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Question
1. Suppose we have a machine that takes a 2 kg mass of fuel, and converts it into 1 kg of mass plus 1 kg of equivalent released energy. Use the formula E=mc2 to estimate the amount of released energy, in joules. (You get the energy in joules if you express mass in kilograms and the speed of light in meters per second.) As we shall see later, this is close to the maximal efficiency for black hole energy sources.
2. Suppose that the energy appears in the form of one kilowatt of electricity (where one watt is one joule per second), a typical personal electricity consumption rate. How long would the 2kg of fuel last? Express the answer in seconds, and in years, using scientific notation.
3. Suppose we use the fuel to provide a continuous kilowatt of power to each of a billion people, a typical average usage. How long does it last then?
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