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A science fiction enthusiast has figured out how to make nanobots with a mass of onehuman...

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Physics

  1. A science fiction enthusiast has figured out how to makenanobots with a mass of onehuman cell (10−12 kg). Eachnanobot is capable of reproducing itself with any material it findsat a rate of 1 nanobot per hour.
    1. Assuming unlimited materials and starting with one nanobot, howmany nanobotsdo we have after 10 days? What is the combined mass ofthose nanobots?
    2. What is the general function, in terms of time t inunits of hours, that tells us how many nanobots we have? Assumethat at t = 0, we have one nanobot.
    3. How long would it take to convert an average car into allnanobots starting witha single nanobot? How many nanobots wouldthat be and what would their total mass be?
    4. How long would it take to convert the entire Earth intonanobots? Assume anEarth mass of 6 × 1024 kg.
    5. How long would it take to convert the entire observableUniverse into nanobots? Assume the mass of the observable Universeis 3 × 1052 kg and ignore travel time and energyconsiderations.

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