Physics 12: Homework #1: due April 12

In addition to the problems assigned from the book, do these required problems as well. Many are adaptations of problems in the book to reduce the pain of gratuitous unit conversions.

Note: it is fine to use g = 10 m/s² for all problems in this class.

  1. Let's spend some time, and a couple of problems, refining the bacteria-jar scenario discussed in class. We'll make the scheme more realistic by allowing a liesurely 30 minutes for each doubling time. In this scenario, if the jar is full at midnight, it will be half-full at 11:30 PM. Note that the fullness of the jar is 1/2N, where N is the number of doubling times before midnight. For convenience and concreteness, let's make our "jar" a cube 100 mm on a side, constituting exactly one liter of volume. The question: at what time is there enough bacteria to constitute a thin film covering the bottom of the jar 0.1 mm thick (barely noticable)? So you're looking for something around one thousandth of the ultimate volume, achieved at midnight. Approximating to the nearest half-hour is perfectly fine.
  2. Now using the same parameters we used above (30 minute doubling time; full at midnight), how many new jars must be found to allow unabated growth for another 24 hours after the first jar is full? This time, the number of jars needed follows 2N. The number is so big as to warrant the use of scientific notation. In addition to the number of jars, express how large this set of jars would be if stacked into a cube, keeping in mind that 1000 jars would stack into a cube one meter on a side. Is the result the size of a room, a building, a mountain, or a planet? Hopefully you are now convinced that exponential growth is hard to maintain. Imagine how preposterous the answers would have been had we stuck to one-minute doubling times!
  3. If global population growth slacks off a bit to 1% per year, and we hit 7 billion people in 2012, in what year would we find 14 billion people?
  4. (modified from Q&P 1.3) If you push a cart along a horizontal surface with a force of 80 Newtons (about 18 pounds), and the cart moves three meters, how much work have you done in Joules?
  5. (modified from Q&P 1.11) A windmill produces 10,000 watts of electric power that is used to heat water. Assume for now that the efficiency is 100%. How long will it take to raise the temperature of 150 liters of water (about a standard 40 gallon hot water heater capacity) from 10°C (50°F) to 50°C (122°F), raising its temperature by by 40°C?
  6. (modified from M.C. 1.1) The product of (2×107)×(3×104)×(4×103) = _______? (Do it in your head to gain superpowers)
  7. (modified from M.C. 1.13) (2×105)×(6×107)/(3×1010) = _______? (Do it in your head to gain superpowers)
  8. (modified from M.C. 1.6) What is the potential energy increase of a 1000 kg auto driven up the 1690 meter elevation gain from San Diego to Palomar Mountain?

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