2, we have 6 2 8 (400m) '1 . 0 0 1 0 s 2.998 10 m/s vx x tt t cc ββ ⎛⎞ ∆∆ ∆= γ∆− = = γ × ⎜⎟ × ⎝⎠ where the Lorentz factor is itself a function of β (see Eq. 37-8). (b) A plot of t as a function of in the range 0 0.01 < < is shown below:
(as the speed approaches that of light) becomes progressively more negative. For the lower speeds with t > 0 t A < t B 0 0.750 β < < , according to Bullwinkle event A occurs before event B just as we observe.

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Problem%20Set%209%20Solutions - 6 Due to the time-dilation...

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